ikkeheltalige

Ikkeheltalige is a mathematical term used to describe real numbers that are not integers. Formally, a real number x is ikkeheltalig if x is not in the set of integers Z. Equivalently, x has a nonzero fractional part, meaning {x} ≠ 0, where {x} = x − floor(x) denotes the fractional part.

Non-integers can be divided into rational and irrational categories. Rational non-integers include numbers such as 3/2 = 1.5, -7/4 = -1.75, and 0.25. Irrational non-integers include numbers like π, e, and √2, whose decimal expansions do not terminate or repeat.

The collection of ikkeheltalige numbers is the real numbers with the integers removed, denoted R \ Z. This set is dense in the real line: between any two real numbers there exists a ikkeheltalig. The property is useful in analysis and number theory, where one often distinguishes integer values from non-integer values, for example when considering continuity, limits, fractional parts, or divisions.

Arithmetic with ikkeheltalige numbers follows standard real arithmetic, but some ordinary closures fail. For example, adding an integer to a ikkeheltalig yields another ikkeheltalig, since x + n has fractional part {x}. However, multiplying a ikkeheltalig by an integer does not necessarily produce a ikkeheltalig; for instance, (1/2) × 2 = 1, which is an integer.

In Danish or Norwegian mathematical usage, ikkeheltalige tal describe non-integer numbers. The term accommodates both rational and irrational cases without implying any particular representation.