A set is a collection of elements that are unique. Conceptually a set is a useful tool to formalize and talk about math problems. For example, mathematicians use sets to define the domain of numbers.

Set of Natural Numbers

The set of natural numbers, also called the counting numbers, contains the numbers 0, 1, 2, 3, ...

Set of Integers

The set of integers is made up of the set of counting integers and each of their negative counter parts.

Set of Rational Numbers

The set of rational numbers can be defined by the quotient of two numbers belonging to the set of integers, where the divisor is non-zero.

Set of Real Numbers

The set of real numbers contains the set of rational numbers as well as irrational numbers like pi, e, and the square root of two.

Set Operators


The set union operation is denoted using the cup symbol. The union of two sets returns the combined elements of both sets. Duplicates are ignored.


The set intersection operator returns the shared elements between two sets. The operator is denoted using the cap symbol.

Set Difference

The set difference operator is denoted using the subtraction symbol. The operator returns the elements in the left-hand set that are not in the right-hand set.


Element of

The element of symbol describes membership to a set. When reading an equation the symbol can be read as "in" or "belongs to".