Robert P. Munafo, 2002 May 7.

Definition : math. In set theories with cardinal counting systems, the second transfinite domain, after Aleph 0. In Cantor's set theory it is the order of the set of countable ordinals. A "countable ordinal" is an ordinal number (like omega plus one, or omega2 + 3omega + 7) that tells the number of elements in a set as well as the order they're being counted. omega is Aleph 0, and in Cantor ordinal counting, the concept of "infinity plus one" is meaningful.

If the continuum hypothesis is true, Aleph-1 is also the number of real numbers and the number of points on the boundary of the Mandelbrot Set. It would also be the order of the power set of any set of order Aleph-0.

See also Aleph-2, continuum.

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2018.     Mu-ency index

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