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Countably Infinite Set

Any Set which can be put in a One-to-One correspondence with the Natural Numbers (or Integers), and so has Cardinal Number $\aleph_0$. Examples of countable sets include the Integers and Algebraic Numbers. Georg Cantor showed that the number of Real Numbers is rigorously larger than a countably infinite set, and the postulate that this number, the ``Continuum,'' is equal to Aleph-1 is called the Continuum Hypothesis.

See also Aleph-0, Aleph-1, Cantor Diagonal Slash, Cardinal Number, Continuum Hypothesis, Countable Set

© 1996-9 Eric W. Weisstein