Cardinal number

Cardinal numbers (or cardinals) are numbers that say how many of something there are, for example: one, two, three, four, five, six. They are sometimes called counting numbers.

The cardinality of a set is the cardinal number that tells how many things are in the set.

In mathematics, people also study infinite cardinal numbers. The first infinite cardinal number was named <math>\aleph_0</math> (pronounced Aleph null, Aleph-zero or Aleph-naught) by Georg Cantor. <math>\aleph_0</math> is the number of numbers that are in the group 0, 1, 2, 3, ... keep going forever. Cantor proved that there are many different infinite cardinal numbers that are bigger than <math>\aleph_0</math>. A famous theorem of Cantor is that the cardinality of the real numbers is larger than the cardinality of the natural numbers.

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