Category
page 1Real numbers
real number
quantity along a continuous line
absolute value
nonnegative number with the same magnitude as a given real number
0.999...
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.
number line
picture of a graduated straight line that serves as abstraction for real numbers; coordinate system in one-dimensional space
Dedekind cut
method of construction of the real numbers
extended real number line
extension of the reals by +∞ and −∞
commensurability
when two functions have co-rational periods, i.e. n T1 = m T2
completeness of the real numbers
concept in mathematics
construction of the real numbers
any constructive definition of the real numbers
function of a real variable
function whose domain a subset of real numbers
Fuzzy number
Real numbers with a multi-valued logical classification
Cantor–Dedekind axiom
thesis in mathematical logic
function of several real variables
function with more than one argument, with all arguments being real variables
absolute difference
absolute value of (x - y), a metric