Cardinality

The set of all Platonic solids has 5 elements. Thus the cardinality of is 5 or, written symbolically, .

In mathematics, cardinality describes a relationship between sets which compares their relative size.[1] For example, the sets and are the same size as they each contain 3 elements. Beginning in the late 19th century, this concept was generalized to infinite sets, which allows one to distinguish between different types of infinity, and to perform arithmetic on them. There are two notions often used when referring to cardinality: one which compares sets directly using bijections and injections, and another which uses cardinal numbers.[2] The cardinality of a set may also be called its size, when no confusion with other notions of size is possible.[a]

When two sets, and , have the same cardinality, it is usually written as ; however, if referring to the cardinal number of an individual set , it is simply denoted , with a vertical bar on each side;[3] this is the same notation as absolute value, and the meaning depends on context. The cardinal number of a set may alternatively be denoted by , , , or .

  1. ^ Stoll, Robert R. Set Theory and Logic. San Francisco, CA: Dover Publications. ISBN 978-0-486-63829-4.
  2. ^ Weisstein, Eric W. "Cardinal Number". MathWorld.
  3. ^ "Cardinality | Brilliant Math & Science Wiki". brilliant.org. Retrieved 2020-08-23.


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