Talk:Example:Antiassociative Structure

I think an invented term warrants a non-trivial (concrete as possible) instance of it rather than just abstract theorems or things become too much of a word game. That being said, I don't know how to introduce examples on this site very well so hopefully someone kind enough could fix this page. --Jshflynn 00:46, 1 August 2012 (UTC)

As I suggested, this is not an invented term - it has already been used at least once before now:

http://www.doc.ic.ac.uk/~sgc/html_papers/colton_ijcar01.html

Also, we have to consider the design of the page title. If we want to use the style "Example:Some Example" then "Example" becomes a new namespace like "Definition" and "Symbol". Might be worth doing. We need opinions from others. --prime mover 05:27, 1 August 2012 (UTC)

Incidentally, I've noticed that this example is flawed because $xy + y$ is not closed on $R_{\ne 0}$. If $x = -1$, then all $y \in \R$ are such that $xy + y = 0$.

A better example is:

$\begin{array}{c|cc}

 & 0 & 1 \\

\hline 0 & 1 & 1 \\ 1 & 0 & 0 \end{array}$

which is also the simplest.

Alternatively the same one you thought of on $\Z_{>0}$ would work. --prime mover 06:10, 1 August 2012 (UTC)

Good spot on the given example. You mention an example of a class of examples where the left regular representation of an element is a constant mapping to some different element and all the right regular representations are the same permutation on $S$. So for this example we could point to the class of examples described.

I would love Examples to be a namespace (though they are really just special proofs). ProofWiki is not an exercise book but there's no reason it can't double up as one (It already functions as a superb dictionary!). At any rate, this is something I live by when studying:

"A good stock of examples, as large as possible, is indispensable for a thorough understanding of any concept. I make it my first job to build one." -P.R.Halmos

It's been on my list of stuff to address. This could be the spur. --prime mover 11:40, 1 August 2012 (UTC)

I recall pleading for an Example namespace somewhere in the past. Details on structure and standard nomenclature have to be discussed. For example how would we name things pertaining to the circle group? Should only Circle Group is Group be in the example namespace? Should it be there at all? And so on. --Lord_Farin 11:19, 2 August 2012 (UTC)

It's very problematic. What makes it such an alluring idea though is this: As an undergraduate studying pure maths "Definition Example and Proof" would make up the bulk of my Google searches. Unless it would be too difficult to implement I would suggest a trial for a few weeks. It would be very interesting to see what you and the others would put together. --Jshflynn 12:57, 2 August 2012 (UTC)

Uh, isn't this supposed to be proving an inequality? --GFauxPas 13:02, 1 August 2012 (UTC)

yeah, sorted. --prime mover 14:13, 1 August 2012 (UTC)