Ikkeheltallige

Ikkeheltallige tall, or non-integers, are real numbers that are not integers. In Norwegian mathematics, a heltall is an integer such as -2, -1, 0, 1, 2, and so on. Therefore, an ikkeheltallige tall is any real number whose fractional part is not zero. It includes all non-integer rationals as well as all irrational numbers.

Examples include 1.5, -3.25, and numbers like pi and sqrt(2). Note that 2.0 or -7.000 is numerically equal to an integer and is not considered non-integer.

Classification: Non-integers can be divided into rational non-integers (numbers that can be expressed as a fraction a/b with integers a, b ≠ 0, where the result is not an integer) and irrational non-integers (numbers that cannot be written as a ratio of integers).

Properties: The set of ikkeheltallige tall is the real numbers minus the integers, written R \ Z. This set is dense in R: between any two real numbers there exists a non-integer. The decimal expansion of non-integers may terminate or repeat (for rational non-integers) or be non-repeating (for irrationals). Arithmetic with non-integers follows standard rules: adding an integer yields a non-integer; the sum of two non-integers can be an integer (for example, 0.5 + 0.5 = 1).

Relation to other sets: Non-integers are all real numbers that are not integers, forming the complement of the integers within the real numbers. They comprise both rational and irrational numbers, unlike integers. In education, the term helps distinguish numbers with fractional parts from whole numbers.

See also: Integers, Rational numbers, Irrational numbers, Real numbers, Decimal expansion.