heltalsdelen

heltalsdelen is a Norwegian mathematical term that refers to the integer part of a real number, also known in English as the whole‑number part. It is defined as the greatest integer less than or equal to the given number. For a real number x, the heltalsdelen is denoted by ⌊x⌋, the floor function. For example, the heltalsdelen of 3.7 is 3, and the heltalsdelen of –2.3 is –3, because –3 is the largest integer not exceeding –2.3.

The opposite component is the fractional part, often written as {x} = x – ⌊x⌋. With the real number 3.7, the fractional part is 0.7. Together, the heltalsdelen and the fractional part reconstruct the original number: x = ⌊x⌋ + {x}. This decomposition is used in number theory, computer science, and numerical analysis for tasks such as truncation and rounding.

In some contexts, particularly in teaching mathematics in Norwegian schools, heltalsdelen is called the "whole number part" and is used to explain concepts such as integer division, the Euclidean algorithm, and the representation of mixed numbers. The term is also employed in programming languages that support integer and floating‑point types, where functions equivalent to floor are used to extract the heltalsdelen from floating‑point values.