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:::::::Mark, Conservapedia does not simply cut and paste quotes from others, many of whom has obvious self-serving biases. The logic underlying the concept of an "elementary proof" is clear and cannot seriously be disputed. You're not addressing the substance of the significance of an "elementary proof." Once you address that, it will become clear that proofs relying on the [[Axiom of Choice]] are not [[elementary proofs]]. It doesn't matter whether any math professors admit that or not. No math professor will publicly admit that the best mathematicians are men rather than women, but that denial does not alter the obvious truth.--[[User:Aschlafly|Andy Schlafly]] 13:23, 25 August 2009 (EDT)
:::::::Mark, Conservapedia does not simply cut and paste quotes from others, many of whom has obvious self-serving biases. The logic underlying the concept of an "elementary proof" is clear and cannot seriously be disputed. You're not addressing the substance of the significance of an "elementary proof." Once you address that, it will become clear that proofs relying on the [[Axiom of Choice]] are not [[elementary proofs]]. It doesn't matter whether any math professors admit that or not. No math professor will publicly admit that the best mathematicians are men rather than women, but that denial does not alter the obvious truth.--[[User:Aschlafly|Andy Schlafly]] 13:23, 25 August 2009 (EDT)
::::::::This article defines a common mathematical term in a way in which it is not used by anyone and seems never to have been used. I infer that your last post cedes that mathematicians don't use it, though I still welcome a citation on the historical point, which should be easy to come by if the usage is indeed "traditional" as you have claimed. I'm not disputing the logic of what you call an "elementary proof", which is clear. I agree with you about the significance of proofs such as you describe, and am not addressing "the substance of the significance of an elementary proof'" only because it's not relevant to the point at hand: what I'm disputing the use of that term, which has a well-established meaning distinct from what you intend and is therefore inappropriate. What use is an encyclopedia article that simply makes up new definitions for well-known terms, even if these new definitions have a clear and important philosophy? This serves no purpose but to confuse readers trying to understand how the term is used and hurt the credibility of CP math generally. Why not invent a new phrase to describe proofs such as those you discuss, whose philosophy I agree is valuable? --[[User:MarkGall|MarkGall]] 13:51, 25 August 2009 (EDT)