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The number 0 may or may not be considered a natural number, [70] [71] but it is an integer, and hence a rational number and a real number. [72] All rational numbers are algebraic numbers, including 0. When the real numbers are extended to form the complex numbers, 0 becomes the origin of the complex plane.
The origin of a Cartesian coordinate system. In mathematics, the origin of a Euclidean space is a special point, usually denoted by the letter O, used as a fixed point of reference for the geometry of the surrounding space. In physical problems, the choice of origin is often arbitrary, meaning any choice of origin will ultimately give the same ...
Thus the origin has coordinates (0, 0), and the points on the positive half-axes, one unit away from the origin, have coordinates (1, 0) and (0, 1). In mathematics, physics, and engineering, the first axis is usually defined or depicted as horizontal and oriented to the right, and the second axis is vertical and oriented upwards.
In this system, an arbitrary point O (the origin) is chosen on a given line. The coordinate of a point P is defined as the signed distance from O to P, where the signed distance is the distance taken as positive or negative depending on which side of the line P lies. Each point is given a unique coordinate and each real number is the coordinate ...
In tennis, the word "love" is used to replace 0 to refer to points, sets and matches. If the score during a game is 30-0, it is read as "thirty-love". Similarly, 3-0 would be read as "three-love" if referring to the score during a tiebreak, the games won during a set, or the sets won during a match. The term was adopted by many other racquet ...
The least ordinal of cardinality ℵ 0 (that is, the initial ordinal of ℵ 0) is ω but many well-ordered sets with cardinal number ℵ 0 have an ordinal number greater than ω. For finite well-ordered sets, there is a one-to-one correspondence between ordinal and cardinal numbers; therefore they can both be expressed by the same natural ...
The use of 0 as a number should be distinguished from its use as a placeholder numeral in place-value systems. Many ancient texts used 0. Babylonian and Egyptian texts used it. Egyptians used the word nfr to denote zero balance in double entry accounting. Indian texts used a Sanskrit word Shunye or shunya to refer to the concept of void.
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 ...