Set members, set-builder notation

A set is a collection of objects. The objects are called elements or members. We usually use capital letters to name sets and list the elements in braces.


1. A = {a, b, c, d, e, f} is a list containing the first six letters of the alphabet.

2. B = {1, 2, 3, 4 … 20} is a set containing the counting numbers 1 through 20.

The empty set (or null set) is a set with no members or elements at all. It is represented by the symbol: { } or Ø.

It would incorrect to write the empty or null set as {Ø}, as the set {Ø} contains one element.

The symbol ∈ is used to mean is an element of, and the symbol ∉ is used to mean is not an element of.

If C = {orange, pineapple, banana}, we can say that banana C, but mango C.

Sometimes we don’t list the members of the set, we use a notation called set-builder notation.

The expression {x | x is a vowel} describes the “set of all x such that x is a vowel”. The bar, |, is read “such that”.


Finite, infinite sets, subsets »