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Philosophical aspects of logic and set theory; truth status of mathematical axioms; Philosophy of Mathematics; philosophical aspects of mathematics in general; relation of mathematics to philosophy; etc. Consider also posting at http://philosophy.stackexchange.com/, where philosophy-of-mathematics is one of the most popular tags.

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Can you prove equivalence without being able to calculate it?

Isn't this done all the time in basic set theory with the Schroeder-Bernstein Theorem, where we deduce equivalence (in this context, the existence of a bijection) without presenting one?