Talk:Integer as Sum of Polygonal Numbers

The structure of the proof can be improved, because it is difficult to follow.

Note that I have changed $(*)$ and $(**)$ to $(\text a)$ and $(\text b)$ to make referring to them mentally clearer. For people whose thinking processes are verbal, it is easier to hang onto $(\text a)$ and $(\text b)$ as a thought than onto $(*)$ and $(**)$ because you can't "say" $(*)$ and $(**)$ like you can $(\text a)$ and $(\text b)$. (Can't really use numbers because those have already been used and overloaded.)

There are several blocks to this proof, and it is not clear what follows from what, because assumptions made "up here" are proved "down there". Clarity as to which bits are which, blocking them off with $\Box$ signs has improved it a little, but it would make more sense to extract them into transcluded lemmata in the usual way. So moving $(\text a)$ and $(\text b)$ into separate pages and calling them lemmas and transcluding them in should be a big improvement.

Be aware to be careful not to let the grammar be incorrect and confusing. It is a common mistake to begin a line with a capital letter when it should not be. See this:


 * Help:Editing/House Style

I have corrected them as I find them. But the teacher in me feels pain whenever I see it. --prime mover (talk) 15:41, 7 May 2020 (EDT)


 * I wish to retain the logical flow of the proof when writing this. Since each justification is a messy manipulation of square roots (conveniently omitted in the original proof), it will obfuscate the flow. However extracting them into lemmas feels weird, since we have to use every information and definition of the variables (to show the elements in the interval satisfy the necessary condition of Cauchy's Lemma).


 * As a note some of my professors love to use $(*)$ stars, $(\dagger)$ daggers and ($\clubsuit$) suits to number things. Rolls off the tongue. RandomUndergrad (talk) 04:48, 8 May 2020 (EDT)


 * I don't know about those professors, but the style has grown up around the use of numbers (or letters if there is already a sequence of numbers going). Note that $*$ is an asterisk, a star is $\star$ -- for those of us to whom it is customary to call them asterisks, $(**)$ is too big a mouthful to be convenient. "asterisk asterisk" as opposed to $(b)$? Seriously? --prime mover (talk) 05:38, 8 May 2020 (EDT)

Apologies, I've given you a hard time over this. You're the one who has done all the hard work, all I can do is poke holes in it. :-)

Please bear with me -- I have a vision of how proofs like this "ought" to look on, having been on this site for a while now. If you like I will finish it off and do that final bit of tidying up. --prime mover (talk) 05:47, 9 May 2020 (EDT)