Cardinality

In mathematics, the cardinality of a set is a measure of the 'number of elements of the set'. For example, the set A = { 2 , 4 , 6 } {displaystyle A={2,4,6}} contains 3 elements, and therefore A {displaystyle 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 is possible. In mathematics, the cardinality of a set is a measure of the 'number of elements of the set'. For example, the set A = { 2 , 4 , 6 } {displaystyle A={2,4,6}} contains 3 elements, and therefore A {displaystyle 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 is possible. The cardinality of a set A {displaystyle A} is usually denoted | A | {displaystyle |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 {displaystyle A} may be denoted by n ( A ) {displaystyle n(A)} , A {displaystyle A} , card ⁡ ( A ) {displaystyle operatorname {card} (A)} , or # A {displaystyle #A} .