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**Construction of the real numbers**— In mathematics, there are several ways of defining the real number system as an ordered field. The synthetic approach gives a list of axioms for the real numbers as a complete ordered field. Under the usual axioms of set theory, one can show that … Wikipedia**Completeness of the real numbers**— Intuitively, completeness implies that there are not any “gaps” (in Dedekind s terminology) or “missing points” in the real number line. This contrasts with the rational numbers, whose corresponding number line has a “gap” at each irrational… … Wikipedia**Real analysis**— Real function redirects here. For the real part of a complex number, see real part. Real analysis, is a branch of mathematical analysis dealing with the set of real numbers and functions of a real variable. In particular, it deals with the… … Wikipedia**real**— real1 [rē′əl, rēl] adj. [OFr < ML realis < L res, thing < IE base * rei , property, thing > Sans rai, wealth, property] 1. existing or happening as or in fact; actual, true, etc.; not merely seeming, pretended, imagined, fictitious,… … English World dictionary**Real number**— For the real numbers used in descriptive set theory, see Baire space (set theory). For the computing datatype, see Floating point number. A symbol of the set of real numbers … Wikipedia**real number**— /ree euhl, reel/, Math. a rational number or the limit of a sequence of rational numbers, as opposed to a complex number. Also called real. [1905 10] * * * In mathematics, a quantity that can be expressed as a finite or infinite decimal expansion … Universalium**Real closed field**— In mathematics, a real closed field is a field F in which any of the following equivalent conditions are true:#There is a total order on F making it an ordered field such that, in this ordering, every positive element of F is a square in F and… … Wikipedia**Real line**— In mathematics, the real line is simply the set R of singleton real numbers.However, this term is usually used when R is to be treated as a space of some sort, such as a topological space or a vector space.The real line has been studied at least… … Wikipedia**Real projective line**— In real analysis, the real projective line (also called the one point compactification of the real line, or the projectively extended real numbers ), is the set mathbb{R}cup{infty}, also denoted by widehat{mathbb{R and by mathbb{R}P^1.The symbol… … Wikipedia**Real data type**— A real data type is a data type used in a computer program to represent an approximation of a real number.Because the real numbers are not countable, computers cannot represent them exactly using a finite amount of information.Most often, a… … Wikipedia