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Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.

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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?