wholepart

Wholepart is a term used to describe the integer part of a real number—the portion of the number that is a whole number, independent of any fractional component. In formal mathematics, this concept is most clearly captured by the floor function, denoted ⌊x⌋, which returns the greatest integer less than or equal to x. For example, ⌊12.34⌋ = 12 and ⌊-2.7⌋ = -3.

In some programming and teaching contexts, the term wholepart is used more loosely to refer to truncation toward zero, where the fractional part is discarded without adjusting the sign. Under this interpretation, -2.7 would be represented as -2. The choice between floor and truncation affects derived quantities such as the fractional part, which can be defined as x − ⌊x⌋ in the floor convention, or x − trunc(x) in the truncation convention.

Mathematically, the floor function ⌊x⌋ is a nondecreasing, integer-valued function that is discontinuous at every integer. It satisfies ⌊x⌋ ≤ x < ⌊x⌋ + 1 for all x. The concept is closely related to the fractional part {x} = x − ⌊x⌋, which measures how far x is from the preceding integer.

In practical use, wholepart appears in number theory, digital representations, measurements, and data processing, where separating an amount into whole units and a remainder is needed. In computing, many languages implement this operation in two ways: flooring (as in math libraries) or truncation toward zero (as in type casting to integers).