What is at the difference bijection and equinumerous?

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I have to explain what a "bijection" function is, but it seems that "equinumerous" is a synonym for bijection. Is that correct?

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1 Answer

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There's no "equinumerous" function or "bijective" set. There are equinumerous sets and bijective functions. Equinumerous sets are sets for which at least a bijection (bijective function) exists.

Sets $A$ and $B$ are equinumerous if there exists a one-to-one and onto correspondence between them. This means that it must exist a function from $A$ to $B$ such that for every element of $B$ there exist just one correspondent element of $A$.

Finite and infinite sets can both be equinumerous.

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