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.