such as numbers, points, functions, etc.

A set is often expressed by listing its elements between commas, enclosed by braces. For example, the collection {2,4,6,8} is a set which has four elements, the numbers 2,4,6 and 8. Some sets have infinitely many elements. For example, consider the collection of all integers,

{..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ...}.

Here the dots indicate a pattern of numbers that continues forever in both the positive and negative directions. A set is called an infinite set if it has infinitely many elements; otherwise it is called a finite set.

Two sets are equal if they contain exactly the same elements. Thus {2,4,6,8} = {4,2,8,6} because even though they are listed in a different order, the elements are identical; but {2,4,6,8} ≠ {2,4,6,7}.

{... -4, -3, -2, -1, 0, 1, 2, 3, 4...} = {0, -1, 1, -2, 2, -3, 3, -4, 4, ...}.

We often let uppercase letters stand for sets. In discussing the set {2,4,6,8} we might declare A = {2,4,6,8} and then use A to stand for {2,4,6,8}.

To express that 2 is an element of the set A, we write 2 ∈ A, and read this as “2 is an element of A,” or “2 is in A,” or just “2 in A.” We also have 4 ∈ A, 6 ∈ A and 8 ∈ A, but 5 ∉ A. We read this last expression as “5 is not an element of A,” or “5 not in A.” Expressions like 6, 2 ∈ A or 2, 4, 8 ∈ A are used to indicate that several things are in a set.