Proofs of Fermat's theorem on sums of two squares. - Euler's proof by infinite descent - Third Part
Strictly speaking in the example I give 9 could be expressed as a sum of two squares if we allowed zero as 9 = 3^2 + 0 however I feel changing number to prime is better than adding more detail to account for zero in all of the statements. Rhuaidhri (talk) 18:09, 18 August 2015 (UTC)
- First: I'm not sure what you mean when you say there appears to be no talk page "for that subject". There definitely is a talk page for the page on proofs of Fermat's Christmas theorem. Yes, we do say that 9 is a sum of three, four, five, etc. squares, so far as I know. If you look at the proof, nowhere does it require that the number be a prime, or that it be written as the sum of two positive squares, so I really do not understand your objection (except that you feel that 0 ought to be excluded, though it is not normally excluded). These are quotes taken from Edwards book (I'll add the reference), where they appear in italics (indicating he is quoting them). Magidin (talk) 19:20, 18 August 2015 (UTC)
- Like I said: it is being quoted from Edwardss book; I've provided the reference now, just before the numbered items begin. Edwards uses "number", presumably taking it from Euler. Given that this is being taken from a reputable source, I would be loath to modify it based on the subjective aesthetics of an editor. Magidin (talk) 20:18, 18 August 2015 (UTC)
- And you presumably also noticed in the talk page that a very similar objection to the one you raised (with 45 and 9) was dealt with before and cleared up; the only place where 0 is explicitly excluded occurs later. If your objection were valid, then the previous step would be wrong as well, because when you divide 45 by 5 you get 9. Magidin (talk) 20:22, 18 August 2015 (UTC)
- "The use of number is ambiguous". It's called context: if you are working in complex analysis, you don't say "complex number" each and every time; if you are working in calculus, you don't say "real number" each and every time. Every word in mathematics has multiple meanings depending on context (do we need to specify every time we say "group" that we are not talking about a collection of individuals hanging out together at the movies?). That's why they are read in context. I did understand your suggestion, I just didn't agree with it, so perhaps don't assume that lack of agreement may represent ignorance, lack of comprehension, or some other failing on my part. As to "natural numbers", whether or not they include zero is actually not a settled topic (see fifth paragraph in the lede of Natural number). To me, a professional mathematician working in algebra, they do, as it happens, and so there is absolutely no problem with the statements, despite your judgement that there is (and again I note that you seem to have missed that if there is a problem with step 3, then there is a problem with step 2 as well, which your additions would not correct either). So, to summarize: I did understand you, I just didn't agree with you. Feel free to make your proposal in the talk page of the article which you can now find, instead of in my personal talk page, or to make the appropriate change in the article (where "appropriate" should perhaps be understood as "in a way that does not falsify quotes"). Magidin (talk)
