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#### sweatingbear

##### Member

- May 3, 2013

- 91

But is this not the wrong way to carry out a proof of a conditional? From what I know, you conventionally have to begin with the antecedent (i.e. the "if"-part), assume it and see if it can lead you to the conclusion (and not the other way around). My spontaneous thought is that we do this because of the quantifiers "for every" and "there exists" but I am not sure.

Example: We wish to show that

\(\displaystyle \lim_{x \rightarrow 2} \, (x^2) = 4 \, .\)

We wish to show that if \(\displaystyle 0 < |x-2| < \delta\) then \(\displaystyle |x^2 - 4| < \epsilon\). Naturally, one would then start off with \(\displaystyle 0 < |x - 2| < \delta\) and go on from there, but according to every example that I have seen that is not the case.

Can somebody help me see things clearer?