Ickheltaliga

Ickheltaliga is a term used to describe numbers that are not integers. In the real number system, it denotes the set of all real numbers that do not belong to the integers Z; equivalently, it is the complement of the integers within the real numbers, written as R \ Z. Such numbers have a nonzero fractional part when expressed in decimal or fraction form.

Examples of ickheltaliga numbers include 3.5, -2.7, sqrt(2), and pi. A real number x is ickheltalig if and only if its fractional part {x} is not zero. This separates non-integers from integers, which have a fractional part of zero.

The set of ickheltaliga numbers is dense in the real numbers and uncountable, since removing the countable set of integers from R leaves a large continuum of points. They are not closed under addition or multiplication: for instance, 0.5 + 0.5 = 1 is an integer, and (sqrt(2)) · (sqrt(2)) = 2 is an integer, although both factors are ickheltaliga.

There are two natural subfamilies: rational non-integers (numbers in Q \ Z) and irrational numbers (numbers in R \ Q). In analysis and number theory, the concept of non-integers is often used in discussions of fractional parts, rounding, measurement error, and the density of real numbers.