# 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 **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "http://tcs.nju.edu.cn:7231/localhost/v1/":): {\displaystyle \aleph_0}**
(pronounced Aleph-zero or Aleph-naught) by Georg Cantor. **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "http://tcs.nju.edu.cn:7231/localhost/v1/":): {\displaystyle \aleph_0}**
is the amount 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 **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "http://tcs.nju.edu.cn:7231/localhost/v1/":): {\displaystyle \aleph_0}**
. A famous theorem of Cantor is that the cardinality of the real numbers is larger than the cardinality of the natural numbers.