Element (mathematics)

In mathematics, an element (or member) of a set is any one of the distinct objects that belong to that set.

For example, given a set called A containing the first four positive integers (

means that the elements of the set A are the numbers 1, 2, 3 and 4.

are the color red, the number 12, and the set B.

[clarification needed] The binary relation "is an element of", also called set membership, is denoted by the symbol "∈".

[1] Equivalent expressions are "x is a member of A", "x belongs to A", "x is in A" and "x lies in A".

[2] Logician George Boolos strongly urged that "contains" be used for membership only, and "includes" for the subset relation only.

The negation of set membership is denoted by the symbol "∉".

The symbol ∈ was first used by Giuseppe Peano, in his 1889 work Arithmetices principia, nova methodo exposita.

[4] Here he wrote on page X: Signum ∈ significat est.

So a ∈ b is read as a is a certain b; …The symbol itself is a stylized lowercase Greek letter epsilon ("ϵ"), the first letter of the word ἐστί, which means "is".

Using the sets defined above, namely A = {1, 2, 3, 4}, B = {1, 2, {3, 4}} and C = {red, green, blue}, the following statements are true: The number of elements in a particular set is a property known as cardinality; informally, this is the size of a set.

As a relation, set membership must have a domain and a range.

Conventionally the domain is called the universe denoted U.