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Internet Technologies/Email spam

Email spam (or just "Spam") is unsolicited email, similar to conventional "junk mail", but often on a larger scale.

Spam is estimated to have cost U.S. organizations over $10 billion (in lost productivity) in 2003.

Various software products are available to block or filter spam. Even lawmakers are stepping up to fight spam- in the United States the Can-Spam Act of 2003 was passed into law.

"Spammers" - people or organizations responsible for sending out email spam - use large lists of email addresses that are collected in a number of ways. One of these means is by using computer programs that search websites for email addresses. An email address that appears on a website is therefore more likely to get spammed, other things being equal. There are various ways of preventing your email being harvested in this way. One is to include it as an image rather than a link. This is not ideal, though, because it means firstly that people will have to type the address themselves, and secondly, it makes the address inaccessible to blind people, or people who browse without images. An alternative, better method, is to use a small piece of 'JavaScript' to insert the email address into the page when it is displayed, keeping it out of the html which an email-collecting spam program might look at. One final method is to create a contact form to display on your website. The website user would fill out the form which when submitted forwards the message to you without displaying your email address. This final method has one drawback in that it circumvents the user's email system and does not provide the user with a record of the email that they sent.

I have also seen many people try the format of me@REMOVETHISaol.com or whatever. The person who has a genuine interest in emailing you will remove the REMOVETHIS part of the eddress before sending, but programmes that gather email addresses en-masse will use it as-is - thus, you do not receive spam. One must be fairly inventive to make this effective; the instance given would be algorithmically handled by most site-scraping email bots.

In addition, there is a new anti-spam feature now available. Named the "Challenge/Response System", this either sends a link, or a word-verification page to a user, the first time they e-mail you. The user must either click the link or enter the word to verify they are not a spamming program. After this, you get the e-mail and they're added to your allow list.

A study, by Brockmann & Company IT consultants showed that challenge-response proved to be superior to appliances, hosted spam filters and commercial filters.Brockmann surveyed more than 500 businesses, with 40% of the respondents having IT responsibilities. The independently funded study resulted in the creation of a spam index to measure how satisfied workers were with their spam technologies.

Despite being less sophisticated than filtering technology sold by antispam and antivirus vendors, the challenge-response method was twice as effective as hosted services for spam prevention. According to the survey, 67% of challenge-response users specified that they are very satisfied with their email experience as compared to next highest technology, hosted services, in which 42% reported that they were very satisfied. Commercial software filters, such as those produced by McAfee, Symantec and Trend Micro, scored the lowest satisfying only 22% of respondents.(SearchSecurity.com, Robert Westervelt Jul. 2007)

www.bluebottle.com currently offers a public beta of this software.

Spam is a very common thing and at one point or another it is something that we have all had. Spam is not only an annoying email, it is a tactics for marketing. However many times you have received this type of email, it is becoming more and more dangerous. It can be generated by businesses as well as individuals. It is used to promote products and is also brought about by things like forwarding ( things like jokes, images or chain letters) spam can be used to gather information from your computer if opened as well as used to send out viruses. It is becoming an increasing threat. Spam has become such an issue, that people now have to have an entire email address just as a "throw away account" an email address specifically catered toward junk mail because if we were to let it, it would take up about 90% of our inbox's, not only is this an issue for our email account but it is also being directed towards our phone, and needs to be handled with caution Email-spam-sample.png Spam is a very common thing and at one point or another it is something that we have all had. Spam is not only an annoying email, it is a tactics for marketing. However many times you have received this type of email, it is becoming more and more dangerous. It can be generated by businesses as well as individuals. It is used to promote products and is also brought about by things like forwarding ( things like jokes, images or chain letters) spam can be used to gather information from your computer if opened as well as used to send out viruses. It is becoming an increasing threat. Spam has become such an issue, that people now have to have an entire email address just as a "throw away account" an email address specifically catered toward junk mail because if we were to let it, it would take up about 90% of our inbox's, not only is this an issue for our email account but it is also being directed towards our phone, and needs to be handled with caution

title: Internet Technologies/Email spam


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High School Mathematics Extensions/Set Theory and Infinite Processes

Introduction
As soon as a child first learns about numbers, they become interested in big ones, a million, a billion, a trillion. They even make up their own, a zillion etc. One of the first mathematical questions a child asks is "what is the largest number?" This will often lead to a short explanation that there are infinitely many numbers.

But there are many different types of infinity - in fact, there are infinite types of infinity! This chapter will try to explain what some of these types mean and the differences between them.

Finite and Infinite Sets
There was once a mathematician called Georg Cantor who created a new branch of mathematics called set theory in the late 19th century. Set theory involves collections of numbers or objects. Here's a set:

 * $$\{1,2,3,4,5\}$$

This set consists of five elements, namely the first five natural numbers. Now consider the set:

 * $$\{6,7,8,9,10\}$$

Are these sets of the same size? Yes, they are. This is because they both have five elements. As we will see later, this method of comparing sizes does not work for all sets. An alternate method for comparing set sizes is to match elements of sets in a one-one fashion.

Think of a small child who wants to compare the number of marbles she has with her brother's collection. Let's say she doesn't know how to count beyond ten. She can still compare the sizes of their collections of marbles by lining up their marbles in two parallel lines. The line on the left contains her marbles while the one on the right contains her brother's. If each marble on the left is aligned with exactly one marble on the right, then they both have the same number of marbles.

We can use the same idea to compare infinite sets. If we can find a way to pair up one member of set A with one member of set B, and if there are no members of A without a partner in B and vice versa then we can say that set A and set B have the same number of members. Formally, two sets $$A$$ and $$B$$ are of the same size if there is a function $$f$$ such that for every $$a$$ in $$A$$, we have $$f(a)$$ in $$B$$ and moreover, for every $$b$$ in $$B$$, there exists an $$a$$ in $$A$$ such that $$f(a) = b$$.

Example
Consider our previous example. We want to know if the sets $$\{1,2,3,4,5\}$$ and $$\{6,7,8,9,10\}$$ have the same size. We can create the following matching.

Example
Let Set N be all counting numbers. N is called the set of natural numbers. 1,2,3,4,5,6,... and so on. Let Set B be the negative numbers -1,-2,-3, ... and so on. Can the members of N and B be paired up? The formal way of saying this is "Can A and B be put into a one to one correspondence"?

Obviously the answer is yes. 1 in set N corresponds with -1 in B. Likewise:
 * N  B
 * 1  -1
 * 2  -2
 * 3  -3

and so on. Here, the one-one function that maps from A to B is $$f(x) = -x$$.

So useful is the set of counting numbers that any set that can be put into a one to one correspondence with it is said to be countably infinite.

Example
The set of integers is the set containing all elements from the set N, the set B and the element 0. That is

{... -3,-2,-1, 0, 1, 2, 3, ...}

The set of integers is usually denoted by Z. Note that N the set of natural numbers is a subset of Z. All members of N are in Z, but not all members of Z are in N.

Is the set of integers countably infinite? In other words, can the set of integers be put in one-one correspondence with the set of all natural numbers?

Since the set N is contained in the set Z, we may be tempted to declare that these two sets are not of the same size. However, we can

 * Z  N
 * 0  1
 * -1  2
 * 1  3
 * -2  4

and so on. We can write this one-one correspondence as a function

$$f(x) = \left\{\begin{array}{cl} \frac{x - 1}{2} & x \text{ is odd} \\ \frac{-x}{2} & x \text{ is even} \end{array} \right. $$

We can verify that this function generates all the integers in Z from the natural numbers in N.

Strange indeed! A subset of Z (namely the natural numbers) has the same size as Z itself! Infinite sets are not like ordinary finite sets. In fact this is sometimes used as a definition of an infinite set. An infinite set is any set which can be put into a one to one correspondence with at least one of its subsets. Rather than saying "The number of members" of a set, people sometimes use the word cardinality or cardinal value. Z and N are said to have the same cardinality.

Exercises

 * 1) Is the number of even numbers the same as the natural numbers?
 * 2) What about the number of square numbers?
 * 3) Is the cardinality of positive even numbers less than 100 equal to the cardinality of natural numbers less than 100? Which set is bigger? How do you know? In what ways do finite sets differ from infinite ones?

Is the set of rational numbers bigger than N?
In this section we will look to see if we can find a set that is bigger than the countable infinity we have looked at so far. To illustrate the idea we can imagine a story.

There was once a criminal who went to prison. The prison was not a nice place so the poor criminal went to the prison master and pleaded to be let out. She replied:

"Oh all right - I'm thinking of a number, every day you can have a go at guessing it. If you get it correct, you can leave."

Now the question is - can the criminal get himself out of jail? (Think about if for a while before you read on)

Obviously it depends on the number. If the prison master chooses a natural number, then the criminal guesses 1, the first day, 2,the second day and so on until he reaches the correct number. Likewise for the integers 0 on the first day, -1 on the second day. 1 on the third day and so on. If the number is very large then it may take a long time to get out of prison but get out he will.

What the prison master needs to do is choose a set that is not countable in this way. Think of a number line. The integers are widely spaced out. There are plenty of numbers in between the integers 0 and 1 for example. So we need to look at denser sets. The first set that springs to most peoples mind are the fractions. There are an infinite number of fractions between 0 and 1 so surely there are more fractions than integers? Is it possible to count fractions? Let's think about that possibility for a while. If we try to use the approach of counting all the fractions between 0 & 1 then go on to 1 - 2 and so on we will come unstuck because we will never finish counting the ones up to 1 ( there are an infinite number of them). But does this mean that they are uncountable ? Think of the situation with the integers. Ordering them ...-2, -1, 0, 1, 2, ... renders them impossible to count, but reordering them 0, -1, 1, -2, 2, ... allows them to be counted.

There is in fact a way of ordering fractions to allow them to be counted. Before we go on to it let's revert to the normal mathematical language. Mathematicians use the term rational number to define what we have been calling fractions. A rational number is any number that can be written in the form p/q where p and q are integers. So 3/4 is rational, as is -1/2. The set of all rational numbers is usually called Q. Note that Z is a subset of Q because any integer can be divided by 1 to make it into a rational. E.g. the number 3 can be written in the form p/q as 3/1.

Now as all the numbers in Q are defined by two numbers p and q it makes sense to write Q out in the form of a table.

$$\begin{matrix}\frac{1}{1} & \frac{1}{2} & \frac{1}{3} & \cdots\\ & & \\\frac{2}{1} & \frac {2}{2} & \frac{2}{3} & \cdots\\ & & \\\frac{3}{1} & \frac{3}{2} & \frac{3}{3} & \cdots\\\vdots & \vdots & \vdots & \ddots\end{matrix}$$

Note that this table isn't an exact representation of Q. It only has the positive members of Q and has a number of multiple entries.( e.g. 1/1 and 2/2 are the same number) We shall call this set Q'. It is simple enough to see that if Q' is countable then so is Q.

So how do we go about counting Q'? If we try counting the first row then the second and so on we will fail because the rows are infinite in length. Likewise if we try to count columns. But look at the diagonals. In one direction they are infinite ( e.g. 1/1, 2/2, 3/3, ...) but in the other direction they are finite. So this set is countable. We count them along the finite diagonals, 1/1, 1/2, 2/1,   1/3, 2/2, 3/1....

Exercises

 * 1) Adapt the method of counting the set Q' to show that the set Q is also countable. How will you include 0 and the negative rationals? How will you solve the problem of multiple entries representing the same number ?
 * 2) Show that $$ \infty \times \infty = \infty $$ (provided that the infinites are both countable)

Can we find any sets that are bigger than N?
So far we have looked at N, Z, and Q and found them all to be the same size, even though N is a subset of Z which is a subset of Q. You might be beginning to think "Is that it? Are all infinities the same size?" In this section we will look at a set that is bigger than N. A set that cannot be put into a one to one correspondence with N, no matter how it is arranged.

The set in question is R: the real numbers. A real number is any number on the number line. Remember that the set Q contains all the numbers that can be written in the form p/q with p and q integers, q different from 0. Most real numbers can never be put in this form and they are named "irrational numbers". Examples of irrational numbers include $$ \pi$$, $$ e,$$ and $$\sqrt{2} $$.

The set R is huge! Much bigger than Q. To get a feel for the different sizes of these two infinite sets consider the decimal expansions of a real number and a rational number. Rational numbers always either terminate:
 * 1/8 = 0.125

or repeat:
 * 1/9 = 0.1111111......

Imagine measuring an object such as a book. If you use a ruler you might get 10cm. If you take a bit more care to and read the mm you might get 10.2cm. You'd then have to go on to more accurate measuring devices such as vernier micrometers and find that you get 10.235cm. Going onto a travelling microscope you may find its 10.235823cm and so on. In general the decimal expansion of any real measurement will be a list of digits that look completely random.

Now imagine you measure a book and found it to be 10.101010101010cm. You'd be pretty surprised wouldn't you? But this is exactly the sort of result you would need to get if the book's length were rational. Rational numbers are dense (you find them all over the number line), infinite, yet much much rarer than real numbers.

How we can prove that R is bigger than Q
It's good to get a feel for the size of infinities as in the previous section. But to be really sure we have to come up with some form of proof. In order to prove that R is bigger than Q we use a classic method. We assume that R is the same size as Q and come up with a contradiction. For the sake of clarity we will restrict our proof to the real numbers between 0 and 1. We will call this set R'. Clearly if we can prove that R' is bigger than Q then R must be bigger than Q also.

If R' was the same size as Q it would mean that it is countable. This means that we would be able to write out some form of list of all the members of R' (This is what countable means, so far we have managed to write out all our infinite sets in the form of an infinitely long list). Let's consider this list.

 * R1
 * R2
 * R3
 * R4

Where R1 is the first number in our list, R2 is the second, and so on. Note that we haven't said what order the list is to be written. For this proof we don't need to say what the order of the list needs to be, only that the members of R are listable (hence countable).

Now lets write out the decimal expansion of each of the numbers in the list.

 * 0.r11r12r13r14...
 * 0.r21r22r23r24...
 * 0.r31r32r33r44...
 * 0.r41r42r43r44...

Here r11 means the first digit after the decimal point of the first number in the list. So if our first number happened to be 0.36921... r11 would be 3, r12 would be 6 and so on. Remember that this list is meant to be complete. By that we mean that it contains every member of R'. What we are going to do in order to prove that R is not countable is to construct a number in R' that is not already on the list. Since the list is supposed to contain every member of R', this will cause a contradiction and therefore show that R' is unlistable.

In order to construct this unlisted number we choose a decimal representation:

 * 0.a1a2a3a4...

Where a1 is the first digit after the point etc.

We let a1 take any value from 0 - 9 inclusive except the digit r11. So if r11 = 3 then a1 can be 0, 1, 2, 4, 5, 6, 7, 8, or 9. Then we let a2 be any digit except r22 (the second digit of the second number on the list). Then a3 be any digit except r33 and so on.

Now if this number, that we have just constructed were on the list somewhere then it would have to be equal to Rsomething. Let's see what Rsomething it might be equal to. It can't be equal to R1 because it has a different first digit (r11 and a1. Nor can it be equal to R2 because it has a different second digit, and so on. In fact it can't be equal to any number on the list because it differs by at least one digit from all of them.

We have done what we set out to do. We have constructed a number that is in R' but is not on the list of all members of R'. This contradiction means that R' is bigger than any list. It is not listable. It is not countable. It is a bigger infinity than Q.

Are there even bigger infinities?
There are but they are difficult to describe. The set of all the possible combinations of any number of real numbers is a bigger infinity than R. However trying to imagine such a set is mind boggling. Let's look instead at a set that looks like it should be bigger than R but turns out not to be.

Remember R', which we defined earlier on as the set of all numbers on the number line between 0 and 1. Let us now consider the set of all numbers in the plane from [0,0] to [1,1]. At first sight it would seem obvious that there must be more points on the whole plane than there are in a line. But in transfinite mathematics the "obvious" is not always true and proof is the only way to go. Cantor spent three years trying to prove it true but failed. His reason for failure was the best possible. It's false.

Each point in this plane is specified by two numbers, the x coordinate and the y coordinate; x and y both belong to R. Lets consider one point in the line. 0.a1a2a3a4.... Can you think of a way of using this one number to specify a point in the plane ? Likewise can you think of a way of combining the two numbers x= 0.x1x2x3x4.... and y= 0.y1y2y3y4.... to specify a point on the line? (think about it before you read on)

One way is to do it is to take
 * a1 = x1
 * a2 = y1
 * a3 = x2
 * a4 = y2

This defines a one to one correspondence between the points in the plane and the points in the line. (Actually, for the sharp amongst you, not quite one to one. Can you spot the problem and how to cure it?)

Exercises

 * 1) Prove that the number of points in a cube is the same as the number of points on one of its sides.

Continuum hypothesis
We shall end the section on infinite sets by looking at the Continuum hypothesis. This hypothesis states that there are no infinities between the natural numbers and the real numbers. Cantor came up with a number system for transfinite numbers. He called the smallest infinity $$\aleph_0$$ with the next biggest one $$\aleph_1$$ and so on. It is easy to prove that the cardinality of N is $$\aleph_0$$ (Write any smaller infinity out as a list. Either the list terminates, in which case it's finite, or it goes on forever, in which case it's the same size as N) but is the cardinality of the reals = $$\aleph_1$$?

To put it another way, the hypotheses states that:
 * There are no infinite sets larger than the set of natural numbers but smaller than the set of real numbers.

The hypothesis is interesting because it has been proved that "It is not possible to prove the hypothesis true or false, using the normal axioms of set theory"

Limits Infinity got rid of
The theory of infinite sets seems weird to us in the 21st century, but in Cantor's day it was downright unpalatable for most mathematicians. In those days the idea of infinity was too troublesome, they tried to avoid it wherever possible.

Unfortunately the mathematical topic called analysis was found to be highly useful in mathematics, physics, engineering. It was far too useful a field to simply drop yet analysis relies on infinity or at least infinite processes. To get around this problem the idea of a limit was invented.

Consider the series
 * $$\frac{1}{1}, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \cdots, \frac{1}{n} \cdots $$

This series is called the harmonic series.

Note that the terms of the series get smaller and smaller as you go further and further along the series. What happens if we let n become infinite? The term would become $$ \frac{1}{\infty}$$

But this doesn't make sense. (Mathematicians consider it sloppy to divide by infinity. Infinity is not a real number, you can't divide by it). A better way to think about it (The way you probably already do think about it, if you've ever considered the matter) is to take this approach: Infinity is very big, bigger than any number you care to think about. So let's let n become bigger and bigger and see if 1/n approaches some fixed number. In this case as n gets bigger and bigger 1/n gets smaller and smaller. So it is reasonable to say that the limit is 0.

In mathematics we write this as
 * $$ \lim_{n \to \infty} \frac {1}{n} = 0 $$

and it reads:
 * the limit of 1/n as n approaches infinity is zero

Note that we are not dividing 1 by infinity and getting the answer 0. We are letting the number n get bigger and bigger and so the reciprocal gets closer and closer to zero. Those 18th Century mathematicians loved this idea because it got rid of the pesky idea of dividing by infinity. At all times n remains finite. Of course, no matter how huge n is, 1/n will not be exactly equal to zero, there is always a small difference. This difference (or error) is usually denoted by ε (epsilon).

info -- infinitely small
 When we talk about infinity, we think of it as something big. But there is also the infinitely small, denoted by ε (epsilon). This animal is closer to zero than any other number. Mathematicians also use the character ε to represent anything small. For example, the famous Hungarian mathematician Paul Erdos used to refer to small children as epsilons.

Examples
Lets look at the function
 * $$ \frac{x^2 + x}{x^2} $$

What is the limit as x approaches infinity ?

This is where the idea of limits really come into its own. Just replacing x with infinity gives us very little:
 * $$ \ \frac{\infty^2 + \infty}{\infty^2} = ? $$

But by using limits we can solve it
 * $$ \lim_{x \to \infty} \frac{x^2 + x}{x^2} = 1 + \lim_{x \to \infty}\frac{ 1}{x} = 1$$

For our second example consider this limit as x approaches infinity of $$ x^3 -x^2 $$

Again lets look at the wrong way to do it. Substituting $$ x = \infty$$ into the expression gives $$ \infty^3 -\infty^2 $$. Note that you cannot say that these two infinities just cancel out to give the answer zero.

Now lets look at doing it the correct way, using limits
 * $$\lim_{x \to \infty}x^3 -x^2 = \lim_{x \to \infty}x^2(x-1) = \infty $$

The last expression is two functions multiplied together. Both of these functions approach infinity as x approaches infinity, so the product is infinity also. This means that the limit does not exist, i.e. there is no finite number that the function approaches as x gets bigger and bigger.

One more just to get you really familiar with how it works. Calculate:
 * $$\lim_{x \to \infty}\frac{\sin x}{x} $$

To make things very clear we shall rewrite it as
 * $$\lim_{x \to \infty}\frac{1}{x}(\sin x) $$

Now to calculate this limit we need to look at the properties of sin(x). Sin(x)is a function that you should already be familiar with (or you soon will be) its value oscillates between 1 and -1 depending on x. This means that the absolute value of sin(x) (the value ignoring the plus or minus sign) is always less than or equal to 1:
 * $$ |\sin x| \le 1$$

So we have 1/x which we already know goes to zero as x goes to infinity multiplied by sin(x) which always remains finite no matter how big x gets. This gives us
 * $$\lim_{x \to \infty}\frac{1}{x}(\sin x) = 0 $$

Exercises
Evaluate the following limits;

 * 1) $$\lim_{x \to \infty}\frac{3x^2 -4}{2x^2 +x} $$
 * 2) $$\lim_{x \to \infty}\frac{x^2 -1}{2x^3 +3} $$
 * 3) $$\lim_{x \to \infty}\frac{cos x}{x^2} $$
 * 4) $$\lim_{x \to \infty}(2x^2 -x^4) $$

Infinite series
Consider the infinite sum 1/1 + 1/2 + 1/4 + 1/8 + 1/16 + .... Do you think that this sum will equal infinity once all the terms have been added ? Let's sum the first few terms.

$$ \begin{matrix} S_1 &=& \frac{1}{1} &=& 1 \\ S_2 &=& \frac{1}{1} + \frac{1}{2} &=& 1.5 \\ S_3 &=& \frac{1}{1} + \frac{1}{2} + \frac{1}{4} &=& 1.75 \\ S_4 &=& \frac{1}{1} + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} &=& 1.8750 \\ \end{matrix} $$

Can you guess what $$S_\infty$$ is ?

Here is another way of looking at it. Imagine a point on a number line moving along as the sum progresses. In the first term the point jumps to the position 1. This is half way from 0 to 2. In the second stage the point jumps to position 1.5 - half way from 1 to 2. At each stage in the process (shown in a different colour on the diagram) the distance to 2 is halved. The point can get as close to the point 2 as you like. You just need to do the appropriate number of jumps, but the point will never actually reach 2 in a finite number of steps. We say that in the limit as n approaches infinity, Sn approaches 2.

Zeno's Paradox
The ancient Greeks had a big problem with summing infinite series. A famous paradox from the philosopher Zeno is as follows:

In the paradox of Achilles and the tortoise, we imagine the Greek hero Achilles in a footrace with the plodding reptile. Because he is so fast a runner, Achilles graciously allows the tortoise a head start of a hundred feet. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run a hundred feet, bringing him to the tortoise's starting point.

During this time, the tortoise has "run" a (much shorter) distance, say one foot. It will then take Achilles some further period of time to run that distance, during which the tortoise will advance farther; and then another period of time to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, Zeno says, swift Achilles can never overtake the tortoise.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
Talk:High School Mathematics Extensions/Set Theory and Infinite Processes

I'm going to be pedantic and whine about

"Infinity is unlike a normal number."

Well, no, it's not. In fact, it's not really a number at all. (Sometimes people treat it like a number -- as if $$\infty$$ were just an unusual, special number, like π is an unusual number. But that leads to all kinds of confusion).

 * "The word "infinity" doesn't represent an actual number that is bigger than all the others; "infinite" just means "without end," and is a way of describing something that never comes to an end. There are infinitely many numbers, because there is no last number. And that's really all it means." http://mathforum.org/library/drmath/view/60400.html

 * "Infinity is not a number, it is an idea." http://perplexus.info/show.php?pid=1341&cid=7939

 * "'infinity' is ... a 'process'." http://www.jatiyah.freeserve.co.uk/infinity.htm

 * "Infinity is not a number; it is the name for a concept." http://mathforum.org/dr.math/faq/faq.large.numbers.html

If there's no objections, I'm going to change the article to say something like "Infinity is not number." and try to make it consistent with the "infinite process" idea.

--DavidCary 22:41, 29 Oct 2004 (UTC)

you have to face up to .03999... = .04000...
etc. in your proof that R is uncountable. One way is to toss out the things ending in all 9's. Then be careful in your construction of the new number.

~reader

examples of aleph-one, aleph-two, etc.
Could anybody please explain or (using the logic-style and/or ;) ) give an example of an aleph-two cardinality series? r3m0t 23:20, 1 Jan 2004 (UTC)
 * No not really. The set of all possible subsets (Called the power set) of a set is always bigger than that set. E.g. if A = {a,b,c} the P(A) = Even for infinite sets the cardinality of  the power set is always higher than the set itself. I believe it's true that

$$P(\aleph^0) = \aleph^1 $$ (I have to check on a book for the proof)

 * but I don't know if $$P(\aleph^1) = \aleph^2 $$

Even so power sets aren't exactly easy to visualize. I think they are too obscure for this book. Theresa knott 13:31, 19 Jan 2004 (UTC)

 * Well, okay. By the way, isn't it usually written $$\aleph_0$$ and not $$\aleph^0$$? I have to go to lessons now (science in fact!) so bye... r3m0t 13:35, 19 Jan 2004 (UTC)

 * Yes - I dashed it off quick without thinking. Theresa knott 14:16, 19 Jan 2004 (UTC)

Here's some examples:
 * Aleph-zero: the set of positive integers -- countably infinite. (Any particular member of this set is a relatively harmless finite integer, like 2999).
 * Aleph-one: set of the real numbers between zero and one -- uncountable. Think of the binary expansion of a real number: 0.x1x2x3x4x5x6..., with a *countably infinite* number of bits (or decimal places, whatever). It takes a (countably) infinite amount of information just to describe a typical real number, a single member of the set. The set of all of them is larger.
 * Aleph-two: one example is the number of open curves of length 1. Imagine you're driving from the start to the end of one particular curve. Any particular point on the curve, you could be turning to the left or to the right. Since there's aleph-one particular points on the curve, it takes aleph-one bits of information just to describe one particular curve. The set of all of them is larger.

Direction
This chapter is already looking interesting. But I'm not sure what direction this chapter is taking. It seems to be more like a book then a textbook; more passive then interactive. I dont know enough about infinity, maybe that's why I dont see where the exercises come in. How do we involve the reader? Xiaodai 15:52, 13 Jan 2004 (UTC)
 * Don't worry, I'll be adding some exercises shortly.Theresa knott 16:12, 13 Jan 2004 (UTC)

Ooh! Let me join in in the big everybody-online-at-the-same-time party! Thing is, I got left behind when I started this... better catch up on some reading :) r3m0t 13:15, 19 Jan 2004 (UTC)
 * Me too, I'm coming to the end of what I can do off the top of my head or from memory. Perhaps you can start by reading what I've already written and making sure it all makes sense. Theresa knott 14:16, 19 Jan 2004 (UTC)

Page Needs to be split
I did a quick print preview and found that this module now runs to 10 pages. I still have more to write on infinite sets and transfinite numbers, so I propose that we split this page. What say you? Theresa knott
 * I say no. Other chapters are already collosal (primes, complex number...) and I think this one should follow. I certainly don't shy away from a long page without first reading a page at least. The reading style is easy and light here for that reason :) r3m0t 17:10, 19 Jan 2004 (UTC)

Whoops, sorry for that "fix", I see what happened now. Never mind :) r3m0t 20:17, 19 Jan 2004 (UTC)
 * That's OK It's part of what makes mathematics difficult. You have to be so precise with the language! one stray 1 in a subscript completely alters the meaning :-( Still with three people regualy checking this page those sort of errors should be picked up. Slightly more worrying is real errors that may have slipped in because of simplifying the formal proofs. "Proper proofs" are dead hard to read, but are very carfefully written to ensure nothing dodgy.Theresa knott 20:25, 19 Jan 2004 (UTC)

I don't understand something in the closed forms section
Copied from the page :So the closed form of
 * 1 + x + x2 + x3 + ...

is

\frac{1}{1 - x} $$

We can equate them:

1 + x + x^2 + x^3 + ... = \frac{1}{1 - x} $$

We are definitely not saying the two expressions are equal in the numerical sense, for example if we substitute x'' = 2 into the equation we get on the right hand side -1, but we know the left hand side equals infinity. Instead we use the closed-forms for their nice algebraic properties.''

It doesn't make sense to equal two things that are not equal. The series converges for |x| less than 1 so shouldn't we say something along these lines ? (I don't know anything about closed ofrms unfortunately) Theresa knott 14:21, 20 Jan 2004 (UTC)

 * This is tricky. They are not equal numerically but are equal algebraicly. Maybe things will clear up when the whole thing is written up. Xiaodai 14:29, 20 Jan 2004 (UTC)#

Okey dokey I'll wait until it's finished Theresa knott 14:32, 20 Jan 2004 (UTC)

Limits in relation to infinity
My original intention was to introduce the more rigorous definition of limits in relation to infinity in this chapter. The explanation of limits already present is intuitively very clear, but to be mean to the readers I would really want to see it expanded upon. I was thinking of covering (lim x -> L = inf) kind of thing as well. Diagrams would be nice. What do you think? Xiaodai 14:40, 20 Jan 2004 (UTC)

I think it's a good idea. Being mean is good as long as the section gets prgressively harder as it goes along so that the readers can choose to stop at a point and still get some good info up to that point. Theresa knott 15:03, 20 Jan 2004 (UTC)

Eh?
(Is very jetlagged, so veracity of comment may not be 100% ;) - didn't Godel go about showing that it really didn't matter whether you took the continuum to be aleph_1 or something "in between" or greater than aleph_1 or something, that basically things would work out either way? Should check later... Dysprosia 01:25, 27 Jan 2004 (UTC)
 * It rings a bell, I'll try to check too. Theresa knott 19:40, 27 Jan 2004 (UTC)
 * OK I've found a good website - here. Basically the continium hypothesis cannot be proved or disproved using the standard set of axioms of set theory. Godel proved that CH being true was consistant with standard set theory and Cohen prove that CH being false was also consistant. So it is not possible to prove CH without adding some new axioms. Theresa knott 13:18, 29 Jan 2004 (UTC)
 * Personally I think that it now looks very convoluted, perhaps it could just be removed? r3m0t (cont) (talk)
 * What does? Its transfinite arithmetic, it's supposed to be convoluted ;) Dysprosia 12:13, 30 Jan 2004 (UTC)
 * It's infinitely convoluted and nothing can be done about it for however long you work on it, except for just removing it. QED. r3m0t (cont) (talk) 12:27, 30 Jan 2004 (UTC)
 * Just removing what ? The question, the whole section on CH, the whole page ? Theresa knott 12:50, 30 Jan 2004 (UTC)
 * Whatever it is, it can't be that bad... Let us know what exactly you have an issue with and we may be able to sort it out... Dysprosia 23:10, 30 Jan 2004 (UTC)
 * I meant the question. No, it isn't that bad ;) r3m0t (cont) (talk) 04:58, 31 Jan 2004 (UTC)
 * OK I'll take the question out. Theresa knott 11:49, 2 Feb 2004 (UTC)

Need feed back
I have finished writing the first example in the Linear Recurrence Relations section. I think it can be improved upon, but i do not know how to go about doing it. That's why i need your feed back. Do you think it's easy enough to understand? But hard enough that they'll need to have a good think about it. If you dont already know the work, did your understanding of generating functions increase? So many questions i want to ask. I want to know what you guys think before I make the next example. Xiaodai 01:12, 5 Feb 2004 (UTC)

 * I've got lost with this whole module recently, but I'll try to read up on it soon. Wish me good luck, for I am soon to do the Maths Challenge! I'll try memorising a few puzzles and gbringing them over :) r3m0t (cont) (talk) 06:55, 5 Feb 2004 (UTC)

Question on "Are there even bigger infinities?"
One way is to do it is to take

a1 = x1   a2 = y1    a3 = x2    a4 = y2. ..

This defines a one to one correspondance between the points in the plane and the points in the line. (Actually, for the sharp amongst you, not quite one to one. Can you spot the problem and how to cure it?)

I've found the problem. This doesn't work for a number that "approach zero" -- A number that is as close to zero as possible but not exactly zero, i.e. 0.000000......(after infinite 0s) 001. For this number, we don't know if the "1" belongs to x or y, so it can be (0.000...01,0) or (0,0.000...01) But I've no ideas on how to cure this. Can anyone help?

 * To get to it, the problem is that you are looking at the plane R2 and not something like Z2. R is uncountable, Z is. Do you see the problem? R2 is not countable then. Dysprosia 13:34, 26 Oct 2004 (UTC)

 * "(after infinite 0s)" ? If we're still talking about real numbers, that would be identical to the real number zero. I don't see what the problem is. (I don't want to get into transfinite numbers just yet).

Natural number definition
Since set theory is being referenced early in the book, shouldn't we use the set-theory notion of Natural numbers, and call the first natural number 0? I know that in various parts of math and science, people begin the "natural numbers" at 1, but here it seems innappropriate. Siroxo 10:20, 15 Mar 2005 (UTC)
 * Good point. Xiaodai 8 July 2005 11:25 (UTC)

Why not add the 0.99999=1 proof
Why not add the interesting 0.99999... = 1. That kind of has stuff to do with infinity, and it is an interesting result.
 * Yes i think it shall be done when someone gets to it.Xiaodai 8 July 2005 11:25 (UTC)

zeno's paradox
there is something wrong, or i dont get the paradox, like its common sense the fast guy will overtake the turtle after some time, just think about it, try it with a friend - you run he walks, see if you can overtake him
 * That's why it's a paradox, because in the explaination your dont pass that guy but in reality you do. There is a contradiction, so it's a paradox. Xiaodai 8 July 2005 11:27 (UTC)
 * Just a note, the key is to realise that the timeframe that the explanation cover is limited. As the distance it descibe decreases indefinitely, the time it takes also decreases indefinitely. So the explanation didn't consider after that timeframe passed. --Lemontea 8 July 2005 14:19 (UTC)

opps, dunno what i was thinking. sorry for wasting your time

well i think that this "zeno's paradox" is pretty weird, but it's like the only thing on this entire page that i actually get, so :). by the way, can anyone give me a numerical example that demonstrates it? [morandi]

WOW, does ((infinty)^2+infinty) / (infinty)^2 = 1?
 * Kind of. But we shall expand on what we mean by infinity later on in the chapter to try and clear everything up. Xiaodai 8 July 2005 11:27 (UTC)

a kind freshman's question
well im a freshman at highschool and i had to look up this infinity concept for extra credit and your website has proven to be useful a bit confusing for me but i get the bigger concept but the one concept that has croosed my mind is that infinity cna be limited when you say x>1 and x<2. just in there the answers are infinite but yet they are limited. you can chose any number between 1 and 2 and the decimal number between 1 and 2 are infinite so you have an infinite number of solutions but yet you are still being limited how can that be? what type of infinity is that?
 * It is true that all the real numbers between 1 and 2 are quite small in magnitude (they are all less than 2). Also all the numbers fit into this line of no more than 1 unit in length. Yet there are infinitely many real numbers in there. It is strange, no doubt. I think you have already noted that "infinitely many" does not mean "very large". In set theory, we have this concept of "countably infinite" and "uncountably infinite". The set of natural number are "countable" in the sense that you can list them one by one in a meaningful order, and there are infinitely many natural numbers. So we call the natural numbers "countably infinite". All the real numbers between 1 and 2 are not "uncountably infinite". That's because you can not count them in a meaningful way. A mathematical way of saying that is: there is no one to one correspondence between the natural numbers and the real numbers. It's like the natural numbers and the real numbers come from two type of infinity, one countable, the other not. Xiaodai 23:19, 7 January 2006 (UTC)

Hi, the point here is not so much concerning the uncountability (viz. just take the rational numbers between 1 and 2, they are countably infinite, and yet your kind of doubt remains to hold). The point here is about the two notions of numbers, one being those which count the elements in a set (here that can be an infinity), and the other, being those on the number line. In this case the infinity is the furthest imaginary point on the right end. If you keep these two interpretations as different in your mind, the problem disappears! Really, the size of the set of rational/real numbers between 1 and 2 is infinite, however, the numerical stickers on them which place them on the number line are bounded (or as you say, "limited"); hence, there is no mathematical inconsistency here in deed. So far as the size of the set is concerned, the numerical identification of its elements does not matter much as you can easily see that the number of points on any two line segments are the same (take a triangle ABC, let R and S be the midpoints of AB and AC resp. for any point P on BC, the line AP cuts the line RS at a unique point Q, giving a one-to-one correspondence between the points on BC, and those on RS -- although the lengths are different). Thus you can keep stretching one of these segments to have bigger and bigger limits, and the number of points on them do not change! In fact you can stretch it all the way to infinity (the "infinity" point on the number line). Try the function $$tan (\pi (x-1)/2$$) on the numbers between 1 and 2 for instance. Hope this helps. Suman

Answers to Exercise
Where can I find answers to exercises?
 * sorry no exercise answers as of yet. Xiaodai 02:01, 15 June 2006 (UTC)

Suggest a Title Change
It seems like the article doesn't really deal with set theory in more than a basic way. Since the bulk of material is concerned with infinity, maybe the title should just be something like "Infinity". Well, maybe not so vague, but at least strip the "Set Theory" from the title, as there is no real discussion of it. --Darkxxxxillusion
 * Thanks. Your observation is correct, but the module will be rewritten to incorporate set theory. That is the plan. Xiaodai 16:51, 17 July 2006 (UTC)

Errata
In "Limits Infinity got rid of, Examples", it is correctly said, that "Sin(x)is a function that you should already be familiar with (or you soon will be) its value oscillates between 1 and -1 depending on x. This means that the absolute value of sin(x) (the value ignoring the plus or minus sign) is always less than or equal to 1:", but then the formula states "|x|<=1". There's no reason for x to behave so: shouldn't that read "|sin(x)|<=1"?

Gulliveig 18:16, 8 January 2007 (UTC)

Mathematics
Algebra Right Steve (discuss • contribs) 20:20, 9 August 2020 (UTC)


text:
Physics Study Guide/Topics

 * 1) Displacement, velocity, and acceleration
 * 2) *Vectors and scalars
 * 3) Force
 * 4) Ropes and tension
 * 5) Gravity
 * 6) Momentum and collision force
 * 7) Energy
 * 8) *Kinetic energy
 * 9) Friction
 * 10) Periodic Motion
 * 11) Torque
 * 12) Circular Motion
 * 13) *Center of Mass
 * 14) *Inertia and moment of inertia
 * 15) Strengths of materials: Stress and strain
 * 16) Thermodynamics
 * 17) *Power
 * 18) Gases
 * 19) *Ideal gases
 * 20) *Pressure and partial pressure
 * 21) Fluids
 * 22) Density
 * 23) Laminar flow in ideal fluids
 * 24) Energy density
 * 25) Real liquids
 * 26) Sheer thickening and thinning fluids

title: Physics Study Guide/Topics


text:
Korean

Welcome to the Korean Wikibook, a free textbook for learning Korean.

Note: To use this book, your web browser must first be configured to display Korean (Hangeul) characters. Check the two boxes below: The boxes show Hangeul characters and jamo. If symbols appear as blank boxes, garbage, or question marks (?), your computer or web browser needs to be configured for the Korean language.

Introduction
Korean is the official language of both the Democratic People's Republic of Korea (North Korea) and the Republic of Korea (South Korea). It is also one of the two official languages in Yanbian Korean Autonomous Prefecture, China. Worldwide, there are about 80 million Korean speakers, most of whom live in China, Japan or the United States outside of the Koreas, but they also represent sizeable minorities in Russia (esp. Far East and Sakhalinsk), New Zealand, Kazakhstan, Canada, Uzbekistan and Australia.

In the Republic of Korea, the language is most often called 한국말 (Han-guk-mal), or more formally, 한국어 (Han-guk-eo) or 국어 (Guk-eo; literally "national language"). In North Korea and Yanbian, the language is most often called 조선말 (Chosŏnmal), or more formally, 조선어 (Chosŏnŏ).

Experts are unsure of the origins of the Korean language, although some believe it to come from the Altaic language tree. It is an agglutinative language, so it has some certain special characteristics that are unlike English. A student of Chinese languages will quickly notice that Korean shares much of their vocabulary, while a Japanese student will also notice similarities in grammar and vocabulary.

Feel free to use English Wiktionary's Korean language Category as a reference for these courses. New students to this type of language may initially progress slowly, but as study progresses, previously unfamiliar aspects of Korean will begin to make sense and new concepts will be more easily learned. Korean grammar is complex but surprisingly also very simple, and always very fun to learn.

Reading and writing

 * Alphabet Introduction
 * Learn to read, write and pronounce Korean (course)
 * /Principles of Orthography/
 * /Essential Pronunciation Rules/
 * /Advanced Pronunciation Rules/
 * /Mini-tutorial Lesson/
 * /Getting started on Hanja/

Vocabulary

 * Expert Hanja Hanja Terms for Expert Level Learners
 * Expert Terms for Expert Level Learners

Conversation
{|
 * - valign="top"

1단계 (LEVEL I): Beginner

 * 1. Greeting
 * 안녕 (informal)
 * 안녕하세요? (general)
 * 안녕하십니까? (formal)
 * 2. Forming sentences
 * 저는 대학생입니다.
 * 3. Connective Particles and Forms
 * -고, -거나, -지만
 * 4. Colors / Shopping
 * 파랑, 빨강, 노랑
 * 5. In a taxi / Distance and Time
 * 택시 / 거리와 시간
 * 6. Family
 * 가족
 * 7. Around the house
 * 집안
 * 8. The workplace / Using the telephone
 * 직장
 * 9. School
 * 학교
 * 10. Onomatopoeia
 * 의성어

2단계 (LEVEL II): High beginner

 * 1. Sports
 * 운동
 * 2. Jobs
 * 직업
 * 3. Downtown
 * 도심
 * 4. Public transportation
 * 대중교통
 * 5. At the hotel
 * 호텔에서
 * 6. At the library
 * 도서관에서
 * 7. At the farm
 * 시골에서
 * 8. Medical care
 * 병원에서
 * 9. The Weather
 * 날씨
 * 10. At the Theater
 * 영화관에서

 * - valign="top"

3단계 (LEVEL III): Low intermediate

 * 1. The human body
 * 인간의 몸
 * 2. Religion
 * 종교
 * 3. Nature
 * 자연
 * 4. The universe
 * 우주
 * 5. Reading a book
 * 책 읽기
 * 6. How much do you love me?
 * 날 얼마나 사랑해?
 * 7. Using computers
 * 컴퓨터 사용하기
 * 8. At the restaurant
 * 식당에서
 * 제9과
 * 제10과

4단계 (LEVEL IV): High intermediate

 * 제1과
 * 제2과
 * 제3과
 * 제4과
 * 제5과
 * 제6과
 * 제7과
 * 제8과
 * 제9과
 * 제10과

 * -valign="top"

5단계 (LEVEL V): Low advanced

 * 제1과
 * 제2과
 * 제3과
 * 제4과
 * 제5과
 * 제6과
 * 제7과
 * 제8과
 * 제9과
 * 제10과

6단계 (LEVEL VI): Advanced

 * 제1과: 마침 제 친구가 전화했기에 망정이지 그렇지 않았으면 비행기를 놓칠 뻔했어요.
 * 제2과
 * 제3과
 * 제4과
 * 제5과
 * 제6과
 * 제7과
 * 제8과
 * 제9과
 * 제10과
 * }

About the Authors

 * Authors

Koreanisch Coréen 한국어 입문 朝鮮語 Koreański ภาษาเกาหลี 韩语

title: Korean


text:
Talk:How to Write an Essay/Free Response

Dear Pingvo,

Here are some of my perspectives on Free Response.

I'm not American, but many things of this type are done all over the world.

When you had the question/cue: "A person's identity is shaped at birth",

a usual and useful point to the breakdown is looking at the key words.

This would be "identity" (the thing belonging to the person. Identity can be things that are similar to other people, as well as the things that make us different, individual or unique) "shaped" (the concept that is being created or changed, or sometimes destroyed) and "birth" (literally, the time when we are all brought into earth, sometimes it can have connotations of a 'spiritual' or 'emotional' birth, particularly when we are looking at literary texts).

It's good to do this kind of discursive analysis. It alone can suggest many directions for the burgeoning essay, though often this is not enough. You have to look at the essay question/cue as a whole thing, that it COMMUNICATES as a question, and is ASKING you something vitally important. It then allows you to COMMUNICATE and EXPRESS many things.

A good philosophical way to go about it is "What if [it were true/not true] that a person's identity [or other thing that stands in its stead] is shaped [what else happens if it's shaped 'the wrong way', or not at all] at birth?" That means essentially reversing the propsition, or subverting it, or considering other possibilities. It's a free response after all! You can do that!

Also free responses are written in certain genres (types of written work that has certain conventions of form and content). Where I study there is a unit of English known as a "Writing Folio". This basically contains all our non-text work. Another important part of our non-text work is where we look critically at things in the media and that's usually called Issues. It's on a current media text.

A free response can be any of these: (Which sounds very much like what you've been doing)
 * A document suited to the workplace like a letter, memorandum, letter or e-mail, or a report
 * A fictional narrative or other extended personal/imaginative piece
 * A non-fictional piece intended to convey complex or technical information
 * A report of an investigation, presented in journalistic style
 * A biographical/autobiographical account
 * A poem/short fictional piece (like a short story)
 * A reflection on an issue dealt with in one or more texts
 * and a piece intended to present a point of view persuasively.

Some of these have VERY DEFINITE how-tos, some of them have great flexibility and others are free for all. Generally the free-for-alls are NOT recommended by teachers. We are told, for example, that poetry loses us marks because it's hard to do.

I notice that in your piece you use several openers and closers, and you put it into four pretty standard paragraphs: an introduction, two paragraphs of argument or discourse and a conclusion. You seem to be commenting about what it means for the plot, the character and the theme; as well as what it means for us out there in the wider world. Nearly all texts comment on something, and it's important for students to show an understanding of this, particularly as they get into more advanced grade/year levels.

The structure of writing is very important as it makes it easier to tell someone what you're going to say. Academic writing has a very strong structure, which is indicated by words and phrases and where they are. If you know these words and phrases, and how to use them appropriately and fluently, then you're halfway there to good academic writing. Ideas, of course, are the other half. They indicate the levels of a text.

Also it's very important to have the sense of authorship, and readership. You must know your audience, purpose and form. In an examination, or in an assessment task for class, you write for a mature and educated readership. Most texts are written for that readership, but the people who assess your exams are a small part of that readership in real life. So focus on them only to the extent that promotes good scholarship and academic truth and freedom. This neccestates original ideas, and thatyou can respond to a situation. So many many examiners complain of trite and regurgitated ideas and structure. This can be corrected by many references to the author and his/her intentions (many text questions do ask about these, directly or indirectly), and how the reader feels/responds/thinks. Many times this reader will be a 'general' or 'ideal' reader, and when or if you encounter post-modernist ideas, there is the idea of many readers and meanings and texts. In post-modernism, we create the text ourselves from the raw material and information we are given, so there's no general or ideal reader as such. Or if there is, it's one who actively engages with the text.

Perhaps most important in a "Free Response", after you have conformed thus to the requirements, is the ability to 'freestyle' or 'improvise'. Of course you must give your reader some idea of where they are heading. I can't very well go into your head and see any freestyling or improvising, but they mark the top students and the top writers. Top writers aren't always top students, as I'm sure you can appreciate! But they can be, they can be!

Ah, thanks for the post. I should probably do some more looking around at other websites talking about AP writing. BTW, I'm not very far into the AP program, having only taken it for a couple of months before I read this essay.

I should probably start with the stricter types of essays (DBQ, etc.). Also, it would be great if a better writer sent in an essay to use. It looks like this will be quite a project, as well as very interesting. ;-) - Pingveno 23:34, 15 Feb 2004 (UTC)


text:
User talk:161.148.96.161

Hello, some nice work you are doing there. Just want to make sure that you yourself wrote the material, or it is releasable under a copyleft license like this site uses .. Thanks, --Karl Wick

title: User talk:161.148.96.161


text:
Interlingua/Basic Interlingua English Dictionary

(Books on Interlingua)

A

 * a to; at; in
 * ab from, since
 * [ad] to; at (= a)
 * accender to light
 * adjutar to help
 * ager to act, do
 * al contraction of a + le
 * [alco] anything, something (= alique)
 * [alcun] any, some (= alicun)
 * alicubi (-ícubi) anywhere, somewhere
 * alicun any, some
 * alique (ál-) anything, something
 * [alora] then (= tunc)
 * [alsi] (-í) also, too (= etiam)
 * alte high
 * altere (ál-) other
 * amar to like, love
 * ambe both
 * amico friend
 * [an] used to introduce a question; if, whether
 * [ancora] still, yet
 * anglese English
 * anniversario anniversary, birthday
 * anno year
 * [anque] (ánke) also, as well, too (= etiam)
 * ante before (prep.)
 * [antea] previously (= ante)
 * aperir to open
 * apparer to appear
 * appellar to call
 * appertiner to belong
 * apportar to bring
 * apprender to learn
 * apud (á-) by, near
 * arbore (ár-) tree
 * arder to burn
 * argento silver
 * ascoltar to listen to
 * asexual asexual
 * assatis (-sá-) rather
 * assecurar to assure, insure
 * [assi] (-sí) so, thus (= si)
 * attacar attack
 * attender to wait for
 * attinger to attain, reach
 * attraher to attract
 * audir to hear
 * augmentar to increase
 * aure ear
 * auro gold
 * avante before
 * ave bird
 * avion aeroplane

B

 * basse low
 * bastante enough; quite
 * batter to beat, hit
 * belle beautiful
 * ben well
 * ben que although
 * besonio need
 * biber to drink
 * billet ticket
 * bira beer
 * bisexual bisexual
 * bon good
 * boteca shop
 * brachio arm
 * bracio arm; brace
 * breve short
 * bucca mouth
 * bureau office

C

 * cader to fall
 * calide (cá-) hot
 * cambiar to change
 * camera (cá-) room
 * campo field
 * capace able, capable
 * caper o sasir grasp or hold
 * capillos hair
 * capite (cá-) head
 * car dear; expensive
 * casa house
 * caso case
 * cata each, every
 * cata uno each (one)
 * causa cause
 * a causa de because of
 * chassar to hunt
 * celar to hide
 * celo sky, heaven
 * cento hundred
 * cercar to look for
 * certe certain
 * cessar to stop
 * [ci] here (= hic)
 * cinque five
 * circa about
 * [circum] about (= circa)
 * citate city, town
 * clauder to close
 * cognoscer to know
 * colliger gather
 * collo neck
 * comenciar to begin
 * como as; how; like
 * comprar to buy
 * comprender to understand
 * con with
 * contar count
 * continer to contain
 * convenir to suit
 * coperir to cover
 * corde heart
 * corpore (cór-) body
 * cosa thing
 * costar cost
 * creder to believe
 * crescer to grow
 * [cuje] whose
 * currer to run
 * curte short
 * cute skin

D

 * dar to give
 * de from; of
 * deber to have to, must, ought; duty
 * debile (dé-) weak
 * dece ten
 * del contraction of de + le
 * deman tomorrow
 * demandar to ask
 * dente tooth
 * depost afterwards, since
 * derecto right
 * [desde] afterwards, since
 * [detra] behind
 * devenir to become
 * dextere (déks-) right
 * dicer to say, tell
 * die day
 * difficile (-fí-) difficult
 * digito (dí-) finger
 * dimension size
 * disparer to disappear
 * dolor pain
 * dono gift
 * dormir to sleep
 * dubita (dú-) doubt
 * ducer to lead
 * dum while
 * [dunque] therefore
 * duo two
 * dur hard
 * durante during
 * durante que while

E

 * e and
 * ecce here is (are), behold
 * effortiar se to make an effort
 * emer to buy
 * [era] was, were, used to be (= esseva)
 * era era
 * es am, is, are
 * [esque] (éske) used to introduce a question
 * esser to be
 * esseva was, were, used to be
 * estate summer
 * estranie strange
 * estranier foreign
 * etate age
 * etiam (é-) also, as well, too
 * evenir to happen
 * ex from, out of
 * exactemente exactly
 * exopere strike,hunger strike(=exopero de fame), worker strike(=exopero de empleos)
 * expensive expensive
 * exprimer (se) to express (oneself)
 * extra besides, outside

F

 * facer to do, make
 * facie face
 * facile (fá-) easy
 * facto deed, fact
 * familia family
 * fatigate tired
 * favor favor
 * per favor please
 * felice happy
 * femina (fé-) woman
 * ferir hit, wound
 * filia daughter
 * filio son
 * fin end
 * a fin de in order to
 * a fin que in order that
 * in fin in short
 * finir to finish
 * foco fire
 * folio leaf
 * foras outside
 * foris outside
 * forsan (fór-) perhaps
 * forte strong
 * fortiar to force
 * fratre brother
 * frigide (frí-) cold
 * fundar to found
 * fundo bottom

G

 * gai gay (merry)
 * gamba leg
 * gambon ham
 * ganiar to gain, win
 * gauder to be glad
 * gaudio joy, happiness
 * gay gay (homosexual)
 * gelato ice cream
 * german German (adj.)
 * gorga throat
 * grande big, great, large
 * grate grateful
 * gratias thank you

H

 * ha has, have
 * haber to have
 * hastar to hurry
 * heri yesterday
 * hiberno winter
 * hic here
 * hodie today
 * homine (hó-) man
 * homo: short for homosexual, usable as an adjective or a noun
 * homosexual: homosexual
 * hora hour; o'clock
 * humero (hú-) shoulder

I

 * ibi there
 * il it; there
 * il ha there is, are
 * illa she, her
 * illac there
 * illas they, them (fem.)
 * ille he, him
 * illes they, them (masc.)
 * illo it; that
 * illos they, them (neutr.)
 * impedir to hinder
 * imprimer to print
 * in in, into
 * incontrar to meet
 * infante child
 * infra below
 * inseniar to teach
 * insimul (-sí-) together
 * integre (ín-) whole
 * inter among, between
 * interim meanwhile
 * intersexual intersex (adj)
 * intersexualitate intersex (n); intersexuality
 * intertanto meanwhile
 * intra within
 * inviar to send
 * ipse -self
 * iste this, these (adj.)
 * isto this (pron.)

J

 * [ja] already, at once (= jam)
 * jacer to lie
 * jam = already, at once
 * jammais ever
 * jectar to throw
 * jentaculo (-tá-) breakfast
 * jocar to play
 * junger to join
 * juvene (jú-) young
 * juxta next to

L

 * la her, it
 * [la] there (= illac)
 * labio lip
 * lacrima (lá-) tear
 * large broad, wide
 * las them (fem.)
 * lassar to leave, let
 * latere (lá-) side
 * lavar to wash
 * le the; him, it
 * leger to read
 * legier (-jér) light (adj.)
 * lente slow
 * les them (masc.)
 * levar to lift
 * leve left (adj.)
 * libere (lí-) free
 * libro book
 * lingua tongue; language
 * littera (lí-) letter
 * lo it
 * lo que what, which
 * loco place
 * longe long
 * '''[lontan] distant
 * lor their
 * los them (neut.)
 * lumine (lú-) light

M

 * [ma] but (= mais)
 * mais but
 * major greater
 * mal bad; badly
 * malgrado in spite of
 * mancar to lack, be missing
 * mangiar (-jár) to eat
 * maniera manner
 * de maniera que so that
 * mano hand
 * mar sea
 * marita wife
 * marito husband
 * matino morning
 * matre mother
 * me me
 * medie half
 * mediedie (-díe) midday
 * melio better (adv.)
 * melior better (adj.)
 * mense month
 * mente mind
 * mentionar to mention
 * mesme same; -self
 * mesmo even
 * mi my
 * micre tiny
 * minor smaller
 * minus (mí-) less, minus
 * a minus que unless
 * al minus at least
 * mitter to put
 * molle soft
 * moneta coin, money
 * monstrar to show
 * morir to die
 * mover to move
 * multe many, much
 * multo very; very much
 * mundo world

N

 * nam because
 * nascer to be born
 * naso nose
 * natar swim, float
 * [necun] no, none, not any (= nulle)
 * [necuno] nobody (= nemo)
 * nemo nobody
 * nette clean
 * ni neither, nor
 * nihil nothing
 * nimie too many, too much
 * no no
 * nocte night
 * nomine (nó-) name
 * non not
 * il non importa que/tan no matter what/how
 * nondum (nón-) not yet
 * nonne? is it (not)?
 * nonobstante nevertheless
 * nos we, us
 * nostre our
 * nove new; nine
 * de nove again
 * novem (nó-) nine
 * nulle no, none
 * nunc now
 * nunquam (nún-) never

O

 * o either, or
 * oblidar to forget
 * obra work
 * obtener to obtain, to get
 * occurrer to happen
 * octo eight
 * oculo (ó-) eye
 * omne all, every
 * [on] one, you, they, people (= uno)
 * [ora] now (= nunc)
 * osso bone

P

 * pagar to pay
 * pan bread
 * pais (-ís) country
 * parer to appear, seem
 * parlar to speak
 * parola word
 * partir to leave
 * parve small
 * passato past (noun)
 * patata potato
 * patre father
 * pauc few
 * pauco a little
 * paupere (páu-) poor
 * pausa guideline
 * pecia piece
 * pectore (péc-) breast
 * pede foot
 * pejo worse (adv.)
 * pejor worse (adj.)
 * pena difficulty
 * a pena hardly, scarcely
 * pensar to think
 * per by, through
 * perder to lose
 * periculo (-rí-) danger
 * perque (perké) because; why
 * pertiner to belong
 * pesante heavy
 * peter to ask
 * petra stone
 * piranha piranha
 * placer to please; pleasure
 * plen full
 * plure several
 * plus more; plus
 * al plus at the most
 * de plus besides, moreover
 * in plus furthermore
 * poc = pauc
 * poco = pauco
 * pois afterwards; for
 * pois que since, because
 * poner to put
 * populo (pó-) people
 * porta door
 * portar to carry
 * post after, behind
 * postea afterwards
 * postmeridie afternoon
 * poter to be able, can; power
 * povre poor
 * precio price; prize
 * prender to take, hold of, catch or seize
 * presso near (adv.)
 * presso a near (prep.)
 * preste quick, ready
 * presto immediately; quickly
 * preter (pré-) beyond, besides
 * prime first
 * pro for; in order to
 * probar to prove, test
 * prohibir forbid
 * promitter to promise
 * proponer to suggest
 * proprie own
 * proque (proké) because; why
 * protruder to protrude:(protrusion) protrusion
 * proxime (pró-) next
 * puera (pú-) girl
 * puero (pú-) boy
 * pulsar to push

Q

 * [qua] like, as
 * qual what, which
 * qualque (quálke) some
 * quando when
 * quante how many, how much
 * quanto as much as; how much
 * quanto a as for
 * quasi almost
 * quatro four
 * que that; what; than; whom
 * qui who
 * quo where (to...)

R

 * rapide (rá-) quick
 * ration reason
 * [re] about
 * recercar search
 * reciper to receive
 * rege king
 * regina queen
 * regno kingdom
 * regratiar to thank
 * regrettar to regret
 * reguardar to look at
 * remaner to remain, stay
 * repasto meal
 * repeter to repeat
 * responder to answer
 * restaurante restaurant
 * restar to remain, stay
 * retornar to come back
 * retro back; ago
 * revenir to come back
 * ric rich
 * rota wheel

S

 * salutar to say hello to
 * salvo but for
 * san healthy
 * sanguine (sán-) blood
 * saper to know
 * a saper namely
 * sasir o caper grasp or hold
 * satis (sá-) enough; fairly, quite
 * scriber to write
 * se her-, him-, it-, oneself, themselves
 * seculo (sé-) century
 * secundo along; according to
 * secur secure; sure
 * sed but
 * seder to sit
 * seliger choose
 * semper always
 * [sempre] always (= semper)
 * senior Mr., sir
 * seniora Mrs., lady
 * senioretta Miss
 * sentir to feel
 * septe seven
 * septimana week
 * sequer to follow
 * [sera] (-rá) will be (= essera)
 * servitor waiter, servant
 * sex six
 * si yes; if; as; so
 * sia be; whether, or
 * simile (sí-) similar
 * sin without
 * sinistre left
 * sino bosom
 * sol alone, single, sole; sun
 * solmente only
 * solo only; solo; soil, floor
 * [son] are (= es)
 * soror sister
 * sortar sort (= kind, class);
 * de sorta que so that
 * sortir to go out, to come out
 * [sovente] often (= subinde)
 * speculo (spé-) mirror
 * sperar to hope
 * stadio stadium; stage (of development)
 * star to stand
 * stomacho (stó-) stomach
 * stoppar to stop
 * strata street
 * su her, his, its, one's
 * sub under
 * subite (sú-) sudden
 * sud south
 * suggerer suggest
 * super (sú-) above, on, over
 * suppa soup
 * supponer to suppose
 * supra above
 * [sur] above, on, over (= super)

T

 * tabula (tá-) table
 * tacer to be silent
 * tal such
 * [tamen] (tá-) however, yet (= totevia)
 * tante so many, so much
 * tanto as; so; so much
 * in tanto que inasmuch as
 * tarde late
 * tassa cup
 * te you (obj.)
 * tempore (tém-) time; weather
 * terra earth
 * testa head
 * tener to hold, keep
 * timer to be afraid of
 * tirar to pull, to shoot
 * toccar to touch
 * tornar to turn
 * tosto early, soon
 * plus tosto rather
 * tote all, every
 * totevia (-ía) nevertheless
 * toto all, everything
 * non del toto not at all
 * tractar to deal with
 * traducer to translate
 * traher to drag, draw
 * tranquille calm, quiet
 * traino train
 * trans across, beyond
 * transgenere transgender
 * travaliar to work
 * tres three
 * [troppo] too, too much
 * trovar to find
 * tu you; your
 * [tum] then
 * tunc then

U

 * ubi where
 * ubique everywhere
 * ulle any, some
 * ultime (úl-) last
 * ultra beyond; besides
 * un a, an; one
 * unquam (ún-) ever
 * urbe town
 * usar to use
 * usque as far as, until
 * utile (ú-) useful

V

 * va go(es), am/is/are going
 * vacue empty
 * vader to go
 * varie various
 * vender to sell
 * ventre stomach
 * venir to come
 * ver true
 * verso towards
 * vespere (vés-) evening
 * vetere (vé-) old
 * vetule (vé-) old
 * via away; road, way
 * viagiar (-jár) to travel
 * vice time; turn
 * a vices at times
 * in vice de instead of
 * vider to see
 * vino wine
 * visage (-áje) face
 * visitar to visit
 * vista sight, view
 * viste considering
 * vita life
 * vitro glass
 * viver to live
 * voce voice
 * volar to fly
 * voler to want, wish
 * vos you
 * vostre your

W

 * west west

Y

 * [ya] already, at once (= ja, jam)

pl:Interlingua:Słownik


text:
User:Maveric149/Sandbox

Template:GeneralChemTOC

title: User:Maveric149/Sandbox


text:
User:Jason Michael Smithson~enwikibooks

One more thing to work on: Environmental Awareness in the 21st Century

Good example of forward, up, and back: US_Constitution_and_Government

title: User:Jason Michael Smithson~enwikibooks


text:
Spanish/Ser

../Verbs/

=Ser=

"Ser" is an irregular verb that means  "to be".

 * Infinitive: ser
 * Present participle:  siendo
 * Past participle: sido

Present

 * Yo soy I am
 * tú eres You (informal) are
 * él/ella/usted es He/she is, you (respectful) are
 * nosotros somos We are
 * (vosotros sois) You (plural, informal) are
 * ellos/ustedes son They / you (plural, formal) are''

(Don't know what Yo, tú, él, and so on mean ? They are pronouns.)

../Imperfect/

 * Yo era  I was
 * tú eras
 * él/ella/usted era
 * nosotros éramos
 * (vosotros erais )
 * ellos/ustedes eran

../Preterite/

 * Yo fui  I was
 * tú fuiste
 * él/ella/usted fue
 * nosotros fuimos
 * (vosotros fuisteis )
 * ellos/ustedes fueron

../Future/

 * Yo seré  I will be
 * tú serás
 * él/ella/usted será
 * nosotros seremos
 * (vosotros seréis )
 * ellos/ustedes serán

— or —

 * Yo voy a ser  I'm going to be
 * tú vas a ser
 * él/ella/usted va a ser
 * nosotros vamos a ser
 * (vosotros vais a ser )
 * ellos/ustedes van a ser

../Subjunctive/

 * Yo sea  I may be or (if) I be
 * tú seas
 * él/ella/usted sea
 * nosotros seamos
 * (vosotros seáis )
 * ellos/ustedes sean

../Imperfect Subjunctive/

 * Yo fuera  I might be or (if) I were
 * tú fueras
 * él/ella/usted fuera
 * nosotros fuéramos
 * (vosotros fuerais )
 * ellos/ustedes fueran

— or —

 * Yo fuese  I might be or (if) I were
 * tú fueses
 * él/ella/usted fuese
 * nosotros fuésemos
 * (vosotros fueseis )
 * ellos/ustedes fuesen

Present perfect subjunctive

 * Yo haya sido   I may have been or had I been
 * tú hayas sido
 * él/ella/usted haya sido
 * nosotros hayamos sido
 * (vosotros hayáis sido )
 * ellos/ustedes hayan sido

Pluperfect subjunctive

 * Yo hubiera sido  (if only) I had been or I might have been
 * tú hubieras sido
 * él/ella/usted hubiera sido
 * nosotros hubiéramos sido
 * (vosotros hubierais sido )
 * ellos/ustedes hubieran sido

— or —

 * Yo hubiese sido  (if only) I had been or I might have been
 * tú hubieses sido
 * él/ella/usted hubiese sido
 * nosotros hubiésemos sido
 * (vosotros hubieseis sido )
 * ellos/ustedes hubiesen sido

../Conditional/

 * Yo sería   I would be
 * tú serías
 * él/ella/usted sería
 * nosotros seríamos
 * (vosotros seríais )
 * ellos/ustedes serían

../Imperative/

 * Yo ---
 * tú sé; no seas  Be; don't be
 * él/ella/usted sea
 * nosotros seamos
 * (vosotros sed; no seáis )
 * ellos/ustedes sean

Compound tenses
These tenses are combinations of the above tenses.

../Present Progressive/

 * Yo estoy siendo  I am being
 * tú estás siendo
 * él/ella/usted está siendo
 * nosotros estamos siendo
 * (vosotros estáis siendo )
 * ellos/ustedes están siendo

../Imperfect Progressive/

 * Yo estaba siendo  I was being
 * tú estabas siendo
 * él/ella/usted estaba siendo
 * nosotros estábamos siendo
 * (vosotros estabáis siendo)
 * ellos/ustedes estaban siendo

../Preterite Progressive/

 * Yo estuve siendo   I was being
 * tú estuviste siendo
 * él/ella/usted estuvo siendo
 * nosotros estuvimos siendo
 * (vosotros estuvisteis siendo )
 * ellos/ustedes estuvieron siendo

../Present Perfect/

 * Yo he sido   I have been
 * tú has sido
 * él/ella/usted ha sido
 * nosotros hemos sido
 * (vosotros habéis sido )
 * ellos/ustedes han sido

../Present Perfect Progressive/

 * Yo he estado siendo  I have been being
 * tú has estado siendo
 * él/ella/usted ha estado siendo
 * nosotros hemos estado siendo
 * (vosotros habéis estado siendo )
 * ellos/ustedes  han estado siendo

../Pluperfect/

 * Yo había sido  I had been being
 * tú habías sido
 * él/ella/usted había sido
 * nosotros habíamos sido
 * (vosotros habíais sido )
 * ellos/ustedes habían sido

../Preterite Perfect/

 * Yo hube sido  I had been being
 * tú hubiste sido
 * él/ella/usted hubo sido
 * nosotros hubimos sido
 * (vosotros hubisteis sido )
 * ellos/ustedes hubieron sido

../Future Perfect/

 * Yo habré sido   I will have been
 * tú habrás sido
 * él/ella/usted habrá sido
 * nosotros habremos sido
 * (vosotros habréis sido )
 * ellos/ustedes habrán sido

../Perfect Conditional/

 * Yo habría sido  I would have been
 * tú habrías sido
 * él/ella/usted habría sido
 * nosotros habríamos sido
 * (vosotros habríais sido )
 * ellos/ustedes habrían sido

title: Spanish/Ser


text:
Cookbook:Pumpkin Pie I

| Dessert | American cuisine | Holiday

Pumpkin pie is a traditional American and Canadian holiday dessert. It consists of a pumpkin-based custard baked in a single pie shell. The pie is traditionally served with whipped cream.

Ingredients

 * 2 cups (480 ml) milk, scalded
 * 2 cups (450 g) cooked and puréed pumpkin (or plain canned pumpkin)
 * 1 cup (240 ml) maple syrup
 * ⅛ cup (30 g) sugar
 * 1 tbsp flour
 * ½ tsp salt
 * 1 tsp ginger
 * 1 tsp cinnamon
 * ¼ tsp nutmeg (optional)
 * 2 large eggs, beaten
 * 1 unbaked 9-inch pie shell

Procedure

 * 1) Preheat oven to 350°F (180°C).
 * 2) Blend all ingredients except the pie shell together to make the filling.
 * 3) Pour the filling into the unbaked pie shell.
 * 4) Bake in the preheated oven for 45 minutes.
 * 5) Let cool and serve.

Notes, tips, and variations

 * This recipe replaces much of the sugar normally found in a pumpkin pie recipe with maple syrup. Use only real 100% maple syrup, not maple-flavored pancake syrup, as their sugar content is different. You can also use brown sugar instead of maple syrup.
 * Prepare the raw pumpkin by skinning and cutting into 1 inch cubes. Bake at 350°F (180°C) for 1 hour and then turn off the heat. Leave the pumpkin in the oven for another hour or two, which will reduce the moisture content. The pumpkin may also be steamed but may end up with too much moisture, resulting in a runny pie. A 10 inch (25 cm)-diameter pumpkin will make 4–6 pies. The pumpkin may also be baked whole and skinned afterwards.
 * Pumpkin pie has no top crust, which makes most forms of decoration impossible; however, for a more aesthetically-pleasing pie, put dollops of real whipped cream on each slice, or add a decorative rim to the side crust with artfully layered dough cut-outs in the shape of fall leaves, squash, or pumpkins.
 * Use a smaller 'sugar pumpkin' instead of the big 'Jack O Lantern' pumpkin. Sugar pumpkins have a firm and smooth texture while the larger 'Jack O Lantern' pumpkin has a more stringy or fibrous texture and more watery flesh.

Variations

 * Chocolate-covered pumpkin pie: After the pie has cooled, melt 2 oz (55 g) of sweetened chocolate (milk or dark) and pour over the top of the pie. Be sure to completely cover the pumpkin. Refrigerate to set the chocolate.
 * Pumpkin Pastries: Roll pie crust pastry thin and cut into circles approx 4" in diameter. Put a spoonful of the cool pumpkin mixture towards one side of the center of the circle. Fold over the crust into a half-circle and firmly crimp the edges closed. Slice three small slits in the top for venting. Place on a greased cookie sheet. Bake only until crust is a light golden-brown, approx 10 minutes.

Substitutions

 * 14 oz (1 can) sweetened condensed milk can replace the scalded milk and maple syrup.
 * 2 cups of plain canned pumpkin can replace the cooked and strained pumpkin. Do not use "pumpkin pie filling", which has added spices. For a discussion on the use of canned pumpkin and the recipes attached, please see the talk page.

Kochbuch/ Kürbiskuchen

title: Cookbook:Pumpkin Pie I


text:
Spanish/Present

../Verbs/

No bones about it. The present tense is EASY. Just memorize the endings for the different verbs and a couple of oddball exceptions and you will be able to talk about any momentary thing that is on your mind. Who needs to plan for the future, dwell on the past, or delve into abstraction anyway ?

There are three verb types in Spanish. They are called -AR, -ER, and -IR verbs. Each of these refers to the last two letters of the infinitive form of the verb. Examples:  -AR: bailar, to dance; -ER: aprender, to learn; and -IR: escribir,  to write.

When you conjugate a verb you take the generic, infinitive form and change the ending to match the person(s) or thing(s) doing whatever action the verb describes. In Spanish, the last two letters come off and another ending goes on in their place. Each verb tense has its own set of six endings for each verb type. Don't worry though, there are patterns there and much of the endings overlap so it is easier to remember them.

The present tense verb endings are as follows:

-ar verbs

 * Yo (I): -o
 * Tú (you, informal): -as
 * El, ella, or usted (he, she, or you, formal):  -a
 * Nosotros (we): -amos
 * Vosotros (you, plural): -áis
 * Ellos, ustedes (they, or you, plural formal): -an

That is:

 * -o
 * -as
 * -a
 * -amos
 * -áis
 * -an

Sometimes the vowel in the ending is accented.

Here is an example conjugation:

Bailar

 * Yo bailo.  I dance.
 * Tú bailas.  You dance.
 * Usted, Él, Ella baila.  You (respectful) dance, he or she dances
 * Nosotros bailamos.  We dance.
 * Vosotros bailáis.  You dance.
 * Ustedes, Ellos, Ellas bailan.  They dance.

Of course, most of the above statements can be restated without any loss of meaning with no pronoun: Bailo -- I dance; bailas, you dance. In Spanish, the verbs change to reflect the person(s) doing the action on them and it is OK to leave off the pronouns, especially when context makes the subject clear.

-er/-ir verbs
-ER and -IR verbs are almost identical, so they are often listed together. The only differences in the present tense are in Nosotros and Vosotros.

For -ER verbs:
 * Yo (I): -o
 * Tú (you, informal): -es
 * El, ella, or usted (he, she, or you, formal):  -e
 * Nosotros (we): -emos
 * Vosotros (you, plural): -éis
 * Ellos, ustedes (they, or you, plural formal): -en

For -IR verbs:
 * Yo (I): -o
 * Tú (you, informal): -es
 * El, ella, or usted (he, she, or you, formal):  -e
 * Nosotros (we): -imos
 * Vosotros (you, plural): -ís
 * Ellos, ustedes (they, or you, plural formal): -en

That is:
 * -o
 * -es
 * -e
 * -emos (for -ER) or :-imos (for -IR)
 * -éis (for -ER) or :-ís (for -IR)
 * -en

Here is an example conjugation of an -ER verb:

Aprender

 * Yo aprendo.  I learn.
 * Tú aprendes.  You learn.
 * Usted aprende.  You (respectful) learn.
 * Nosotros aprendemos.  We learn.
 * Vosotros aprendéis.  You learn.
 * Ellos aprenden.  They learn.

Here's an example conjugation of an -IR verb:

Escribir

 * Yo escribo.  I write.
 * Tú escribes.  You write.
 * Usted escribe.  You (respectful) write.
 * Nosotros escribimos.  We write.
 * Vosotros escribís.  You write.
 * Ellos escriben.  They write.

Ser

 * Yo soy. I am.
 * Tú eres.  You are.
 * El/Ella/Ud. es.  He/She/You(formal) is.
 * Nosotros/Nosotras somos.  We are.
 * Vosotros sois.  You are (plural).
 * Ellos/Ellas son. They are.

Ir

 * Yo voy.  I go.
 * Tú vas.  You go. (A statement, not technically a command)
 * Ella va.  She goes.
 * Nosotros vamos.  We go.
 * Ustedes van.  Y'all go.

Tener

 * tengo
 * tienes
 * tiene
 * tenemos
 * tienen

Note that the first "e" turns to "ie" in all of the conjugations except the "nosotros" form. That is a pattern that you will see repeated.

title: Spanish/Present


text:
Cookbook talk:Pumpkin Pie I

originaly from Wikipedia article Pumpkin pie.

Page history from Wikipedia

 * (cur) (last) . . 17:44, 3 Jan 2004 . . Gentgeen (transwiking recipe to wikibooks)
 * (cur) (last) . . 09:59, 15 Nov 2003 . . Guaka (degr C)
 * (cur) (last) . . M 09:58, 15 Nov 2003 . . Guaka (spelling, wikilink)
 * (cur) (last) . . M 15:22, 13 Nov 2003 . . Rmhermen
 * (cur) (last) . . 15:20, 13 Nov 2003 . . Gentgeen (gave reason for not using pancake syrup)
 * (cur) (last) . . 17:08, 7 Nov 2003 . . Gentgeen (wikified, rewording)
 * (cur) (last) . . 17:21, 6 Nov 2003 . . 206.65.37.136
 * (cur) (last) . . M 12:51, 6 Nov 2003 . . Jengod
 * (cur) (last) . . 02:45, 6 Nov 2003 . . Gentgeen (format)
 * (cur) (last) . . 02:44, 6 Nov 2003 . . Gentgeen

What do you do if you do not have an oven to cook your pumpkin pies in?
Every year in October, I enjoy spending my time cooking pumpkin pies. I've always loved having the soothing smell of a freshly baked pumpkin pie emanate through my place. I also enjoy sharing my pies with the people around me. I have even cooked pies for the cashiers that ring up my ingredients. This year, I am living in an apartment that does not have an oven. What ever shall I do now? I dont want to give up my pie baking tradition. Is there some alternative to an oven? Could I cook my pie on the stove? Can I roast it over an open fire? How do military people living in the wild cook their pumpkin pies? Any options that you can give me would be well appreciated. I am a desperate man. The Worst kind of desperate man. I am man who is need of home cooked pumpkin pie.

Microwave?
A microwave will do strange things to home-made pastry, but if you are using a bought crust then about 15 min on a slightly-less-than-high power should set the filling. If you want to get really into microwave pies, a browning dish is a good investment. It distributes the heat better than standard dishes and allows things to cook more like they do in the oven.

Christinelaura 07:22, 29 July 2007 (UTC)

Why not use a can of pumpkin
This was snipped from the recipe page.

I'm not sure why the above recipe would be better than picking up a can of pumpkin in the store, and then buying the ingredients they specify in the recipe on the back. I'm not saying the above recipe isn't better, just that I have no way of judging, and nobody even claimed that it is. So, I'm going to all this trouble to point it out because I usually follow the in-store prodedure I outlined here, and two years ago I actually tested 3 of them and discovered big differences.

Libby's brand won to my taste, followed by One-Pie brand, followed by some Whole Food's organic label. My taste runs toward sweeter, very moist (shiny!), not too "nutmeg-y" pumpkin pie, served good and cold. I'm not a shill for Libby's; in fact, I wanted One-Pie to win since that's what I'd always used before, and I like the look of the label better. Also, I have no idea if there are differences in the pumpkin itself, of just in the recipes, and I didn't test the different combinations. But there were significant differences so it's worth figuring out which one you like.

because!
The obvious benefit of the recipe is that you can adjust the spices to suit your tastes. No guesswork as to which brand of filling tastes better.

You should also consider that the stuff sold as "pumpkin pie filling" is sometimes actually hubbard squash. It essentially tastes the same and yields a pie of the same texture, but I think it has a better shelf life or something, so it's sold as pumpkin pie filling.

Also keep in mind that you can use a pumpkin for more than just pie. Bread, muffins, cake, soup, and so on. You can make a couple pies, a loaf of bread, and some muffins all from a single decent-sized pumpkin.

It's healthier to eat things that you prepare yourself than stuff from a can. Messedrocker 03:25, 16 Jun 2005 (UTC)

because!!
--Duk 03:48, 17 October 2005 (UTC)
 * 1) If you grow pumpkins in your own garden you need this recipe.
 * 2) If you make a bunch of pies, this recipe is much less expensive than buying canned pumpkin.

 * I've added in an optional substitution of canned pumpkin for puree made from a fresh pumpkin. I agree that using fresh ingredients is optimal, but if that were the only way to make pumpkin pie, well damn, nobody in their right mind would ever make pumpkin pie. Canned will work fine; it has the same texture, flavor, and moisture content as the recipe expects. Jessicapierce 19:25, 3 May 2007 (UTC)

because !!!
Some people live in countries (e.g. Germany) where fresh pumpkin (or at least certain winter squashes like butternut and red kuri) are available but canned pumpkin isn't. Mahagaja (discuss • contribs) 14:59, 18 October 2018 (UTC)

Different recipies
What's the procedure on different recipes. Say another recipe for canned pumpkin, and another more standard recipe (-maple syrup (very expensive), +condensed milk). Do we just name the article Pumpkin Pie (2) ? --Duk 04:01, 17 October 2005 (UTC)

 * Often what is done is if there are going to be several of the same kind of dish, like Brownies, the plainly named one becomes the index, a new recipe page is made with the original recipe giving it a descriptor, like, minty, deep-dish, cherry, or whatever and the new one is made similarly with a descriptor.  If one is the core, original recipe, or very close to it, that one takes up the base name or the name of Plain X, Original X, Simple X, that kinda deal.   So you can end up with Maple Pumpkin Pie, Spiced Pumpkin Pie, Simple Pumpkin Pie and Orgasmic Pumpkin Pie if there are enough recipes that are sufficiently different. 65.95.228.247 04:32, 17 October 2005 (UTC)

 * We could make this a disambiguation page, and find unique names for the recipes. This one could become "Pumpkin-Maple Pie", while one with canned pie filling could be "Easy Pumpkin Pie", or something similar.  Another option, as seen at Cookbook:Guacamole, is to simply add another recipe (or 5) to the page. Gentgeen 05:08, 17 October 2005 (UTC)  PS: Don't you love edit conflicts? :) Gentgeen

Amount of Filling
Deep dish nine inch pie shells (from the frozen section of the supermarket) hold four cups of filling. This recipe adds up to about six cups of filling. Is this recipe for a larger pie dish (traditional pyrex or ceramic type)? --Duk 03:59, 17 October 2005 (UTC)

 * I've never had a problem making this fit a 4 cup shell. Maybe the whole adds up to less volume than its parts. Gentgeen 05:08, 17 October 2005 (UTC)

Why is scalding the milk listed in this recipe
Scalding is traditionally called for to destroy the enzymes that would thicken the milk during the cooking process, but pasteurization accomplishes this, and you would be hard pressed to find unpasteurized milk in most countries. Therefore, I find it rather needless and redundant to be listed. 01:05, 15 October 2006 (GMT)

title: Cookbook talk:Pumpkin Pie I


text:
Cookbook:Dessert

Typically, a dessert is a food that comes at the end of a meal. Its taste is usually sweet, but sometimes strong, as with many cheeses. The word comes from the Old French desservir, meaning "to clear the table." Common desserts include cakes, cookies, fruits, pastries, pies, ice cream, and candies.

Recipes

fr:Cuisine:Desserts ספר מתכונים/קינוחים hy:Եփութուխ:Աղանդեր

title: Cookbook:Dessert


text:
Cookbook:Crème Brûlée I

| Dessert

This recipe for crème brûlée should provide a crackly crust over a cold custard, balanced in sweetness, egg and cream content. The procedure is due to Dawn Yanagihara. For additional information on the dish, see the crème brûlée disambiguation page.

Procedure

 * 1) With the oven rack adjusted to its lower middle position, preheat the oven to 300°F (150°C). Fold a kitchen towel to cover the bottom of a large roasting pan and arrange 12 ea. 5-ounce (150 ml) ramekins on the towel. The ramekins should not touch each other or the side of the roasting pan. If the roasting pan is not large enough, scale down the recipe.
 * 2) Combine 3 cups of the cream and sugar in a medium saucepan. With a paring knife, halve the vanilla beans lengthwise and scrape the seeds into the saucepan. Submerge the pods in the cream. Bring the mixture to a boil over medium heat, stirring occasionally to dissolve the sugar. Remove the saucepan from the heat and steep the mixture for 20 minutes to infuse the flavor.
 * 3) Meanwhile, separate the eggs, placing the yolks in a large bowl and storing the whites for another use. Bring a kettle of water to a boil.  After the cream has steeped remove the pods and stir in the remaining 3 cups of cream to cool the mixture.
 * 4) Whisk the egg yolks until they are evenly combined. Add a cup of the cream mixture to the yolks and whisk until combined. Continue adding cups of cream and whisking until evenly colored. Pour the mixture through a fine mesh strainer into a second bowl. Ladle the mixture into the 12 ramekins.
 * 5) Place the roasting pan onto the oven rack and pour in boiling water until it reaches ⅔ the height of the ramekins. Do not splash water into the ramekins. Bake until an instant-read thermometer registers 170–175°F (77–79°C) or until the edges of the custard are set, with a spot in the center about the size of a quarter remaining wiggly. The baking time depends upon the height of the ramekins. If shallow, start checking at 30 minutes. Higher ramekins can take up to an hour to bake.
 * 6) Remove ramekins from roasting pan and cool to room temperature on a wire rack. Place on a shallow tray, cover with plastic wrap, and chill in the refrigerator for at least 4 hours. Before serving, uncover the ramekins and soak up any condensation with paper toweling. Spread 1 teaspoon turbinado sugar on each, tilting and tapping to spread the sugar evenly. Spread sugar only on the number of ramekins that will be served. The others can be stored for several days in the refrigerator for later use.
 * 7) Ignite a propane blowtorch and caramelize the sugar on each ramekin. Take care to direct the flame away from any ignitable material. Avoid the miniature butane torch since its flame is not adequate for uniform caramelization in a reasonable amount of time, and the finished dish may taste of butane. Re-chill the ramekins for not more than 45 minutes.  A longer time leads to softening of the caramelized crust.
 * 8) Serve and enjoy!

Notes, tips, and variations

 * Without a torch the sugar may also be caramelized in these ways:
 * After spreading the sugar over the ramekins, place them as close as you can under a very hot broiler. Watch them closely because this method tends to be uneven and burn. Too long under the broiler can also result in the custard turning into a sort of chunky soup which is not a very appealing texture. Works best with fine granulated sugar.
 * Heat the sugar in a saucepan over medium heat without stirring until it starts to melt, then stir with a wooden spoon until caramelization occurs (this is easier to tell with white sugar than Turbinado) and spoon over the ramekins, tilting and rotating them to cover with an even layer.
 * Alternately, combine the sugar with half as much water by volume, bring to a simmer over medium-high heat, and cook without stirring 3 to 5 minutes, tilting the pan as required to ensure even caramelization. If the caramel hardens due to cooling, warm over low heat until it is again pourable.
 * Regular granulated sugar may also be used for the caramelization process in place of the brown sugar.
 * A towel may also be placed into the roasting pan prior to adding the water to help distribute the heat across the bottom of the ramekins evenly as well as insulate the bottoms from the heat coming through the bottom of the pan.
 * Make sure that before adding the cream to the egg yolks, the cream has cooled down. If one adds hot cream, the yolks will start to clot, ruining the final product.
 * It is possible to substitute half-and-half or milk for the cream, provided that a few more egg yolks are added for texture.

title: Cookbook:Crème Brûlée I


text:
Cookbook talk:Crème Brûlée I

Page history from Wikipedia article Crème brûlée.

* (cur) (last). . 00:13, 4 Jan 2004. . Gentgeen (transwiking recipe to wikibooks) * (cur) (last). . 19:04, 14 Oct 2003. . 66.32.186.103 (Turbinado) * (cur) (last). . M 04:41, 21 Mar 2003. . Looxix (accidentaly -> accidentally ) * (cur) (last). . M 17:49, 10 Feb 2003. . Mintguy (Britian > Britain) * (cur) (last). . 10:20, 4 Feb 2003. . Mintguy (origin) * (cur) (last). . 16:24, 24 Jan 2003. . The Anome (get.. it.. right!) * (cur) (last). . 22:22, 22 Jan 2003. . Maveric149 (#REDIRECT Crème brulée) * (cur) (last). . 22:14, 22 Jan 2003. . JSF

In Great Britian we do not measure sugar in fluid ounces but we weigh it. Should the 9 fluid ounces read just ounces? I'll change it and see if it is left.

Alternative Language Links
... seems all broken as of today 2010-02-27 --eckes

title: Cookbook talk:Crème Brûlée I


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User:Petros~enwikibooks

Petros is a Web Designer in Canberra, Australia. Married with two young children.

Interests:

 * Acting
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title: User:Petros~enwikibooks


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User:Kzhr

&

I'm a Japanese User on Japanese Wikipedia.

title: User:Kzhr


text:
Bicycles/Maintenance and Repair

Bicycles throughout the world are made with standardized, interchangeable parts. Unlike many modern products, the technology used in bicycles is simple enough to allow many riders to repair their own vehicles with a minimum of effort.

For any cyclist, bicycle maintenance is a particularly useful skillset to acquire. Every skill learned in this area—no matter how simple or complex—can aid in keeping your bike in good working order, save you money, and make the difference between pushing your bike home or riding it.

Contents

 * Appendix
 * Chains
 * Setting chain length
 * Chain sizes
 * Chain cleaning and lubrication
 * Checking a chain for wear
 * Removing a bicycle chain
 * Mending a broken chain
 * Installing a new chain
 * Chain rings
 * Bottom brackets
 * Bottom bracket overhaul
 * Brakes
 * Adjusting Rim Brakes
 * Coaster brakes
 * Cables and Housings
 * Cleaning parts
 * Cranks
 * Derailleurs
 * Front-derailleur adjustment
 * Rear-derailleur adjustment
 * Frames
 * Freewheels & cassettes
 * Gear-changing Dimensions: Tables with gear shifting data.
 * Glossary
 * Handlebars & stems
 * Headsets
 * Headset overhaul
 * Hubs
 * Cleaning and repacking a hub
 * Maintenance schedules
 * Pedals
 * Removing pedals
 * Saddles & seatposts
 * Shifters
 * Rapidfire shifter lubrication – (i.e. Shimano A20)
 * SRAM Gripshift 3.0 'comp' Cable Replacement
 * Suspension
 * Front suspension lubrication
 * Tools & supplies
 * Wheels & Tires
 * Fixing a flat (AKA a puncture)
 * Inflating Tires
 * Truing a wheel (adjusting rims so that they don't appear to wobble as the wheels spin)
 * Fitting and Repair for Tubeless Ready Tyre on to Tubeless Ready Rim

Manual de la bicicleta Mécanique vélo Riparazione della bicicletta Polkupyörän huolto ja korjaus

title: Bicycles/Maintenance and Repair