Element (mathematics)

Writing "''A'' = {1, 2, 3, 4}", means that the elements of the set ''A'' are the numbers 1, 2, 3 and 4. Groups of elements of ''A'', for example {1, 2}, are Subset s of ''A''.

Elements can themselves be sets. For example consider the set ''B'' = {1, 2, {3, 4} }. The elements of ''B'' are ''not'' 1, 2, 3, and 4. Rather, there are only three elements of ''B'', namely the numbers 1 and 2, and the set {3, 4}.

The elements of a set can be anything. For example, ''C'' = {red, green, blue}, is the set whose elements are the colors red, green and blue.

The Relation "is an element of", also called set membership, is denoted by "∈", and writing "''x'' ∈ ''A''", means that ''x'' is an element of ''A''. Equivalently one can say or write "''x'' is a member of ''A''", "''x'' '''belongs''' to ''A''", "''x'' is '''in''' ''A''", or ''A'' '''contains''' ''x''. The Negation of set membership, is denoted by "∉".

Examples (using the sets defined above):

2 ∈ ''A''

{3, 4} ∈ ''B''

{3, 4} is a member of ''B''

3 ∉ ''B''

The number of elements in a particular set is a property known as Cardinality , informally this is the size of a set. In the above examples the cardinality of the set ''A'' is 4, while the cardinality of the sets ''B'' and ''C'' is 3. An infinite set is a set with an infinite number of elements, while a finite set is a set with a finite number of elements. The above examples are examples of finite sets. An example of an infinite set is the set of Natural Numbers .

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Element (mathematics)

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