Integer

The integers consist of the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero. The set of all integers is usually denoted in mathematics by Z (or Z in blackboard bold, mathbb{Z}), which stands for Zahlen (German for "numbers"). They are also known as the whole numbers, although that term is also used to refer only to the positive integers (with or without zero). Like the natural numbers, the integers form a countably infinite set.

Integers in computing

An integer is often one of the primitive datatypes in computer languages. However, these "integers" can only represent a subset of all mathematical integers, since "real-world" computers are of finite capacity. Integer datatypes are typically implemented using a fixed number of bits, and even variable-length representations eventually run out of storage space when trying to represent especially large numbers. On the other hand, theoretical models of digital computers, e.g., Turing machines, usually do have infinite (but only countable) capacity.

Related Topics:
Datatype - Computer language - Subset - Bit - Digital computer - Turing machine - Countable

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