Talk:Elementary proof

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Who uses this concept?

I don't think that it is correct that anyone calls a proof "elementary" just because it does not use the square root of (-1). Nor is it true that an elementary proof is necessarily preferred.

It is not an assumption that (-1) can have a square root. It can be proved. Nor is the square root unique. (-1) has 2 square roots, if it has any.

I suggest killing this article. It just isn't useful. RSchlafly 00:11, 5 February 2007 (EST)

If the test were what is "useful", then most math articles should be deleted!

I'd love to see a proof that the following exists and is unique (plus and minus roots):

--Aschlafly 20:12, 6 February 2007 (EST)

Existence depends on what system you are operating in. Uniqueness is fairly easy if you are operating in a field. Proposition: in any field F, with c and element of F, the equation x² = c has at most 2 solutions. Proof: Consider x² = c. this implies that x² − c = 0. We may assume that c has at least one square root (call it c^{1 / 2}). So we have (x + c^{1 / 2})(x − c^{1 / 2}). Now, since fields have no zero divisors (easy excercise), we must have x + c^{1 / 2} = 0 or x − c^{1 / 2} = 0 which gives us only two choices. Q.E.D. JoshuaZ 20:44, 6 February 2007 (EST)