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Equivalent sets are sets that have the same cardinality. For finite sets it means that they have the same number of distinct elements.

For infinite sets, though, things get a bit complicated. Then it is possible for a set to be equivalent to a proper subset of itself: for example, the set of all integers is equivalent to the set of all even integers. What is required is a one-to-one mapping, f(x) = 2x, from the first set to the second.

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10y ago

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