Definition: Countable and Uncountable

If a set A has the same cardinality as N (the natural numbers), then we say that A is countable. In other words, a set is countable if there is a bijection from that set to N.

An alternate way to define countable is: if there is a way to enumerate the elements of a set, then the set has the same cardinality as N and is called countable.

A set that is not countable (and not finite) is called uncountable.

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