Definition
Element of a set
An element of a set is one object that belongs to that set.
What it means
Think of a set as a collection with a membership rule. An element is one thing that passes the rule and belongs in the collection. In a set, belonging matters; the order of the elements does not.
Remember it
Ask one question: does this object belong inside the set?
Example
Let S = {triangle, square, circle}. Square is an element of S, so square ∈ S. Star is not listed and does not satisfy this set’s membership, so star ∉ S.
Watch for
An element and a subset are different: 2 ∈ {1, 2}, while {2} is a one-element subset of {1, 2}.
Common mix-up
The braces are not part of an element unless the element itself is a set. The number 2 and the set {2} are different objects.
Exact meaning
An element of a set is an object that belongs to the set under its stated definition. Membership is written x ∈ A, and non-membership is written x ∉ A. An element may be a number, shape, word, object, or even another set.