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These include infinite and infinitesimal numbers which possess certain properties of the real numbers. Surreal numbers: A number system that includes the hyperreal numbers as well as the ordinals. Fuzzy numbers: A generalization of the real numbers, in which each element is a connected set of possible values with weights.
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 ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
The number system that results depends on what base is used for the digits: any base is possible, but a prime number base provides the best mathematical properties. The set of the p-adic numbers contains the rational numbers, but is not contained in the complex numbers.
A factorial x! is the product of all numbers from 1 to x. The first: 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600 (sequence A000142 in the OEIS). 0! = 1 is sometimes included. A k-smooth number (for a natural number k) has its prime factors ≤ k (so it is also j-smooth for any j > k).
Natural numbers are also used as labels, like jersey numbers on a sports team, where they serve as nominal numbers and do not have mathematical properties. [5] The natural numbers form a set, commonly symbolized as a bold N or blackboard bold . Many other number sets are built from the natural numbers.
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The main kinds of numbers employed in arithmetic are natural numbers, whole numbers, integers, rational numbers, and real numbers. [12] The natural numbers are whole numbers that start from 1 and go to infinity. They exclude 0 and negative numbers.