The set of numbers on the number line that are not rational numbers; i.e. that cannot be expressed in the form / where and are integers.

The set of numbers which cannot be represented as fractions. Examples are and p

subset of real numbers whose decimal representations neither repeat nor terminate; may also be defined as the subset of real numbers which are not rational numbers (e.g., both Ö and are irrational)

Numbers that cannot be written as fractions where both the numerator and denominator are integers and the denominator is not zero. For example, and are irrational numbers. An irrational number can be represented by a nonterminating, nonrepeating decimal. For example, the decimal for , 3.141592653…, continues without a repeating pattern. The number 1.10100100010000… is irrational; there is a pattern in the decimal, but it does not repeat.

A numbers that cannot be obtained by dividing one integer by another

A set of numbers that cannot be represented as an exact ratio of two integers. For example, the square root of 2.