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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]
Positive numbers: Real numbers that are greater than zero. Negative numbers: Real numbers that are less than zero. Because zero itself has no sign, neither the positive numbers nor the negative numbers include zero. When zero is a possibility, the following terms are often used: Non-negative numbers: Real numbers that are greater than or equal ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
In his final scientific work, Two New Sciences, Galileo Galilei made apparently contradictory statements about the positive integers. First, a square is an integer which is the square of an integer. First, a square is an integer which is the square of an integer.
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.
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."
Other rings of integers may admit more units. The Gaussian integers have four units, the previous two as well as ±i. The Eisenstein integers Z[exp(2πi / 3)] have six units. The integers in real quadratic number fields have infinitely many units. For example, in Z[√ 3], every power of 2 + √ 3 is a unit, and all these powers are distinct.
The register width of a processor determines the range of values that can be represented in its registers. Though the vast majority of computers can perform multiple-precision arithmetic on operands in memory, allowing numbers to be arbitrarily long and overflow to be avoided, the register width limits the sizes of numbers that can be operated on (e.g., added or subtracted) using a single ...