Talk:Infinite Ramsey's Theorem

Link
I see that $k,n \in \N$ is a link. However, with SVG rendering option of MathJax, this does not display as a link. I therefore suggest that we discourage this use. Also, the fact that right-clicking the TeX produces MathJax's context menu rather than the browser's pleads against it. --Lord_Farin (talk) 12:22, 7 September 2012 (UTC)


 * Fixed - link not really needed here. --prime mover (talk) 18:05, 7 September 2012 (UTC)

Newton notation
The family of all subsets of cardinality $n$ of a set $X$ should be denoted by $\binom X n$, so that


 * $\left|{\binom X n}\right| = \binom {\left|{X}\right|} n$

in the finite case. (In my experience $X^{(n)}$ would most of the time stand for the $n$-th symmetric product). Wlod (talk) 07:29, 26 December 2012 (UTC)


 * By "should" in the above, I would argue for the less dogmatic and ideologically exclusive "could". In the context of consistency on this website, however, it would make sense to employ your suggestion.


 * The $n$th symmetric product, from my experience, would usually be denoted $X^n$.


 * $X^n$ stands almost always for the Cartesian power (of course), not for the symmetric power. Wlod (talk) 15:41, 26 December 2012 (UTC)


 * The $X^{(n)}$ notation would imply the $n$th derivative of $X$, although the relevance of that concept in this context is probably questionable.


 * I would also suggest the need for a page demonstrating the proof of the above statement, but question its direct relevance to the proof being demonstrated on this particular page. --prime mover (talk) 10:44, 26 December 2012 (UTC)

Proof
The present proof is correct. First I glanced at it, then I proved the theorem in my mind (without looking at the written proof--this theorem is very nice but easy), and only then I was able to verify the given proof (possibly I have overlooked minor formal problems, I am not a patient reader even if I try). It's good that it is basically a healthy proof. On the other hand it's not written neatly on the detail level. There are unnecessary complications which make reading it hard, too hard. Wlod (talk) 07:26, 26 December 2012 (UTC)