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cardinality
In mathematics, the cardinality of a set is a measure of the "number of elements of the set". For example, the set A = contains 3 elements, and therefore A has a cardinality of 3. There are two approaches to cardinality – one which compares sets directly using bijections and injections, and another which uses cardinal numbers.
The cardinality of a set is also called its size, when no confusion with other notions of size〔Such as length and area in geometry. – A line of finite length is a set of points that has infinite cardinality.〕 is possible.
The cardinality of a set ''A'' is usually denoted | ''A'' |, with a vertical bar on each side; this is the same notation as absolute value and the meaning depends on context. Alternatively, the cardinality of a set ''A'' may be denoted by n(''A''), ''A'', card(''A''), or # ''A''.
==Comparing sets==
While the cardinality of a finite set is just the number of its elements, extending the notion to infinite sets usually starts with defining the notion of comparison of arbitrary (in particular infinite) sets.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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