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The Set Theory symbol for a Set having the same Cardinal Number as the ``small'' Infinite Set of Integers. The Algebraic Numbers also belong to $\aleph_0$. Rather surprising properties satisfied by $\aleph_0$ include

\end{displaymath} (1)

\end{displaymath} (2)

\end{displaymath} (3)

where $f$ is any Finite Set. However,
\end{displaymath} (4)

where $C$ is the Continuum.

See also Aleph-1, Cardinal Number, Continuum, Continuum Hypothesis, Countably Infinite Set, Finite, Infinite, Transfinite Number, Uncountably Infinite Set

© 1996-9 Eric W. Weisstein