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User:JakeNelson~enwikibooks

I live in Bloomington, Minnesota, near the Mall of America. I am a computer science/economics student, and have worked in television production. I have also worked in proofreading, and expect to be applying that a fair bit.

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

title: User:JakeNelson~enwikibooks


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Wikibooks:Reading room

Welcome to the reading room, the Wikibooks forum consisting of discussion rooms:
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 * To start a new discussion, enter one of the discussion rooms listed below.
 * If you can't find an older discussion, check in the archive pages. Old discussions are archived regularly.
 * Please choose one of the rooms below to post messages, rather than posting messages to this page!

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title: Wikibooks:Reading room


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User talk:Toby Bartels

Toby: You seem to gave endorsed both Wikitext and Wikibooks as name options. I'd like to argue in favor of Wikibooks. I've used Wikitext in writing some things, and I get myself confused (probably a personal problem, but there might be someone else just as stupid.. ;-) ). I think we should use Wikitext when we speak of the markup language, or any material that uses it. That would include 'pedia, 'quote, etc. Wikibook is an accurate description and allows the distinction between Wikitext and Wikibooks. LouI 11:26 29 Jul 2003 (UTC)

Yeah -- I use WikiText to describe wiki-editable text. --mav 11:29 29 Jul 2003 (UTC)

I do think that "Wikibooks" is probably better. (See my URL suggestion -- it uses that.) I just believe that "Wikitext" is also OK. I could well change my vote strategically to emphasise this if necessary. (Even in a non-binding survey, different voting patterns can have different strategic effects on the psychology of the reader. ^_^) -- Toby Bartels 14:14 29 Jul 2003 (UTC)

title: User talk:Toby Bartels


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Organic Chemistry/Periodic table

Some of the good news about organic chemistry is that it focuses on a subset of the periodic table, so there are fewer elements to worry about. These are the main elements with which we must concern ourselves, although occasionally a few others will be used in reactions.

Organic chemistry > Periodic table shortened for organic chemistry

title: Organic Chemistry/Periodic table


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Calculus/Limits/An Introduction to Limits

Limits, the first step into calculus, explain the complex nature of the subject. It is used to define the process of derivation and integration. It is also used in other circumstances to intuitively demonstrate the process of "approaching".

Intuitive Look into Limits
The limit is one of the greatest tools in the hands of any mathematician. We will give the limit an approach. Because mathematics came only due to approaches... remember?!

We designate limit in the form:
 * $$\lim_{x\to a}f(x)$$

This is read as "The limit of $$f$$ of $$x$$ as $$x$$ approaches $$a$$". This is an important thing to remember, it is basic notation which is accepted by the world.

We'll take up later the question of how we can determine whether a limit exists for $$f(x)$$ at $$a$$ and, if so, what it is. For now, we'll look at it from an intuitive standpoint.

Let's say that the function that we're interested in is $$f(x)=x^2$$, and that we're interested in its limit as $$x$$ approaches $$2$$. Using the above notation, we can write the limit that we're interested in as follows:
 * $$\lim_{x\to2}x^2$$

One way to try to evaluate what this limit is would be to choose values near 2, compute $$f(x)$$ for each, and see what happens as they get closer to 2. There are two ways to approach values near 2. One is to approach from below, and the other is to approach from above:

The table above is the case from below.

The table above is the case from above.

We can see from the tables that as $$x$$ grows closer and closer to 2, $$f(x)$$ seems to get closer and closer to 4, regardless of whether $$x$$ approaches 2 from above or from below. For this reason, we feel reasonably confident that the limit of $$x^2$$ as $$x$$ approaches 2 is 4, or, written in limit notation,
 * $$\lim_{x\to2}x^2=4$$

We could have also just substituted 2 into $$x^2$$ and evaluated: $$(2)^2=4$$. However, this will not work with all limits.

Now let's look at another example. Suppose we're interested in the behavior of the function $$f(x)=\frac{1}{x-2}$$ as $$x$$ approaches 2. Here's the limit in limit notation:
 * $$\lim_{x\to 2}\frac{1}{x-2}$$

Just as before, we can compute function values as $$x$$ approaches 2 from below and from above. Here's a table, approaching from below:

And here from above:

In this case, the function doesn't seem to be approaching a single value as $$x$$ approaches 2, but instead becomes an extremely large positive or negative number (depending on the direction of approach). Well, one says such a limit does not exist because no finite number is approached. This arises the concept of infinity: an undefined quantity and the limit is also called infinite limit or limit without a bound.

Note that we cannot just substitute 2 into $$\frac{1}{x-2}$$ and evaluate as we could with the first example, since we would be dividing by 0.

Both of these examples may seem trivial, but consider the following function:
 * $$f(x)=\frac{x^2(x-2)}{x-2}$$

This function is the same as
 * $$f(x)=\left\{\begin{matrix}x^2&\text{if }x\ne2\\ \mbox{undefined}&\text{if }x=2\end{matrix}\right.$$

Note that these functions are really completely identical; not just "almost the same," but actually, in terms of the definition of a function, completely the same; they give exactly the same output for every input.

In elementary algebra, a typical approach is to simply say that we can cancel the term $$(x-2)$$, and then we have the function $$f(x)=x^2$$. However, that would be inaccurate; the function that we have now is not really the same as the one we started with, because it is defined when $$x=2$$, and our original function was specifically not defined when $$x=2$$. This may seem like a minor point, but from making this kind of assumptions we can easily derive absurd results, such that $$0=1$$ (see Mathematical Fallacy § All numbers equal all other numbers in Wikipedia for a complete example). Even without calculus we can avoid this error by stating that:
 * $$f(x)=\frac{x^2(x-2)}{x-2}=x^2\text{ when }x\ne2$$

In calculus, we can introduce a more intuitive and also correct way of looking at this type of function. What we want is to be able to say that, although the function isn't defined when $$x=2$$, it works almost as if it was. It may not get there, but it gets really, really close. For instance, $$f(1.99999)=3.99996$$. The only question that we have is: what do we mean by "close"?

Informal Definition of a Limit
As the precise definition of a limit is a bit technical, it is easier to start with an informal definition; we'll explain the formal definition later.

We suppose that a function $$f$$ is defined for $$x$$ near $$c$$ (but we do not require that it be defined when $$x=c$$).

Notice that the definition of a limit is not concerned with the value of $$f(x)$$ when $$x=c$$ (which may exist or may not). All we care about are the values of $$f(x)$$ when $$x$$ is close to $$c$$, on either the left or the right (i.e. less or greater).

Limit can also be understood as: $$x$$ is infinitely approaching to $$c$$ but never equals to $$c$$, just like the function $$f(x)=\frac{1}{x}$$, which infinitely approaches to $$0$$ but never equals $$0$$.

Rules and Identities
Now that we have defined, informally, what a limit is, we will list some rules that are useful for working with and computing limits. You will be able to prove all these once we formally define the fundamental concept of the limit of a function.

First, the constant rule states that if $$f(x)=b$$ (that is, $$f$$ is constant for all $$x$$) then the limit as $$x$$ approaches $$c$$ must be equal to $$b$$. In other words

 * Example: $$\lim_{x\to6}5=5$$

Second, the identity rule states that if $$f(x)=x$$ (that is, $$f$$ just gives back whatever number you put in) then the limit of $$f$$ as $$x$$ approaches $$c$$ is equal to $$c$$. That is,

 * Example: $$\lim_{x\to6}x=6$$

The next few rules tell us how, given the values of some limits, to compute others.

Notice that in the last rule we need to require that $$M$$ is not equal to 0 (otherwise we would be dividing by zero which is an undefined operation).

These rules are known as identities; they are the scalar product, sum, difference, product, and quotient rules for limits. (A scalar is a constant, and, when you multiply a function by a constant, we say that you are performing scalar multiplication.)

Using these rules we can deduce another. Namely, using the rule for products many times we get that
 * $$\lim_{x\to c}f(x)^n=\left(\lim_{x\to c}f(x)\right)^n=L^n$$ for a positive integer $$n$$.

This is called the power rule.

As a result, we can safely say that all limits for polynomial functions can be deduced into several limits that satisfy the identity rule and thus easier to compute. Find the limit $$\lim_{x\to 2}4x^3$$.
 * Example 1

We need to simplify the problem, since we have no rules about this expression by itself. We know from the identity rule above that $$\lim_{x\to2}x=2$$. By the power rule, $$\lim_{x\to2}x^3=\left(\lim_{x\to2}x\right)^3=2^3=8$$. Lastly, by the scalar multiplication rule, we get $$\lim_{x\to2}4x^3=4\cdot\lim_{x\to2}x^3=4\cdot 8=32$$.

$$\blacksquare$$ Find the limit $$\lim_{x\to2}\Big[4x^3+5x+7\Big]$$.
 * Example 2

To do this informally, we split up the expression, once again, into its components. As above, $$\lim_{x\to2}4x^3=32$$.

Also $$\lim_{x\to2}5x=5\cdot\lim_{x\to2}x=5\cdot 2=10$$ and $$\lim_{x\to2}7=7$$. Adding these together gives
 * $$\lim_{x\to2}\Big[4x^3+5x+7\Big]=\lim_{x\to2}4x^3+\lim_{x\to2}5x+\lim_{x\to2}7=32+10+7=49$$.

Find the limit $$\lim_{x\to2}\frac{4x^3+5x+7}{(x-4)(x+10)}$$.
 * $$\blacksquare$$
 * Example 3

From the previous example the limit of the numerator is $$\lim_{x\to 2}\Big[4x^3+5x+7\Big]=49$$. The limit of the denominator is
 * $$\lim_{x\to2}(x-4)(x+10)=\lim_{x\to2}\big[x-4\big]\cdot\lim_{x\to2}\big[x+10\big]=(2-4)(2+10)=-24$$

As the limit of the denominator is not equal to zero we can divide. This gives
 * $$\lim_{x\to2}\frac{4x^3+5x+7}{(x-4)(x+10)}=-\frac{49}{24}$$.

Find the limit $$\lim_{x\to4}\frac{x^4-16x+7}{4x-5}$$.
 * $$\blacksquare$$
 * Example 4

We apply the same process here as we did in the previous set of examples;
 * $$\lim_{x\to4}\frac{x^4-16x+7}{4x-5}=\frac{\lim\limits_{x\to4}\Big[x^4-16x+7\Big]}{\lim\limits_{x\to4}\Big[4x-5\Big]}=\frac{\lim\limits_{x\to4}x^4-\lim\limits_{x\to4}16x+\lim\limits_{x\to4}7}{\lim\limits_{x\to4}4x-\lim\limits_{x\to4}5}$$.

We can evaluate each of these; $$\lim_{x\to4}(x^4)=256\ ,\ \lim_{x\to4}(16x)=64\ ,\ \lim_{x\to4}(7)=7\ ,\ \lim_{x\to4}(4x)=16\ ,\ \lim_{x\to4}(5)=5.$$ Thus, the answer is $$\frac{199}{11}$$. Find the limit $$\lim_{x\to2}\frac{x^2-3x+2}{x-2}$$.
 * $$\blacksquare$$
 * Example 5

In this example, evaluating the result directly will result in a division by 0. While you can determine the answer experimentally, a mathematical solution is possible as well.

First, the numerator is a polynomial that may be factored: $$\lim_{x\to2}\frac{(x-2)(x-1)}{x-2}$$

Now, you can divide both the numerator and denominator by $$(x-2)$$: $$\lim_{x\to2}(x-1)=(2-1)=1$$

Remember that the limit is a method to determine the approaching value of a function instead of the value of the function itself. So, though the function is undefined at $$x=2$$, the value of the function is approaching to $$1$$ when $$x \rightarrow 2$$
 * $$\blacksquare$$
 * Example 6

Find the limit $$\lim_{x\to0}\left[\frac{1-\cos(x)}{x}\right]$$.

To evaluate this seemingly complex limit, we will need to recall some sine and cosine identities (see Chapter ). We will also have to use two new facts. First, if $$f(x)$$ is a trigonometric function (that is, one of sine, cosine, tangent, cotangent, secant and cosecant functions), and is defined at $$a$$, then $$\lim_{x\to a}f(x)=f(a)$$.

Second, $$\lim_{x\to 0}\frac{\sin(x)}{x}=1$$. This can be proved using squeeze theorem. Note that L'Hospital's rule is not allowed to be used to evaluate this limit because it causes circular reasoning,

in the sense that differentiating $$\sin x$$.requires this limit to equal one, which is exactly the equation that is being proven.

Method 1 (before learning L'Hôpital's rule):

To evaluate the limit, recognize that $$1-\cos(x)$$ can be multiplied by $$1+\cos(x)$$ to obtain $$1-\cos^2(x)$$ which, by our trig identities, is $$\sin^2(x)$$. So, multiply the top and bottom by $$1+\cos(x)$$. (This is allowed because it is identical to multiplying by one.) This is a standard trick for evaluating limits of fractions; multiply the numerator and the denominator by a carefully chosen expression which will make the expression simplify somehow. In this case, we should end up with:

 * $$\lim_{x\to0}\left[\frac{1-\cos(x)}{x}\right]$$
 * $$=\lim_{x\to0}\left[\frac{1-\cos(x)}{x}\cdot\frac{1}{1}\right]$$
 * $$=\lim_{x\to0}\left[\frac{1-\cos(x)}{x}\cdot\frac{1+\cos(x)}{1+\cos(x)}\right]$$
 * $$=\lim_{x\to0}\frac{\big(1-\cos(x)\big)\big(1+\cos(x)\big)}{x\big(1+\cos(x)\big)}$$
 * $$=\lim_{x\to0}\frac{1-\cos^2(x)}{x\big(1+\cos(x)\big)}$$
 * $$=\lim_{x\to0}\frac{\sin^2(x)}{x\big(1+\cos(x)\big)}$$
 * $$=\lim_{x\to0}\left[\frac{\sin(x)}{x}\cdot\frac{\sin(x)}{1+\cos(x)}\right]$$.
 * }
 * $$=\lim_{x\to0}\frac{1-\cos^2(x)}{x\big(1+\cos(x)\big)}$$
 * $$=\lim_{x\to0}\frac{\sin^2(x)}{x\big(1+\cos(x)\big)}$$
 * $$=\lim_{x\to0}\left[\frac{\sin(x)}{x}\cdot\frac{\sin(x)}{1+\cos(x)}\right]$$.
 * }
 * $$=\lim_{x\to0}\frac{\sin^2(x)}{x\big(1+\cos(x)\big)}$$
 * $$=\lim_{x\to0}\left[\frac{\sin(x)}{x}\cdot\frac{\sin(x)}{1+\cos(x)}\right]$$.
 * }
 * $$=\lim_{x\to0}\left[\frac{\sin(x)}{x}\cdot\frac{\sin(x)}{1+\cos(x)}\right]$$.
 * }
 * }

Our next step should be to break this up into $$\lim_{x\to0}\left[\frac{\sin(x)}{x}\right]\cdot\lim_{x\to0}\left[\frac{\sin(x)}{1+\cos(x)}\right]$$ by the product rule. As mentioned above, $$\lim_{x\to0}\left[\frac{\sin(x)}{x}\right]=1$$. Next, $$\lim_{x\to0}\left[\frac{\sin(x)}{1+\cos(x)}\right]=\frac{\lim\limits_{x\to0}\big[\sin(x)\big]}{\lim\limits_{x\to0}\big[1+\cos(x)\big]}=\frac{0}{1+\cos(0)}=0$$.

Thus, by multiplying these two results, we obtain 0.

$$\blacksquare$$

Note that we also cannot apply L'Hospital's rule to evaluate this limit because it causes circular reasoning.

We will now present an amazingly useful result, even though we cannot prove it yet. We can find the limit at $$c$$ of any polynomial or rational function, as long as that rational function is defined at $$c$$ (so we are not dividing by 0). That is, $$c$$ must be in the domain of the function.

We already learned this for trigonometric functions, so we see that it is easy to find limits of polynomial, rational or trigonometric functions wherever they are defined. In fact, this is true even for combinations of these functions; thus, for example, $$\lim_{x\to1}\bigg[\sin(x^2)+4\cos^3(3x-1)\bigg]=\sin(1^2)+4\cos^3(3\cdot 1-1)=\sin 1+4\cos^32$$.

The Squeeze Theorem
The Squeeze Theorem is very important in calculus, where it is typically used to find the limit of a function by comparison with two other functions whose limits are known.

It is called the Squeeze Theorem because it refers to a function $$f$$ whose values are squeezed between the values of two other functions $$g$$ and $$h$$, both of which have the same limit $$L$$. If the value of $$f$$ is trapped between the values of the two functions $$g$$ and $$h$$, the values of $$f$$ must also approach $$L$$.

Expressed more precisely:

Example: Compute $$\lim_{x\to0}x\cdot\sin\left(\tfrac{1}{x}\right)$$.

Since we know that"$-1 \le \sin(\frac{1}{x}) \le 1$"Multiplying $$x$$ into the inequality yields"x"Now we apply the squeeze theorem"x"Since $$\lim_{x\to0}-|x|=\lim_{x\to0}|x|=0$$,

$$\lim_{x\to0}x\cdot\sin\left(\tfrac{1}{x}\right)=0$$

$$\blacksquare$$

Finding Limits
Now, we will discuss how, in practice, to find limits. First, if the function can be built out of rational, trigonometric, logarithmic, or exponential functions, then if a number $$c$$ is in the domain of the function, then the limit at $$c$$ is simply the value of the function at $$c$$:"$\lim_{x \to c} f(x)=f(c)$ when $f(x)$ can be built out of rational, trigonometric, logarithmic, or exponential functions and $c \in$ the Domain of $f(x)$"If $$c$$ is not in the domain of the function, then in many cases (as with rational functions) the domain of the function includes all the points near $$c$$, but not $$c$$ itself. An example would be if we wanted to find $$\lim_{x\to0}\frac{x}{x}$$, where the domain includes all numbers besides 0.

In that case, in order to find $$\lim_{x\to c}f(x)$$ we want to find a function $$g(x)$$ similar to $$f(x)$$, except with the hole at $$c$$ filled in. The limits of $$f$$ and $$g$$ will be the same, as can be seen from the definition of a limit. By definition, the limit depends on $$f(x)$$ only at the points where $$x$$ is close to $$c$$ but not equal to it, so the limit at $$c$$ does not depend on the value of the function at $$c$$. Therefore, if $$\lim_{x\to c}g(x)=L$$, $$\lim_{x\to c}f(x)=L$$ also. And since the domain of our new function $$g$$ includes $$c$$, we can now (assuming $$g$$ is still built out of rational, trigonometric, logarithmic and exponential functions) just evaluate it at $$c$$ as before. Thus we have $$\lim_{x\to c}f(x)=g(c)$$.

In our example, this is easy; canceling the $$x$$'s gives $$g(x)=1$$, which equals $$f(x)=\frac{x}{x}$$ at all points except 0. Thus, we have $$\lim_{x\to0}\frac{x}{x}=\lim_{x\to0}1=1$$. In general, when computing limits of rational functions, it's a good idea to look for common factors in the numerator and denominator.

Specific DNE Situations
Note that the limit might not exist at all (DNE means "does not exist"). There are a number of ways in which this can occur:

"Gap"
 * Gap example.png is a gap (not just a single point) where the function is not defined. As an example, in
 * $$f(x)=\sqrt{x^2-16}$$

 * $$\lim_{x\to c}f(x)$$ does not exist when $$-4\le c\le4$$. There is no way to "approach" the middle of the graph. Note that the function also has no limit at the endpoints of the two curves generated (at $$c=-4$$ and $$c=4$$). For the limit to exist, the point must be approachable from both the left and the right.

 * Note also that there is no limit at a totally isolated point on a graph.

 * "Jump"
 * If the graph suddenly jumps to a different level, there is no limit at the point of the jump. For example, let $$f(x)$$ be the greatest integer $$\le x$$. Then, if $$c$$ is an integer, when $$x$$ approaches $$c$$ from the right $$f(x)=c$$, while when $$x$$ approaches $$c$$ from the left $$f(x)=c-1$$. Thus $$\lim_{x\to c}f(x)$$ will not exist.

 * Vertical asymptote: In $$f(x)=\frac{1}{x^2}$$
 * the graph gets arbitrarily high as it approaches 0, so there is no limit. (In this case we sometimes say the limit is infinite; see the next section.)

]
 * Infinite oscillation: These next two can be tricky to visualize. In this one, we mean that a graph continually rises above and falls below a horizontal line. In fact, it does this infinitely often as you approach a certain $$x$$-value. This often means that there is no limit, as the graph never approaches a particular value. However, if the height (and depth) of each oscillation diminishes as the graph approaches the $$x$$-value, so that the oscillations get arbitrarily smaller, then there might actually be a limit.
 * The use of oscillation naturally calls to mind the trigonometric functions. An example of a trigonometric function that does not have a limit as $$x$$ approaches 0 is
 * $$f(x)=\sin\left(\tfrac{1}{x}\right)$$
 * As $$x$$ gets closer to 0 the function keeps oscillating between $$-1$$ and 1. In fact, $$\sin\left(\tfrac{1}{x}\right)$$ oscillates an infinite number of times on the interval between 0 and any positive value of $$x$$. The sine function is equal to 0 whenever $$x=k\pi$$, where $$k$$ is a positive integer. Between every two integers $$k$$ , $$\sin(x)$$ goes back and forth between 0 and $$-1$$ or 0 and 1. Hence, $$\sin\left(\tfrac{1}{x}\right)=0$$ for every $$x=\tfrac{1}{k\pi}$$. In between consecutive pairs of these values, $$\tfrac{1}{k\pi}$$ and $$\tfrac{1}{(k+1)\pi}$$ , $$\sin\left(\tfrac{1}{x}\right)$$ goes back and forth from 0, to either $$-1$$ or 1 and back to 0. We may also observe that there are an infinite number of such pairs, and they are all between 0 and $$1/\pi$$. There are a finite number of such pairs between any positive value of $$x$$ and $$\tfrac{1}{\pi}$$ , so there must be infinitely many between any positive value of $$x$$ and 0. From our reasoning we may conclude that, as $$x$$ approaches 0 from the right, the function $$\sin\left(\tfrac{1}{x}\right)$$ does not approach any specific value. Thus, $$\lim_{x\to0}\sin\left(\tfrac{1}{x}\right)$$ does not exist.

Determining Limits
The formal way to determine whether a limit exists is to find out whether the value of the limit is the same when approaching from below and above (see at the top of this chapter). The notation for the limit approaching from below (in increasing order) is"$\lim_{x\to c^-}f(x)$, notice the negative sign on the constant $c$"The notation for the limit approaching from above (from decreasing order) is"$\lim_{x\to c^+}f(x)$, notice the positive sign on the constant $c$"For example, let us find the limits of $$f(x)=\frac{1}{x}$$ when $$x$$ is approaching $$0$$ in both directions. In other words, find $$\lim_{x\to 0^-}\frac{1}{x}$$ and $$\lim_{x\to 0^+}\frac{1}{x}$$. Recall the table we made when we are trying to intuitively feel the limit. We can use that to help us. However, if familiar enough with reciprocal functions, we can simply determine the two values by imagining the graph of the function.

The following table is when $$x$$ is approaching from below. Thus, we found that when $$x$$ is approaching from below to $$0$$, the function approaches negative infinity. In mathematical terms:

$$\lim_{x\to 0^-}\frac{1}{x}=-\infty$$

Now let's talk about the approach from above. "We found that $\lim_{x\to 0^+}\frac{1}{x}=\infty$"$$\blacksquare$$

The method of determining if limits exist is relatively intuitive. It only requires some practice to be familiar with the process. Let's use the same example: find $$\lim_{x\to 0}\frac{1}{x}$$. Since we already found that $$\lim_{x\to 0^-}\frac{1}{x}=-\infty$$ and $$\lim_{x\to 0^+}\frac{1}{x}=\infty$$, and obviously,

$$\lim_{x\to 0^-}\frac{1}{x}\ne\lim_{x\to 0^+}\frac{1}{x}$$

We can say that $$\lim_{x\to 0}\frac{1}{x}$$ does not exist. $$\blacksquare$$

Infinity Situations
Now consider the function
 * $$g(x)=\frac{1}{x^2}$$

What is the limit as $$x$$ approaches zero? The value of $$g(0)$$ does not exist; it is not defined.

Notice, also, that we can make $$g(x)$$ as large as we like, by choosing a small $$x$$, as long as $$x\ne0$$. For example, to make $$g(x)$$ equal to $$10^{12}$$, we choose $$x$$ to be $$10^{-6}$$. Thus, $$\lim_{x\to0}\frac{1}{x^2}$$ does not exist.

However, we do know something about what happens to $$g(x)$$ when $$x$$ gets close to 0 without reaching it. We want to say we can make $$g(x)$$ arbitrarily large (as large as we like) by taking $$x$$ to be sufficiently close to 0, but not equal to 0. We express this symbolically as follows:
 * $$\lim_{x\to0}g(x)=\lim_{x\to0}\frac{1}{x^2}=\infty$$

Note that the limit does not exist at $$0$$ ; for a limit, being $$\infty$$ is a special kind of not existing. In general, we make the following definition.

An example of the second half of the definition would be that $$\lim_{x\to0}-\frac{1}{x^2}=-\infty$$.

Applications of Limits
To see the power of the concept of the limit, let's consider a moving car. Suppose we have a car whose position is linear with respect to time (that is, a graph plotting the position with respect to time will show a straight line). We want to find the velocity. This is easy to do from algebra; we just take the slope, and that's our velocity.

But unfortunately, things in the real world don't always travel in nice straight lines. Cars speed up, slow down, and generally behave in ways that make it difficult to calculate their velocities.

Now what we really want to do is to find the velocity at a given moment (the instantaneous velocity). The trouble is that in order to find the velocity we need two points, while at any given time, we only have one point. We can, of course, always find the average speed of the car, given two points in time, but we want to find the speed of the car at one precise moment.

This is the basic trick of differential calculus, the first of the two main subjects of this book. We take the average speed at two moments in time, and then make those two moments in time closer and closer together. We then see what the limit of the slope is as these two moments in time are closer and closer, and say that this limit is the slope at a single instant.

We will study this process in much greater depth later in the book. First, however, we will need to study limits more carefully.


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Re-use of text

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es:Wikilibros:Copyrights pl:Wikibooks:Prawa autorskie ta:விக்கிநூல்கள்:காப்புரிமைகள் vi:Wikibooks:Quyền tác giả

title: Wikibooks:Copyrights


text:
Wikibooks:GNU Free Documentation License

Version 1.3, 3 November 2008 Copyright (C) 2000, 2001, 2002, 2007, 2008 Free Software Foundation, Inc.

Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed.

0. PREAMBLE
The purpose of this License is to make a manual, textbook, or other functional and useful document "free" in the sense of freedom: to assure everyone the effective freedom to copy and redistribute it, with or without modifying it, either commercially or noncommercially. Secondarily, this License preserves for the author and publisher a way to get credit for their work, while not being considered responsible for modifications made by others.

This License is a kind of "copyleft", which means that derivative works of the document must themselves be free in the same sense. It complements the GNU General Public License, which is a copyleft license designed for free software.

We have designed this License in order to use it for manuals for free software, because free software needs free documentation: a free program should come with manuals providing the same freedoms that the software does. But this License is not limited to software manuals; it can be used for any textual work, regardless of subject matter or whether it is published as a printed book. We recommend this License principally for works whose purpose is instruction or reference.

1. APPLICABILITY AND DEFINITIONS
This License applies to any manual or other work, in any medium, that contains a notice placed by the copyright holder saying it can be distributed under the terms of this License. Such a notice grants a world-wide, royalty-free license, unlimited in duration, to use that work under the conditions stated herein. The "Document", below, refers to any such manual or work. Any member of the public is a licensee, and is addressed as "you". You accept the license if you copy, modify or distribute the work in a way requiring permission under copyright law.

A "Modified Version" of the Document means any work containing the Document or a portion of it, either copied verbatim, or with modifications and/or translated into another language.

A "Secondary Section" is a named appendix or a front-matter section of the Document that deals exclusively with the relationship of the publishers or authors of the Document to the Document's overall subject (or to related matters) and contains nothing that could fall directly within that overall subject. (Thus, if the Document is in part a textbook of mathematics, a Secondary Section may not explain any mathematics.) The relationship could be a matter of historical connection with the subject or with related matters, or of legal, commercial, philosophical, ethical or political position regarding them.

The "Invariant Sections" are certain Secondary Sections whose titles are designated, as being those of Invariant Sections, in the notice that says that the Document is released under this License. If a section does not fit the above definition of Secondary then it is not allowed to be designated as Invariant. The Document may contain zero Invariant Sections. If the Document does not identify any Invariant Sections then there are none.

The "Cover Texts" are certain short passages of text that are listed, as Front-Cover Texts or Back-Cover Texts, in the notice that says that the Document is released under this License. A Front-Cover Text may be at most 5 words, and a Back-Cover Text may be at most 25 words.

A "Transparent" copy of the Document means a machine-readable copy, represented in a format whose specification is available to the general public, that is suitable for revising the document straightforwardly with generic text editors or (for images composed of pixels) generic paint programs or (for drawings) some widely available drawing editor, and that is suitable for input to text formatters or for automatic translation to a variety of formats suitable for input to text formatters. A copy made in an otherwise Transparent file format whose markup, or absence of markup, has been arranged to thwart or discourage subsequent modification by readers is not Transparent. An image format is not Transparent if used for any substantial amount of text. A copy that is not "Transparent" is called "Opaque".

Examples of suitable formats for Transparent copies include plain ASCII without markup, Texinfo input format, LaTeX input format, SGML or XML using a publicly available DTD, and standard-conforming simple HTML, PostScript or PDF designed for human modification. Examples of transparent image formats include PNG, XCF and JPG. Opaque formats include proprietary formats that can be read and edited only by proprietary word processors, SGML or XML for which the DTD and/or processing tools are not generally available, and the machine-generated HTML, PostScript or PDF produced by some word processors for output purposes only.

The "Title Page" means, for a printed book, the title page itself, plus such following pages as are needed to hold, legibly, the material this License requires to appear in the title page. For works in formats which do not have any title page as such, "Title Page" means the text near the most prominent appearance of the work's title, preceding the beginning of the body of the text.

The "publisher" means any person or entity that distributes copies of the Document to the public.

A section "Entitled XYZ" means a named subunit of the Document whose title either is precisely XYZ or contains XYZ in parentheses following text that translates XYZ in another language. (Here XYZ stands for a specific section name mentioned below, such as "Acknowledgements", "Dedications", "Endorsements", or "History".) To "Preserve the Title" of such a section when you modify the Document means that it remains a section "Entitled XYZ" according to this definition.

The Document may include Warranty Disclaimers next to the notice which states that this License applies to the Document. These Warranty Disclaimers are considered to be included by reference in this License, but only as regards disclaiming warranties: any other implication that these Warranty Disclaimers may have is void and has no effect on the meaning of this License.

2. VERBATIM COPYING
You may copy and distribute the Document in any medium, either commercially or noncommercially, provided that this License, the copyright notices, and the license notice saying this License applies to the Document are reproduced in all copies, and that you add no other conditions whatsoever to those of this License. You may not use technical measures to obstruct or control the reading or further copying of the copies you make or distribute. However, you may accept compensation in exchange for copies. If you distribute a large enough number of copies you must also follow the conditions in section 3.

You may also lend copies, under the same conditions stated above, and you may publicly display copies.

3. COPYING IN QUANTITY
If you publish printed copies (or copies in media that commonly have printed covers) of the Document, numbering more than 100, and the Document's license notice requires Cover Texts, you must enclose the copies in covers that carry, clearly and legibly, all these Cover Texts: Front-Cover Texts on the front cover, and Back-Cover Texts on the back cover. Both covers must also clearly and legibly identify you as the publisher of these copies. The front cover must present the full title with all words of the title equally prominent and visible. You may add other material on the covers in addition. Copying with changes limited to the covers, as long as they preserve the title of the Document and satisfy these conditions, can be treated as verbatim copying in other respects.

If the required texts for either cover are too voluminous to fit legibly, you should put the first ones listed (as many as fit reasonably) on the actual cover, and continue the rest onto adjacent pages.

If you publish or distribute Opaque copies of the Document numbering more than 100, you must either include a machine-readable Transparent copy along with each Opaque copy, or state in or with each Opaque copy a computer-network location from which the general network-using public has access to download using public-standard network protocols a complete Transparent copy of the Document, free of added material. If you use the latter option, you must take reasonably prudent steps, when you begin distribution of Opaque copies in quantity, to ensure that this Transparent copy will remain thus accessible at the stated location until at least one year after the last time you distribute an Opaque copy (directly or through your agents or retailers) of that edition to the public.

It is requested, but not required, that you contact the authors of the Document well before redistributing any large number of copies, to give them a chance to provide you with an updated version of the Document.

4. MODIFICATIONS
You may copy and distribute a Modified Version of the Document under the conditions of sections 2 and 3 above, provided that you release the Modified Version under precisely this License, with the Modified Version filling the role of the Document, thus licensing distribution and modification of the Modified Version to whoever possesses a copy of it. In addition, you must do these things in the Modified Version:

 Use in the Title Page (and on the covers, if any) a title distinct from that of the Document, and from those of previous versions (which should, if there were any, be listed in the History section of the Document). You may use the same title as a previous version if the original publisher of that version gives permission. List on the Title Page, as authors, one or more persons or entities responsible for authorship of the modifications in the Modified Version, together with at least five of the principal authors of the Document (all of its principal authors, if it has fewer than five), unless they release you from this requirement. State on the Title page the name of the publisher of the Modified Version, as the publisher. Preserve all the copyright notices of the Document. Add an appropriate copyright notice for your modifications adjacent to the other copyright notices. Include, immediately after the copyright notices, a license notice giving the public permission to use the Modified Version under the terms of this License, in the form shown in the Addendum below. Preserve in that license notice the full lists of Invariant Sections and required Cover Texts given in the Document's license notice.
Include an unaltered copy of this License.

Preserve the section Entitled "History", Preserve its Title, and add to it an item stating at least the title, year, new authors, and publisher of the Modified Version as given on the Title Page. If there is no section Entitled "History" in the Document, create one stating the title, year, authors, and publisher of the Document as given on its Title Page, then add an item describing the Modified Version as stated in the previous sentence.

Preserve the network location, if any, given in the Document for public access to a Transparent copy of the Document, and likewise the network locations given in the Document for previous versions it was based on. These may be placed in the "History" section. You may omit a network location for a work that was published at least four years before the Document itself, or if the original publisher of the version it refers to gives permission.

For any section Entitled "Acknowledgements" or "Dedications", Preserve the Title of the section, and preserve in the section all the substance and tone of each of the contributor acknowledgements and/or dedications given therein.

Preserve all the Invariant Sections of the Document, unaltered in their text and in their titles. Section numbers or the equivalent are not considered part of the section titles.

Delete any section Entitled "Endorsements". Such a section may not be included in the Modified version.

Do not retitle any existing section to be Entitled "Endorsements" or to conflict in title with any Invariant Section.

Preserve any Warranty Disclaimers.

If the Modified Version includes new front-matter sections or appendices that qualify as Secondary Sections and contain no material copied from the Document, you may at your option designate some or all of these sections as invariant. To do this, add their titles to the list of Invariant Sections in the Modified Version's license notice. These titles must be distinct from any other section titles.

You may add a section Entitled "Endorsements", provided it contains nothing but endorsements of your Modified Version by various parties—for example, statements of peer review or that the text has been approved by an organization as the authoritative definition of a standard.

You may add a passage of up to five words as a Front-Cover Text, and a passage of up to 25 words as a Back-Cover Text, to the end of the list of Cover Texts in the Modified Version. Only one passage of Front-Cover Text and one of Back-Cover Text may be added by (or through arrangements made by) any one entity. If the Document already includes a cover text for the same cover, previously added by you or by arrangement made by the same entity you are acting on behalf of, you may not add another; but you may replace the old one, on explicit permission from the previous publisher that added the old one.

The author(s) and publisher(s) of the Document do not by this License give permission to use their names for publicity for or to assert or imply endorsement of any Modified Version.

5. COMBINING DOCUMENTS
You may combine the Document with other documents released under this License, under the terms defined in section 4 above for modified versions, provided that you include in the combination all of the Invariant Sections of all of the original documents, unmodified, and list them all as Invariant Sections of your combined work in its license notice, and that you preserve all their Warranty Disclaimers.

The combined work need only contain one copy of this License, and multiple identical Invariant Sections may be replaced with a single copy. If there are multiple Invariant Sections with the same name but different contents, make the title of each such section unique by adding at the end of it, in parentheses, the name of the original author or publisher of that section if known, or else a unique number. Make the same adjustment to the section titles in the list of Invariant Sections in the license notice of the combined work.

In the combination, you must combine any sections Entitled "History" in the various original documents, forming one section Entitled "History"; likewise combine any sections Entitled "Acknowledgements", and any sections Entitled "Dedications". You must delete all sections Entitled "Endorsements".

6. COLLECTIONS OF DOCUMENTS
You may make a collection consisting of the Document and other documents released under this License, and replace the individual copies of this License in the various documents with a single copy that is included in the collection, provided that you follow the rules of this License for verbatim copying of each of the documents in all other respects.

You may extract a single document from such a collection, and distribute it individually under this License, provided you insert a copy of this License into the extracted document, and follow this License in all other respects regarding verbatim copying of that document.

7. AGGREGATION WITH INDEPENDENT WORKS
A compilation of the Document or its derivatives with other separate and independent documents or works, in or on a volume of a storage or distribution medium, is called an "aggregate" if the copyright resulting from the compilation is not used to limit the legal rights of the compilation's users beyond what the individual works permit. When the Document is included in an aggregate, this License does not apply to the other works in the aggregate which are not themselves derivative works of the Document.

If the Cover Text requirement of section 3 is applicable to these copies of the Document, then if the Document is less than one half of the entire aggregate, the Document's Cover Texts may be placed on covers that bracket the Document within the aggregate, or the electronic equivalent of covers if the Document is in electronic form. Otherwise they must appear on printed covers that bracket the whole aggregate.

8. TRANSLATION
Translation is considered a kind of modification, so you may distribute translations of the Document under the terms of section 4. Replacing Invariant Sections with translations requires special permission from their copyright holders, but you may include translations of some or all Invariant Sections in addition to the original versions of these Invariant Sections. You may include a translation of this License, and all the license notices in the Document, and any Warranty Disclaimers, provided that you also include the original English version of this License and the original versions of those notices and disclaimers. In case of a disagreement between the translation and the original version of this License or a notice or disclaimer, the original version will prevail.

If a section in the Document is Entitled "Acknowledgements", "Dedications", or "History", the requirement (section 4) to Preserve its Title (section 1) will typically require changing the actual title.

9. TERMINATION
You may not copy, modify, sublicense, or distribute the Document except as expressly provided under this License. Any attempt otherwise to copy, modify, sublicense, or distribute it is void, and will automatically terminate your rights under this License.

However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation.

Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice.

Termination of your rights under this section does not terminate the licenses of parties who have received copies or rights from you under this License. If your rights have been terminated and not permanently reinstated, receipt of a copy of some or all of the same material does not give you any rights to use it.

10. FUTURE REVISIONS OF THIS LICENSE
The Free Software Foundation may publish new, revised versions of the GNU Free Documentation License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. See http://www.gnu.org/copyleft/.

Each version of the License is given a distinguishing version number. If the Document specifies that a particular numbered version of this License "or any later version" applies to it, you have the option of following the terms and conditions either of that specified version or of any later version that has been published (not as a draft) by the Free Software Foundation. If the Document does not specify a version number of this License, you may choose any version ever published (not as a draft) by the Free Software Foundation. If the Document specifies that a proxy can decide which future versions of this License can be used, that proxy's public statement of acceptance of a version permanently authorizes you to choose that version for the Document.

11. RELICENSING
"Massive Multiauthor Collaboration Site" (or "MMC Site") means any World Wide Web server that publishes copyrightable works and also provides prominent facilities for anybody to edit those works. A public wiki that anybody can edit is an example of such a server. A "Massive Multiauthor Collaboration" (or "MMC") contained in the site means any set of copyrightable works thus published on the MMC site.

"CC-BY-SA" means the Creative Commons Attribution-Share Alike 3.0 license published by Creative Commons Corporation, a not-for-profit corporation with a principal place of business in San Francisco, California, as well as future copyleft versions of that license published by that same organization.

"Incorporate" means to publish or republish a Document, in whole or in part, as part of another Document.

An MMC is "eligible for relicensing" if it is licensed under this License, and if all works that were first published under this License somewhere other than this MMC, and subsequently incorporated in whole or in part into the MMC, (1) had no cover texts or invariant sections, and (2) were thus incorporated prior to November 1, 2008.

The operator of an MMC Site may republish an MMC contained in the site under CC-BY-SA on the same site at any time before August 1, 2009, provided the MMC is eligible for relicensing. = How to use this License for your documents =

To use this License in a document you have written, include a copy of the License in the document and put the following copyright and license notices just after the title page:

 * Copyright (c) YEAR  YOUR NAME.
 * Permission is granted to copy, distribute and/or modify this document
 * under the terms of the GNU Free Documentation License, Version 1.3
 * or any later version published by the Free Software Foundation;
 * with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
 * A copy of the license is included in the section entitled "GNU
 * Free Documentation License".

If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the "with...Texts." line with this:

 * with the Invariant Sections being LIST THEIR TITLES, with the
 * Front-Cover Texts being LIST, and with the Back-Cover Texts being LIST.

If you have Invariant Sections without Cover Texts, or some other combination of the three, merge those two alternatives to suit the situation.

If your document contains nontrivial examples of program code, we recommend releasing these examples in parallel under your choice of free software license, such as the GNU General Public License, to permit their use in free software.

de:Wikibooks:GNU Free Documentation License es:Wikilibros:GNU Free Documentation License it:Wikibooks:Testo della GNU Free Documentation License ja:Wikibooks:Text of GNU Free Documentation License pt:Wikilivros:GNU Free Documentation License


text:
Wikibooks:Boilerplate request for permission

This page is intended as boilerplate text for requesting permission to re-use somebody else's content in Wikibooks. Usually, to do this, they must re-license it under the CC-BY-SA license. For more, read Copyrights.

,

I really liked your ! I found it very informative and useful. I would love to use it in a project I'm involved with called Wikibooks, so I'm seeking your permission.

Wikibooks http://wikibooks.org is a collection of free non-fiction books (only textbooks) that is collaboratively-edited by volunteers from around the world. You might have heard of our sister project, Wikipedia ( http://wikipedia.org ), which is a very large online encyclopedia. The Wikibooks project is hoping to duplicate Wikipedia's success in the realm of collaboratively-edited textbooks.

I'd like to include your materials in this Wikibook http://wikibooks.org/wiki/. To get a sense of the freedom of Wikibooks, you could even edit this without registration right now.

However, we can only use your materials if you are willing to grant permission for us to use your above referenced work under terms of the Creative Commons Attribution/Share-Alike License 3.0. This means anybody will have the right to share your materials and update them: for example, to keep up with new information. You can read this license in full at:

http://en.wikibooks.org/wiki/Wikibooks:Creative_Commons_Attribution-ShareAlike_3.0_Unported_License

The license also expressly protects authors "from being considered responsible for modifications made by others" while ensuring that authors get credit for their work. There is more information on our copyright policy at:

http://wikibooks.org/wiki/Wikibooks:Copyrights

If you agree, we will credit you for your work in the resulting Wikibook's author's page. We would also state that your work is being used with your express permission and we will provide a web link back to:

Thank you for your time.

Kindly,


text:
Wikibooks:Talk page

What is a talk page?
A talk page is a special page containing discussion about the contents of its associated "subject" page. To view the talk page of a module (or any other page in Wikibooks), click on the "Discuss this page" link in the sidebar or at the bottom of the screen. When you are in the talk page, clicking on "View module" will take you back to the main module.

Inevitably, there will arise situations in which collaborators on a module can benefit mutually from discussing the module--thus we have designated a namespace specifically for such discussions.

What is it used for?
On Wikibooks, the purpose of a talk page is to help to improve the contents of the main page, from an neutral point of view. Questions, challenges, excised text (due to truly egregious confusion or bias, for example), arguments relevant to changing the text, and commentary on the main page is all fair play.

Wikibooks is not a soapbox, it's a collection of non-fiction books. In other words, talk about the module, not about the subject. It's only the habits we encourage that keeps Wikibooks from turning into another H2G2 or Everything2. See also: Wikipetiquette

That said, Wikibookians are fallible creatures, so it's entirely natural that a bit of partisan wrangling takes place on talk pages - and occasionally this even leads to improvements in the module! So there's a fair degree of tolerance, and most Wikibookians succumb to a bit of wrangling from time to time.

User talk pages
Your user page has a talk page as well. There is a link to it in the header next to your name (if you use a "skin" other than the default it may be somewhere else). Also, if edits are made to it by others, the text You have new messages will appear at the top of the page. These pages can be used for occasional personal communication among users; but note that these pages are public. If you want to communicate privately, use e-mail.

To write in another user's talk page, click the Discuss this page link on your sidebar when you view the user page (which you can do by clicking on a user's nickname). On the list of recent changes and on your watchlist, you can directly access a user's talk page by following the (Talk) link behind the user's name / IP address.

"Post a comment" feature
For editing a talk page, one can optionally use the "Post a comment" feature, but only for a new thread and for a reply to be put at the bottom of the last thread.

 * For a new thread, fill in the "Subject/headline" box. Then the edit summary is automatically the same as the new section header.

 * For a reply to be put at the bottom of the last thread, do not fill in the "Subject/headline" box. In this case it is not possible to supply an edit summary. Instead, edit the previous thread.

When using "Post a comment", an edit conflict is impossible. However, in the case that you are not starting a new thread but replying to an existing one, your response may be appended to a newly created post that was added while you wrote yours. It is therefore generally recommended to use section editing to respond, and "Post a comment" to start new threads. If your comment is accidentally misplaced, just edit the page and move it.

Standards and conventions of writing and layout
A few community standards do apply to talk pages, these are not to be taken strictly as "rules" but were evolved by users to make the talk pages more useful and easier to read. Often the talk pages of controversial topics can be very heavily used.

 * Sign your posts: To sign a post, type three tildes, and they will be replaced with your username after saving, like this: Karl Wick. Type four tildes ( ~ ), and they will be replaced with your username and time stamp, like this: Karl Wick 03:44 Jul 10, 2003 (UTC). On Wikibooks we recommend that you try to always sign your posts on talk pages. You can also use a pseudonym, or just "--anon".

 * Use indenting to keep the conversation straight: The first contributor is all the way to the left, the next person starts with one colon, the next person starts with two colons.  Then, when the first contributor responds, she starts at the left margin again, and the second and third persons continue to mark themselves with one and two colons respectively,  In that way, who is saying what is clear.

 * Separate discussion topics: Put each new topic under a different headline ( == Subject == ). The "Post a comment" feature accomplishes this automatically when you enter a subject line. The edit summary is automatically the same as this header. Thus every thread is a section. This allows section editing of the thread in question. You can also use horizontal lines, although some users strongly dislike them.

 * Proceed vertically: The further down the contribution to talk, the later it was made.

 * Feel free to ignore typographical conventions: Do as you please to make your points clear.  The Manual of Style is for just modules and Wikibooks.

 * Make links freely: Links to modules are as useful on talk pages as anywhere else, and links to non-existent modules can help get them onto the most wanted pages list.

 * Don't edit other people's words: Please don't ever do this (except for obvious typing errors) but editing or deleting your own words is up to you.  (but contrast this with suggestions on refactoring below - this could be considered a simplistic approach)

 * Archive rather than delete: When a talk page's content has become extremely large or the discussion of the issue in hand has simply died down and no one has a reasonable chance of adding to it. Then create a new page. (See Help:How to contribute for details.) Place the page in a talk or Wikibooks namespace. Give it an explanatory name. Often people simply add "archive" to the original name. Explain on the archive page where the text you plan to archive will come from and provide a link. Cut the relevant content from the original page and paste it into the new page. Replace the text on the original page with a link to the archive.

 * Summarize discussion (or refactor): After a discussion on a page has died down for several weeks or the discussion has become heated and long, you (if you can be smart and respectful at the same time) might replace the discussion with a summary of major points, as though you were (!) writing an encyclopedia module about the discussion. If the discussion entailed opposing arguments, present the arguments from an unbiased point of view. Where possible, distinguish the common ground from the points of contention. See Refactoring talk pages below.

 * Keep to the topic: Not layout, but worth keeping in mind.  Talk page discussions can be much more humorous and POV than the typical module, but personal attacks don't do much to make modules better.

Example
This module is great. mav 18:20 Jul 30, 2003 (UTC)

 * No it isn't! --fish

 * Yes it is! --wojahowicz

 * I was talking to mav! --fish

 * Now, now. Toby Bartels

- Need this more?

We need a module on kindness more than we need this mess. --Alfred the butler

 * Yeah, but what about rubber baby buggy bumpers? -- Comissioner gordon

Refactoring talk pages
from editing policy

A point of terminology: the notion of refactoring, in the context of a wiki, means basically cleaning up and reorganizing a page such that all the useful information on the page is preserved and made more accessible. It's relatively rare that one needs to entirely refactor a Wikibooks module--usually, edits and additions are what is necessary.

The purpose of talk pages is to assist in creating better modules. Therefore, the purpose of refactoring talk page discussions is to help create good textbook modules, at least in the long run. A short-run purpose is to channel a discussion in a useful direction, that is, to help aim it at the future time when it can be used in an textbook module.

There are a number of talk or other discussion oriented pages which could use a bit of traditional Wiki refactoring. There's useful content there, sometimes, that can be transferred to the module itself. Sometimes large chunks of old talk pages can be completely wiped out with no harm done--feel free to do so, unless you think there's some value in preserving the discussion. In refactoring a talk page, one solid recommendation is to use the traditional wiki refactoring technique of adding a summary with whatever consensus we've arrived at the top, grouping separate discussion items together, and placing them towards the bottom.

da:Hjælp:Hvordan bruger jeg diskussionssiderne

title: Wikibooks:Talk page


text:
Wikibooks talk:Talk page

Adapted from en:Wikipedia:Talk page

I say we make this an official guideline (because it doesnt need the weight of an enforced policy). -- 21:56, 28 November 2005 (UTC)

 * Wouldn't this be better as a Help page in the help namespace rather than as a policy? Jguk 12:19, 9 May 2006 (UTC)

A guideline at best. Kellen T 16:45, 12 May 2006 (UTC)

Move To Reject, and include in Help Namespace
I think we all have the gist of this one. It doesnt need to be an actual policy, however the information here is certainly valuable enough to keep around. I am motioning to Reject this proposal, and move the information here to the help namespace. --Whiteknight (talk) (projects) 16:43, 12 July 2006 (UTC)

 * Agreed. Kellen T 17:32, 12 July 2006 (UTC)

 * Agreed, just another thing why Archive rather than delete, the talk history is a safer (a restricted number can edit it) and takes less resources (as in space, navigation),work consuming (no need to be managed) place to keep the, herr, history of the page. --Panic 00:23, 10 October 2006 (UTC)

 * The search feature only allows you to search existing pages, not their histories. --Swift 05:22, 10 October 2006 (UTC)

Done. I have moved this page to rejected. I will work on moving the relevant text from this policy to the help namespace. --Whiteknight (talk) (projects) 00:26, 10 October 2006 (UTC)

Is it permissible to copy the contents of the existing books whose copyrights have expired verbatim
I am looking at few books in the http://www.archive.org/search.php?query=shabda. As per the site, the content is in public domain. However, I am not sure if we can re-type the content to create an wiki book.

The reason why I want to recreate the book instead of using the scanned versions specified are a. they are scanned versions and are not being searchable b. since the books specified are quite old, sometimes the content is not very clear.

Please let me know, if wikbooks discourages recreation of books whose copyrights have expired. —Preceding unsigned comment added by Ksrikanth gen (discuss • contribs)

 * For books that have actually been published and which are now in the public domain, Wikisource is your best bet. There, source documents are preserved with few changes other than proofreading.  Wikibooks is good if you plan to create a new textbook from scratch. – Adrignola talk 21:44, 5 August 2010 (UTC)

Proposal: move page to Category:Useful Wikibooks pages
Hi all.

I don't know how many people are still watching this page. But nonetheless I have a proposal on its use:

 * Remove the page from Category:Wikibooks rejected policies and guidelines and remove header describing it as a "rejected Wikibooks policy or guideline".
 * Add it to Category:Useful Wikibooks pages and adjust its content to reflects this.

The reason for doing this is, as far as I know, there doesn't exist a page on wb describing how to use talk pages and best practices for using them. So the help system needs a page to help newbies on how they could be used. "Category:Useful Wikibooks pages" contains mainly help pages on various topics, and this could be useful to people who want to learn about wb usage. Any views on this? -- Jules (Mrjulesd) 10:42, 8 October 2019 (UTC)

title: Wikibooks talk:Talk page


text:
Artificial Intelligence

Welcome to the Wikibook about Artificial Intelligence.

Book Contents
The following is a first proposal for a basic layout. This is not yet complete, ideas are welcome. Discuss on the talk page or just add them here.

The book is laid out into 5 sections, with increasing detail and complexity. Each section contains a number of chapters. In addition to regular chapters, there are case-study chapters that investigate full and complex AI systems using several techniques from the regular chapters (as well as perhaps some new ones).

Introduction
Overview
 * Preface
 * /How you can help/
 * What is Artificial Intelligence?
 * History of Artificial Intelligence
 * A chronological look at milestones in Artificial Intelligence

 * /AI Agents and their Environments/
 * Artificial intelligence paradigms and schools of thought

General concepts

 * Knowledge Representation
 * Semantic Networks

 * Logic
 * Representational perspectives
 * Zero-order logic: Propositional calculus
 * Attributional logic
 * First-order predicate logic
 * Second-order logic

 * Search
 * Exhaustive search
 * Depth-first search
 * Breadth-first search
 * Finite state automata
 * Heuristic search
 * Best-first search
 * A* Search
 * Bidirectional Search
 * Tabu Search
 * Beam Search
 * Adversarial search
 * Minimax Search
 * Alpha-Beta Pruning
 * Expectimax Search
 * Iterative Improvement
 * Hill Climbing

 * Probability: Describing the basics (philosophical and mathematical) of probability theory inference.

Basic AI topics

 * Planning, Decision making and Problem Solving: Expanding on the search chapter to show how simple agents and simple intelligent behavior can be created. Examples are solving a puzzle, navigating a small maze (with pits and monsters) or planning a trip to the supermarket.
 * Uncertainty: Introduction to reasoning, planning and decision making with uncertainty.
 * Case Study - Building a (relatively) strong game AI: Building a strong AI for some game (to be chosen) that combines techniques from the planning and uncertainty chapters. This should go deeper than the simplified algorithms that most books describe and actually produce a strong playing AI.

 * Inference in Logic: Backward and Forward chaining, Resolution and Logic Programming.
 * Knowledge Engineering: Ways to describe and store complicated knowledge. Databases, OO concepts, knowledge bases, representing space and time, inference from large datasets, diagnosis system etc.

 * Natural Language: Stuff like Markov models, POS taggers and CFG's.
 * Machine Learning (ML): The basic idea of Machine Learning is to study pattern recognition, make predictions, improve predictions based on examples or data. Example of Machine Learning concepts such as supervised learning, unsupervised learning, semi-supervised learning, reinforcement learning and deep learning.
 * Case Study - Deep Learning: Describes the use of deep architecture (i.e. Deep Belief Networks, Convolutional Neural Networks) in handwritten character recognition.
 * Case Study - Artificial Life: Describes an environment with several evolving agents and some different techniques to construct agents. This should be able to draw on and compare pretty much all the chapters from section 2 (including the natural language chapter).
 * Philosophical Issues for Artificial Intelligence: Discusses AI problems typically dealt with by philosophers, such as what is theoretically possible to achieve with AI, whether programs can be conscious, or feel pain, intentionality, and symbol grounding.

More advanced topics and techniques in AI

 * /Bayesian Decision Theory/
 * Neural Networks and related models
 * Natural Neural Networks and modeling of the Brain
 * Distributed Processing and other advanced Networks

 * Advanced Expert Systems: Expands on the basic expert systems explained in Knowledge Engineering in section 2. Includes more in depth explanation of Bayesian Networks than in the Machine Learning section.

 * Case Study - Data Mining: Describes mining a large dataset (perhaps some part of the wikipedia database) using machine learning algorithms, using software like Weka.
 * Case Study - Data Analysis: Describes manipulation of data using statistical computing tool such as R programming in K-means clustering, decision tree, random forest, adaptive boosting and support vector machine (supported by R Foundation, an open source software foundation).

 * Advanced Natural Language: A description of the various techniques for dealing with tenses, sentence focus, presuppositions, etc. in NLP and NLG. This focuses mostly on the underlying structure of language and how to translate into some logical language, rather than statistical methods and models.
 * Natural Language Learning: Deals with more advanced statistical models for learning to understand language.

 * Case Study - Dialogue System: Building system that can communicate (intelligently) in written natural language. In a nutshell, trying to pass the Turing test. Three basic paradigms; case based reasoning (like ALICE), Logic based (translating everything to and from some extended version of predicate logic) and some machine learning based solution.

Highly specific AI topics and techniques

 * Machine Vision: Interpreting visual data. Face recognition, 3d reconstruction etc.
 * Bayesian Decision Theory
 * Linear Discriminants and Perceptron
 * Support Vector Machines
 * Parameteric Techniques
 * Non-parametric Techniques
 * Speech Recognition, Text to Speech and OCR
 * Advanced Logics: Advanced logic systems.
 * Reinforcement Learning
 * Robotics: Detailed and technical introduction to the three basic paradigms of robotics. Deals with software and hardware. (Define: situated robotics.)

AI Circuits and algorithms

 * Theory of boolean intelligence
 * /1 - Bit Learner/
 * N-bit learning circuit
 * Circuit encoded in Java
 * My research results...

The Future of Artificial Intelligence

 * The Singularity: Will AIs ever have a greater intelligence than human beings?
 * Spiritual Machines vs. Rational Agents: Will AIs fix spirituality?

Appendices

 * Index, topics in alphabetical order
 * Resources, bibliography and further reading

title: Artificial Intelligence


text:
User:Hashar

Hello !

I am coming from the french wikipedia. Unfortunatly, my english isn't good enough to write anything correct. I will try to help anyway specially on french and internet related textbooks.

Links

French Linked Changes

Kill

title: User:Hashar


text:
Help:Contents

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title: Help:Contents