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Countable set

Set theory

A set whose elements can be listed in a sequence indexed by the natural numbers, possibly terminating. Equivalently, a set no larger than the set of natural numbers.

What is usually left out

Countability is less restrictive than it sounds. The rationals are countable despite being dense in the reals, and so are the algebraic numbers. The reals are not, which means almost every real number is transcendental even though exhibiting a specific one is hard.

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