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)

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)