infinite (original) (raw)

A set S is infinite if it is not finite (http://planetmath.org/Finite); that is, there is no n∈ℕ for which there is a bijection between n and S.

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  {0,1}
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  {1,2,3,4,5}
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  {1,1.5,e,π}

Some examples of infinite sets:

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  {1,2,3,4,…}.
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  The primes: {2,3,5,7,11,…}.
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  An interval of the reals: (0,1).

The first three examples are countable, but the last is uncountable.