Real numbers

quantity along a continuous line

nonnegative number with the same magnitude as a given real number

upright=1.35|class=skin-invert-image|thumb|alt=Stylistic impression of the repeating decimal 0.9999..., representing the digit 9 repeating infinitely 0.999... is a repeating decimal that represents the number 1. The three dots represent an infinite list of "9" digits. Following the standard rules for representing real numbers in decimal notation, its value is the smallest number greater than or equal to every number in the sequence 0.9, 0.99, 0.999, and so on. It can be proved that this number is1; that is, 0.999\ldots = 1.

picture of a graduated straight line that serves as abstraction for real numbers; coordinate system in one-dimensional space

method of construction of the real numbers

extension of the reals by +∞ and −∞

when two functions have co-rational periods, i.e. n T1 = m T2

concept in mathematics

any constructive definition of the real numbers

function whose domain a subset of real numbers

Real numbers with a multi-valued logical classification

thesis in mathematical logic

function with more than one argument, with all arguments being real variables

absolute value of (x - y), a metric