noninteger

A noninteger is a real number that is not an integer. In set terms, it is any element of the real numbers R that does not belong to the integers Z. Equivalently, a real number x is a noninteger if its fractional part is nonzero, or if floor(x) ≠ x. Nonintegers include all numbers with a nonzero fractional part, whether positive or negative.

Nonintegers can be divided into rational and irrational categories. Some are rational, such as 1/2, 3.5, and −7.25, which can be expressed as a ratio of integers. Others are irrational, such as √2, π, and e, which cannot be written as a simple fraction and have nonrepeating, non-terminating decimal representations. The set of nonintegers comprises both these types and excludes only the whole numbers like ..., −2, −1, 0, 1, 2, ...

Key properties include that nonintegers are dense in the real numbers: between any two real numbers there exist infinitely many nonintegers. They form a large, non-discrete subset of R, in contrast to the integers, which are discrete. The concept is common in mathematics and in computing, where noninteger values correspond to fractional or floating-point numbers as opposed to whole-number integers. This distinction underpins rounding, truncation, and flooring operations, and it is relevant in measurements, statistics, and numerical analysis.