wholenumber

Wholenumber is a term used to refer to the set of non-negative integers: 0, 1, 2, 3, ... In mathematics, the wholenumber set is commonly treated as the subset of integers consisting of zero and the positive integers. Some sources use wholenumber and whole number as synonyms for non-negative integers; others align natural numbers with or without zero. When zero is included, the set is commonly described as {0,1,2,...}, denoted Z≥0 or N0 in various texts.

In arithmetic, wholenumbers are closed under addition and multiplication, and they form a semiring under these operations. They are not closed under subtraction, since 0 − 1 yields a negative integer not in the set. They are not closed under division in general, since most divisions of non-negative integers do not yield an integer.

In computing, a wholenumber is often implemented as an unsigned or non-negative integer data type. Common bit widths include 8, 16, 32, and 64 bits, with ranges 0 to 2^n−1 for n bits (e.g., 8-bit: 0–255; 32-bit: 0–4294967295; 64-bit: 0–18446744073709551615).

Wholenumbers are used in counting discrete objects, statistics, and computer algorithms where negative values are not meaningful. They are particularly common in indexing, counters, and combinatorial calculations. They relate to other concepts such as natural numbers, which are defined differently in various contexts, and integers, which include negative values.

See also natural numbers, integers, unsigned integer, arithmetic.