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The integers arranged on a number line. An integer is the number zero , a positive natural number (1, 2, 3, . . .), or the negation of a positive natural number (−1, −2, −3, . . .). [1] The negations or additive inverses of the positive natural numbers are referred to as negative integers. [2]
Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.
The natural numbers form a subset of the integers. As there is no common standard for the inclusion or not of zero in the natural numbers, the natural numbers without zero are commonly referred to as positive integers, and the natural numbers with zero are referred to as non-negative integers.
Sometimes, the whole numbers are the natural numbers plus zero. In other cases, the whole numbers refer to all of the integers, including negative integers. [3] The counting numbers are another term for the natural numbers, particularly in primary school education, and are ambiguous as well although typically start at 1. [4]
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
[1] Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry).
The set of all integers is usually denoted by Z (or Z in blackboard bold, ), which stands for Zahlen (German for "numbers"). Articles about integers are automatically sorted in numerical order. Do not set a sort key in them, unless thousands separators are used.
In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers. Integral data types may be of different sizes and may or may not be allowed to contain negative values. Integers are commonly represented in a computer as a group of binary digits (bits). The size of the grouping ...