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The word integer comes from the Latin integer meaning "whole" or (literally) "untouched", from in ("not") plus tangere ("to touch"). "Entire" derives from the same origin via the French word entier, which means both entire and integer. [9] Historically the term was used for a number that was a multiple of 1, [10] [11] or to the whole part of a ...
Prime number: A positive integer with exactly two positive divisors: itself and 1. The primes form an infinite sequence 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ... Composite number: A positive integer that can be factored into a product of smaller positive integers. Every integer greater than one is either prime or composite.
An integer for which the average of its positive divisors is also an integer. A003601: Colossally abundant numbers: 2, 6, 12, 60, 120, 360, 2520, 5040, 55440, 720720, ... A number n is colossally abundant if there is an ε > 0 such that for all k > 1,
Within the context of integers, addition of one also plays a special role: for any integer a, the integer (a + 1) is the least integer greater than a, also known as the successor of a. [23] For instance, 3 is the successor of 2 and 7 is the successor of 6.
A rational number is a number that can be expressed as a fraction with an integer numerator and a positive integer denominator. Negative denominators are allowed, but are commonly avoided, as every rational number is equal to a fraction with positive denominator.
An integral type with n bits can encode 2 n numbers; for example an unsigned type typically represents the non-negative values 0 through 2 n − 1. Other encodings of integer values to bit patterns are sometimes used, for example binary-coded decimal or Gray code, or as printed character codes such as ASCII.
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With this definition, given a natural number n, the sentence "a set S has n elements" can be formally defined as "there exists a bijection from n to S." This formalizes the operation of counting the elements of S. Also, n ≤ m if and only if n is a subset of m. In other words, the set inclusion defines the usual total order on the natural