text:
User talk:Pavao~enwikiversity

 Hello Pavao, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Pavao. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Pavao~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:47, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:17, 19 April 2015 (UTC)

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

title: User talk:Pavao~enwikiversity


text:
User talk:KarolP.

 Hello KarolP., and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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title: User talk:KarolP.


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User talk:Sharat~enwikiversity

 Hello Sharat, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Cybiko123 13:09, 9 May 2010 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Sharat. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Sharat~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:59, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:22, 19 April 2015 (UTC)

title: User talk:Sharat~enwikiversity


text:
User talk:Nd~enwikiversity

 Hello Nd, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Cybiko123 13:09, 9 May 2010 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Nd. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Nd~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:45, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:17, 19 April 2015 (UTC)

title: User talk:Nd~enwikiversity


text:
User talk:Okkar~enwikiversity

 Hello Okkar, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Cybiko123 13:10, 9 May 2010 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Okkar. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Okkar~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:40, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:17, 19 April 2015 (UTC)

title: User talk:Okkar~enwikiversity


text:
User talk:Jldriggers

 Hello Jldriggers, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Cybiko123 13:10, 9 May 2010 (UTC)

title: User talk:Jldriggers


text:
User talk:Peterladage

 Hello Peterladage, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Cybiko123 15:37, 9 May 2010 (UTC)

title: User talk:Peterladage


text:
User talk:Nolii

 Hello Nolii, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

 * Take a guided tour and learn to edit.
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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Cybiko123 15:37, 9 May 2010 (UTC)

title: User talk:Nolii


text:
User talk:Qiu Min

 Hello Qiu Min, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

 * Take a guided tour and learn to edit.
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 * Give feedback about your initial observations
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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Cybiko123 15:38, 9 May 2010 (UTC)

title: User talk:Qiu Min


text:
User:Pundit

{| align="right" I am currently one of the users, administrators, bureaucrats and mediators on Polish Wikipedia, sporadically present as a regular user also on Wikimedia and commons. I currently also am a steward of Wikimedia (please, contact me there if needed).

I have been around this mortal coil for about  seconds.

I am a tenured associate professor of management at Kozminski University in Warsaw, Poland.

My interests include action research, open collaboration communities, organization studies, knowledge intensive work, professional culture, ethnography. I am a social constructivist doing qualitative research.

Years 2004-2005 I spent as a Fulbright scholar at Cornell University. In 2007 I spent a semester as a visiting scholar at Harvard University. In 2008 I spent a semester as a visiting scholar at University of California Berkeley. 2011-2012 I spent as a visiting scholar at Harvard University.

Over the years I have been a recipient of some scholar awards and scholarships from different institutions, including also Kosciuszko Foundation, Polish National Science Foundation, Collegium Invisibile, Polish Ministry of Science, and others.

I am an author of several books on management and on ESL published in Polish, with a rough total circulation of about 20000 copies so far. Three of my other Polish books are forthcoming. My publications in English include articles in academic journals, a book, as well as three edited ones.

For five years I practiced aikido, which I had to drop because of knee problems. Since 1995 very irregularly I've been practicing karate, alternating Gosoku-ryu, shotokan, Wado-ryu and, most recently, Enshin. My other hobbies include RPG, battodo, sailing, windsurfing, bridge (game), scrabble.

I also run a couple of popular Polish portals, such as ling.pl (the most popular Polish online dictionary), angielski.edu.pl (the biggest Polish portal on ESL), and others, with an average popularity of about 20 million monthly pageviews.

 * My personal homepage is available here.

title: User:Pundit


text:
Limit (mathematics)

The concept of the limit is the cornerstone of calculus, analysis, and topology. For starters, the limit of a function at a point is, intuitively, the value that the function "approaches" as its argument "approaches" that point. That idea needs to be refined carefully to get a satisfactory definition.

Limit of a Function
Here is an example. Suppose a function is
 * $$f(x) = \frac{x^2-x-6}{x^2-2x-3}\,$$

What is the limit of f(x) as x approaches 3? This could be written
 * $$\lim_{x\to 3}f(x)\,$$

We can't just evaluate f(3), because the numerator and denominator are both zero. But there's a trick here—we can divide (x-3) into both numerator and denominator, getting
 * $$f(x) = \frac{x+2}{x+1}\,$$

so the limit is 5/4. (That does't actually prove that the limit is 5/4. Once we have defined the limit correctly, we will need a few theorems about limits and continuous functions to establish this result.  It is nevertheless true.)

Now try an example that isn't trivial. Let
 * $$f(x) = x^x\,$$

This function is well-defined for x>0, using the general definition that involves the exponential and natural logarithm functions. We can calculate f(x) for various values: f(5) = 3125 f(2) = 4 f(0.5) = 0.7071 f(0.3) = 0.6968 f(0.2) = 0.7248 It got smaller, but now it's getting bigger. What's happening? f(0.1) = 0.7943 f(0.01) = 0.95499 f(0.0001) = 0.999079 f(0.000001) = 0.99998618 It looks as though it's approaching 1. Is it? And what does that mean? f(1 trillionth) = 0.999999999972369

Remember that f(0) doesn't exist. So we really have to be careful.

We are going to say that the limit of f(x), as x approaches 0, is 1. What that means is this:

We can get f(x) arbitrarily close to 1 if we choose an x sufficiently close to zero. If we want f(x) within one quadrillionth of 1, $$x = 10^{-17}\,$$ will do. We never have to set x to zero exactly, and we never have to get f(x) = 1 exactly.

In the general case, for arbitrary functions, we might want to say something like
 * $$\lim_{x\to X}f(x) = Y\,$$

For Every Epsilon ...
Stated precisely, given any tolerance ε (by tradition, the letter ε is always used), x being sufficiently close to X will get f(x) within ε of Y. That condition is formally written:
 * $$|f(x) - Y| < \varepsilon\,$$

In this example ($$f(x) = x^x\,$$, X=0, Y=1), when ε is $$10^{-15}\,$$ (one quadrillionth), $$x < 10^{-17}\,$$ satisfies the condition.

... There Exists a Delta
The way we formalize the notion of x being very close to X is:

 * "There is a number δ (by tradition it's always δ) such that, whenever x is within δ of X, f(x) is within ε of Y".

That is written:
 * Whenever $$0 < |x - X| < \delta, |f(x) - Y| < \varepsilon\,$$

In our example, if ε is $$10^{-15}\,$$, δ = $$10^{-17}\,$$ works. That is, any $$x < 10^{-17}\,$$ will guarantee $$|f(x)-1| < 10^{-15}\,$$.

The Full Definition
So here is the full definition:

 * $$\lim_{x\to X} f(x) = Y\,$$ means

 * For every ε > 0, there is a δ > 0 such that, whenever $$0 < |x-X| < \delta, |f(x)-Y| < \varepsilon\,$$

So the definition is sort of like a bet or a contract—"For any epsilon you can give me, I can come up with a delta."

A few things to note:
 * We require ε > 0. Specifying a required tolerance of zero is not allowed.  We only have to be able to get f(x) within an arbitrarily close but nonzero tolerance of Y.  We don't ever have to get it exactly equal to Y.
 * We have 0 < |x-X| < δ, not just |x-X| < δ. That is, we never have to calculate f(X) exactly.  f(X) doesn't need to be defined.  In the example we are considering, $$0^0\,$$ isn't defined.

This definition, and variations of it, are the central point of calculus, analysis, and topology. The phrase "For every ε there is a δ" is ingrained into the consciousness of every mathematics student. This notion of a "bet" could be considered to set the branches of mathematics that follow (calculus, topology, ...) apart from the earlier branches (arithmetic, algebra, geometry, ...) Students who have mastered the notion of "For every ε there is a δ" are ready for higher mathematics.

In our example of $$f(x) = x^x\,$$, we haven't actually satisfied the definition of the limit, because f(x) isn't defined for negative x. There are more restrictive notions of "limit from the left" and "limit from the right". We have the limit from the right of $$x^x = 1\,$$, which means
 * For every ε > 0, there is a δ > 0 such that, whenever 0 < x-X < δ, |f(x)-Y| < ε

We still haven't proved that the limit is actually 1. We just gave some accurate calculations strongly suggesting that it is. In fact it is, and the proof requires a few theorems about limits, continuous functions, and the exponential and natural logarithm functions.

The Limit of f(x) is Infinity
With this precise (or, as mathematicians say, rigorous) definition of a limit, we can examine variations that involve "infinity". Remember, Infinity is not a number. It is only through the magic of the epsilon-delta formulation that we can make sense of it.

We might say something like "The limit of f(x), as x approaches X, is infinity." What that means is that we replace the
 * $$|f(x) - Y| < \varepsilon\,$$

with
 * $$f(x) > M\,$$

That is,
 * For every M > 0, there is a δ > 0 such that, whenever $$0 < |x-X| < \delta, f(x) > M\,$$

Consider the function
 * $$f(x) = \frac{1}{(x-3)^2}\,$$

If you graph this, there is an "infinitely high" peak at x=3. We have:
 * $$\lim_{x\to 3}f(x) = \infty\,$$

If we set $$M = 10^{20}\,$$, $$\delta = 10^{-10}\,$$ will win the bet.

For a limit of minus infinity, we set M to some huge negative number, so
 * $$\lim_{x\to X}f(x) = - \infty\,$$

means
 * For every M < 0, there is a δ > 0 such that, whenever $$0 < |x-X| < \delta, f(x) < M\,$$

The limit of f(x) as x Goes to Infinity
Infinity can also make an appearance in the function's domain, as in "The limit of f(x), as x approaches infinity, is 3." What that means is that we replace the
 * $$0 < |x - X| < \delta\,$$

with
 * $$x > M\,$$

That is,
 * For every ε > 0, there is an M such that, whenever $$x > M, |f(x)-Y| < \varepsilon\,$$

Consider the function
 * $$f(x) = \frac{3x+5}{x}\,$$

If you graph this, it goes off to a value of 3 toward the right. We have:
 * $$\lim_{x\to \infty}f(x) = 3\,$$

If we set $$\varepsilon = 10^{-10}\,$$, $$M = 10^{11}\,$$ will win the bet.

We can do a similar thing for the limit as x goes to minus infinity.

The limit of f(x) as x Goes to Infinity is Infinity
A function like $$f(x) = e^x\,$$ combines both inifinites. We write
 * $$\lim_{x\to \infty}e^x = \infty\,$$

Here we replace both δ and ε:
 * For every N > 0, there is an M such that, whenever $$x > M, f(x) > N\,$$

Limit of a Sequence
An important type of limit is the limit of a sequence of numbers $$(a_n)_{n\in N} = (a_1, a_2, a_3, ...)$$. When we say that this sequence has a limit A, we are essentially using the definition above for x going to infinity, but using n instead of x:
 * $$\lim_{n\to \infty}a_n = A,\,$$

means that
 * For every ε > 0, there is an M such that, whenever $$n > M, |a_n-A| < \varepsilon\,$$

When a sequence has a limit like that, we say that the sequence converges to that limit.

Infinite Sums
It is important to distinguish between the limit of the sequence, as defined above, and the much more commonly used limit of the partial sums of the sequence. If we have a sequence $$(a_n) = (a_1, a_2, a_3, ...)$$, we also have a sequence of "partial sums", the nth item of which is the sum of the first n items in the original sequence:
 * $$s_n = \sum_{i=1}^n a_n\,$$

If $$s_n\,$$ converges to A, we say that the infinite sum $$a_n\,$$ converges to A, written like this:
 * $$\sum_{i=1}^\infty a_n = A\,$$

For example, the sequence
 * $$a_n = \frac{1}{n!}\,$$

(where the exclamation point is the factorial operation) converges to the number known as "e":
 * $$\sum_{i=0}^\infty \frac{1}{n!} = e\,$$

This is the only sense in which a summation going to infinity is meaningful.

title: Limit (mathematics)


text:
Group (mathematics)

A group is a mathematical abstraction consisting of a set of "elements" and an "operation". The operation takes two elements and yield an element. It is perhaps best visualized as addition. The operation must satisfy these properties:
 * (closure) The operation is always defined, yielding an element in the set.
 * (associativity) Denoting the operation as addition, it satisfies $$x + (y + z) = (x + y) + z$$ for all x, y, and z.
 * (identity) There is an "identity element", which we could call "0", such that $$x + 0 = 0 + x = x$$ for all x.
 * (inverse) Every element has an "inverse element" which, when combined with the element itself, yields the identity.  Denoting the inverse of x as -x, we have $$x + (-x) = (-x) + x = 0$$ for all x.

The operation is not required to be commutative ($$x + y = y + x$$) though, for many groups, it is. Groups for which the operation is commutative are called abelian (uh-BEEL-i-an), in honor of Niels Henrik Abel. But note that "abelian" is not capitalized.

Examples
Groups abound throughout mathematics, physics, and related fields. Some are finite and some infinite. Here are some examples:

 * The integers, with addition, This is often denoted $$(\mathbb{Z},+)\,$$.  The identity is zero, and the inverse of x is -x.

 * Similarly for the rationals, denoted $$(\mathbb{Q},+)$$, the reals, denoted $$(\mathbb{R},+)$$, and the complex numbers, denoted $$(\mathbb{C},+)$$.

 * The nonzero rationals, reals, and complex numbers, with multiplication: $$(\mathbb{Q},\cdot)$$, $$(\mathbb{R},\cdot)$$, and $$(\mathbb{C},\cdot)$$. The identities for these are 1, or the complex number 1+0i.  The inverse of an element is its reciprocal, 1/x.

 * For any natural number n, the integers modulo n, denoted $$(\mathbb{Z}_n,+)$$. The elements are the integers {0, 1, ... n-1}, the operation is addition modulo n, and the inverse of x is (-x) mod n.  These groups are finite.

 * Vector spaces of any dimension, with vector addition.

 * For any n, the nonsingular n×n matrices of rational, real, or complex numbers. The operation is matrix multiplication—note that matrix multiplication is not commutative, though it is associative.  The identity element is just the identity matrix, and the inverse is the usual matrix inverse.  These groups are the "general linear groups", denoted GL(n).  They are not abelian if n is greater than 1.  The "special linear groups", denoted SL(n), are the groups of matrices with determinant 1.

 * For any n, the orthogonal real n×n matrices, or the unitary complex n×n matrices. These groups are important in a number of practical and theoretical areas, and are denoted O(n) and U(n), respectively.  The determinant of such a matrix has an absolute value of 1.  (For unitary matrices, the determinant is a complex number with modulus 1.)  When the determinant is required to be 1, they also form a group, the "special orthogonal" or "special unitary" groups SO(n) and SU(n).

Transformation groups
Another very common type of group is a group of "transformations" of some kind, such as the group of rotations, translations, and reflections of some geometrical figure. (This group is called the "Euclidean group".) The group operation for a transformation group is "composition", that is, doing one operation followed by another. The composition operation is usually written with a small circle, as in "$$f \circ g\,$$". By convention, this means "do transformation g, then do transformation f", that is, the transformations are done from right to left. The identity of the group is the transformation that does nothing, and the inverse is the transformation that "undoes" a given transformation.

Another famous transformation group is the group of moves on a Rubik's cube.

Permutation groups
A very simple and instructive transformation is the permutation (reordering) on N objects. That is, a transformation rearranges the order of some set of N objects. These transformations form the permutation groups, denoted S(n).

For S(2), we have two objects, call them A and B. The possible permutations are:
 * Do nothing. This is the identity element of the group, and is of course its own inverse.
 * Swap A <=> B. This is the only other group element.  It is its own inverse.

For S(3), call the objects A, B, and C. The possible permutations are:
 * Do nothing. This is the identity element of the group, and is of course its own inverse.
 * Swap A <=> B. This is its own inverse.
 * Swap B <=> C. This is its own inverse.
 * Swap A <=> C. This is its own inverse.
 * Cyclically rearrange: A => B, B => C, and C => A. The inverse of this is the permutation below.
 * Cyclically rearrange: C => B, B => A, and A => C. The inverse of this is the permutation above.

As an example of the group operation, if we do A => B, B => C, and C => A, and then swap A <=> B, the result will be that of swapping B and C. If we do the transformations in the other order, the result will be that of swapping A and C.  So this group (and all groups S(n) for n greater than 2), is non-abelian.

The groups S(n) have n! (n factorial) elements.

Symmetry groups
Groups provide a way of giving a precise meaning to symmetry. A symmetry is defined as the group of transformations that leave the geometric figure unchanged. For example, the (near) symmetry of the human face could be characterized by the group consisting of two elements: {no transformation, left-right reflection}. The symmetries of the square are characterized by the group consisting of rotations by a multiple of 90 degrees, and reflections along horizontal, vertical, or diagonal axes. When the details are worked out, this group is seen to have 8 elements.

The group of symmetries of the sphere (that is, all rotations in 3 dimensions) is the group of orthogonal 3x3 matrices with determinant 1. That is, it is SO(3). An interesting theorem relating to eigenvalues says that any such rotation has fixed points, that is, any rotation of the sphere is a rotation around some axis. This theorem is an example of the usefulness of group theory, eigenvectors, and complex numbers to prove interesting geometrical results.

title: Group (mathematics)


text: File:Xtothex.jpg

title: File:Xtothex.jpg


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User talk:Lap2042

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text:
Survey research and design in psychology/Tutorials/Lab report workshop

This lab report workshop - aka big statistics    p a r t y     - will be:
 * Week 12 Wed 09:00 - 17:00 (12B16)
 * Week 12 Wed 17:30 - 20:30 (Online)
 * Week 12 Fri 11:30 to 13:30 "final fling" (12B16)

Feel free to come along for as much time as you like to get hands-on help with the lab report.

There will be a waitlist on the whiteboard - just add your name and a tutor will come around to see folks in order.


text:
User:Cirt/monobook.css

body {background:#CCFFFF;}
 * 1) centralNotice {display: none;}

title: User:Cirt/monobook.css


title: File:9.A.FFT.pdf


text: File:Teaching.FBD.jpg

title: File:Teaching.FBD.jpg


text:
Talk:German Language/German I

Rather than use "der Mann", "die Frau", and "das Mädchen" for examples of semantic and then arbitary gender, it would be better, since any word ending with "chen" is neuter, to use the famous trio knife, fork and spoon (das Messer, die Gabel und der Löffel).

BigRat

Hard & soft 'g'
"g is always 'hard', like in goat, and k at the end of a word" This is not correct. In "fertig", for example, the g is pronounced like the ch of "ich".
 * Indeed not. Another is 'Tag'.Krutbulle 14:21, 27 October 2010 (UTC)

I believe the article is now correctly explaining how g is pronounced. Alfakol 22:45, 1 November 2010 (UTC)

Misleading rule?
The following does not seem to ever hold, yet it claims it always holds: "Notice that in both the Accusative in Nominative cases, the ending of the third person personal pronouns corresponds to the declension of the definite articles, this is true for the Genitive and Dative cases, and can help very much when the correct declension of an article or a personal pronoun slips your mind." Krutbulle 14:20, 27 October 2010 (UTC)

7.2.1
The text explains DO personal pronoun comes before IO personal pronoun. However the examples show it the other way around, unless I am completely confused here. Krutbulle 15:05, 27 October 2010 (UTC)

5.2
about the Ihr-Imperativ: you wouldn't say "Kommen Sie hier!", it's either: "Kommen Sie hier her!" or "Kommen Sie her!", because you would use the verb herkommen in this structure, you could also say "Kommen Sie!" without any place-reference.

6.
Isn't it better to use the german writing for Genetive, Accusative and so on? Would be "Nominativ", "Genitiv", "Dativ" and "Akkusativ". and in the example of the smart fathern in the Genetive-Section: "Der Vater des Junges ist klug", des Junges is wrong, it's "des Jungen", don't know why, but "des Junges" is neutral you would use it maybe instead of the word whelp, not for a human boy.

7.3
Nobody says "Ich lehre dich Deutsch", even though it is correct. You say "Ich bringe dir Deutsch bei." A better example may be "jemanden das Fürchten lehren", which is also an idiom. In passive voice, however, Dativ remains correct: "Jemandem wurde das Fürchten gelehrt." --80.187.104.73 (discuss) 21:11, 17 November 2017 (UTC)

title: Talk:German Language/German I


text:
Dotted whole notes

A dotted whole note equals 6 beats,but it all depends what time signature you playing a dotted whole note in. In a 6/4 time signature a dotted whole note would equal 6 beats. But in a time signature with the denominator of 8 the value of a dotted note changes.

In a time signature with the denominator of 8 every note goes up by half. For example, in 6/8 an eighth note, which equals half of a beat, equals one beat in a 6/8 time signature or any other time signature with the denominator of 8. A quarter note equals 1 beat in a 4/4 or 2/4 or any other time signature with a denominator of 4. But in a denominator of 8 time signature, a quarter note equals two beats, because it goes up by half of its value. So where would you use a dotted whole note in 6/8 time signature? You can't, because the change in the value of the dotted whole note won't be able to equal out the number of beats in a 6/8 time signature. So it's best to use a dotted whole note in 12/8 time signature, because a dotted whole note would equal 12 beats in a time signature with the denominator of 8. If you are confused about how music notation works, then I'd suggest that a good foundation needs to be laid out about music notation and reading theory. Some good links would be musicresources.com, pianonanny.com, or try googling and searching for some good music theory websites.

title: Dotted whole notes


text:
Dotted Whole Notes

A dotted whole note equals 6 beats. It all depends what time signature you playing a dotted whole note in. In a 6/4 time signature a dotted whole not would equal 6 beats. but in a time signature with the denominator of 8 the value of a dotted note changes.

In a time signature with the denominator of 8 every note goes up by half. For example, in 6/8 a eighth note, which equals half of a beat, equals one beat in a 6/8 time signature or any other time signature with the denominator of 8. A quarter note equals 1 beat in a 4/4 or 2/4 or any other time signature with a denominator of 4. But in a denominator of 8 time signature, a quarter note equals two beats, because it goes up by half of its value. So where would you use a dotted whole note in 6/8 time signature? You can't, because the change in the value of the dotted whole note won't be able to equal out the number of beats in a 6/8 time signature. So it's best to use a dotted whole note in 12/8 time signature, because a dotted whole note would equal 12 beats in a time signature with the denominator of 8. If you are confused about how music notation works, then I'd suggest that a good foundation needs to be laid out about music note and reading theory. Some good links would be musicresources.com, pianonanny.com, or try googling and searching for some good music theory websites.

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title: Dotted Whole Notes


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User talk:Jonathan ma1976

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User talk:Correll~enwikiversity

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Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

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User talk:Sarann23

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Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Vandana. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Vandana~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 00:10, 18 March 2015 (UTC)

Renamed
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User talk:Jeriwilkins

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User:Morza

Hi!. I'm spanish, contact here.

title: User:Morza


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User talk:Nemo88~enwikiversity

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Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Nemo88. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Nemo88~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:39, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:17, 19 April 2015 (UTC)

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User talk:Roentgeno

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 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Cybiko123 01:49, 11 May 2010 (UTC)

title: User talk:Jenbobbitt


text:
User talk:Corajudd

 Hello Corajudd, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Cybiko123 01:49, 11 May 2010 (UTC)

title: User talk:Corajudd


text:
User talk:Dero~enwikiversity

 Hello Dero, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Cybiko123 01:50, 11 May 2010 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Dero. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Dero~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:33, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:06, 19 April 2015 (UTC)

title: User talk:Dero~enwikiversity