CARDINALITY of a set S, denoted by |S|, is the NUMBER of elements of the set. The number is ALSO referred as the cardinal number. If a set has an infinite number of elements, its cardinality is ∞.

Example − |{1,4,3,5}|=4,|{1,2,3,4,5,…}|=∞|

If there are two sets X and Y,

• |X|=|Y| denotes two sets X and Y having same cardinality. It occurs when the number of elements in X is EXACTLY equal to the number of elements in Y. In this case, there exists a bijective function ‘f’ from X to Y.
• |X|≤|Y| denotes that set X’s cardinality is less than or equal to set Y’s cardinality. It occurs when number of elements in X is less than or equal to that of Y. Here, there exists an injective function ‘f’ from X to Y.
• |X|<|Y| denotes that set X’s cardinality is less than set Y’s cardinality. It occurs when number of elements in X is less than that of Y. Here, the function ‘f’ from X to Y is injective function but not bijective.
• If |X|≤|Y| and |X|≤|Y|then |X|=|Y|. The sets X and Y are commonly referred as equivalent sets.

Cardinality of a set S, denoted by |S|, is the number of elements of the set. The number is also referred as the cardinal number. If a set has an infinite number of elements, its cardinality is ∞.

Example − |{1,4,3,5}|=4,|{1,2,3,4,5,…}|=∞|

If there are two sets X and Y,