Definition
Set membership
Set membership tells whether a particular object is an element of a set.
What it means
Ask, “Is this one object in the collection described by the set?” A list inside braces or the rule that defines the set decides the answer. Being drawn close to a set in a picture does not make an object a member.
Remember it
One object, one set: is it in?
Example
Let E = {2, 4, 6, 8}. Since 6 is listed, 6 ∈ E. Since 5 is not one of the even numbers in E, 5 ∉ E.
Watch for
An element can itself be a set, but membership still asks whether that one object belongs to the set being considered.
Common mix-up
Do not swap ∈ with ⊆. Use ∈ for an element belonging to a set and ⊆ for one set being a subset of another.
Exact meaning
An object x belongs to a set S exactly when x is one of the elements specified by S; this is written x ∈ S. If x is not an element of S, write x ∉ S.