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all integers, {..., −1, 0, 1, 2, ...} is a countably infinite set. The set of all even integers is also a countably infinite set, even if it is a proper subset of the integers.

The set of all rational numbers is a countably infinite set as there is a bijection to the set of integers.

Uncountably infinite sets

The set of all real numbers is an uncountably infinite set. The set of all irrational numbers

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