- #1
Mr Davis 97
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Say we have a proposition like "##\sqrt{2}## is an irrational number." So I know that this statement in particular cannot really be proved directly; you must use contradiction. However, I am not concerned with exactly with what the statement says, but rather its structure. Evidently, it is not in the if-then form. Or in other words, the proposition is not phrased as an implication. We know that to prove implications directly, we show that q being true results from p being true. However, for the proposition like "##\sqrt{2}## is an irrational number," it seems that there is only a conclusion q, and thus there is no implication. Thus, what would be the logical form of proving this directly, if there is no implication? Can you only prove statements of this syntactic form it indirectly?