Nonintegers

Nonintegers are real numbers that are not integers. The integers form the set {..., -2, -1, 0, 1, 2, ...}, and every real number outside this set is a noninteger. This category includes rational nonintegers, such as 3/4 and -5/2, and irrational nonintegers, such as sqrt(2) and pi. Decimal representations help distinguish them: rational nonintegers may have finite decimals (like 0.5) or infinite repeating decimals (like 0.333...). Irrational nonintegers have nonrepeating, nonterminating decimals (like sqrt(2) ≈ 1.41421356...).

Note that whether a value is an integer or not is a matter of its numerical value, not merely how it is written. For example, 2.0 equals the integer 2, so it is not a noninteger, even though it includes a decimal point.

Nonintegers are dense in the real numbers: between any two real numbers there exist infinitely many nonintegers. The set of nonintegers is uncountable, since it equals the real numbers with the integers removed. They are central in analysis and appear in contexts such as measurement, continuity, and approximation.

In computing and numerical work, nonintegers are commonly represented as floating-point numbers, which store approximate non-integer values for arithmetic. The term highlights the distinction from whole numbers in mathematics and computer science.