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>Nonconstructive proofs of existence in rare Not so sure about that. I'd also dispute that they are inherently more difficult (assume X doesn't exist... )
by pervycreeper 11y ago
>Nonconstructive proofs of existence in rare
Not so sure about that. I'd also dispute that they are inherently more difficult (assume X doesn't exist... )
- mturmon 11y agoI have to agree with you. There are plenty of times in math classes where I've been assured that "Theorem 1 guarantees that there exists a unique solution...", but where this solution is in no sense easily known. As an example, a maximizer of some convex function over a convex set. Sure, it exists, but constructing it is another matter! As another example, solutions to differential equations of a given form. The form guarantees a solution exists, but the solution may difficult to pin down. One more example: Borel sets. Hmm, now that I'm going: the square root of 2. It is a number that satisfies a simple property, but constructing it is considerably more difficult.