# Category: Real numbers

0.999...
In mathematics, 0.999... (also written as 0.9, in repeating decimal notation) denotes the repeating decimal consisting of an unending sequence of 9s after the decimal point. This repeating decimal rep
Absolute value
In mathematics, the absolute value or modulus of a real number , denoted , is the non-negative value of without regard to its sign. Namely, if x is a positive number, and if is negative (in which case
Extended real number line
In mathematics, the affinely extended real number system is obtained from the real number system by adding two infinity elements: and where the infinities are treated as actual numbers. It is useful i
Real coordinate space
In mathematics, the real coordinate space of dimension n, denoted Rn (/ɑːrˈɛn/ ar-EN) or , is the set of the n-tuples of real numbers, that is the set of all sequences of n real numbers. With componen
Zero sharp
In the mathematical discipline of set theory, 0# (zero sharp, also 0#) is the set of true formulae about indiscernibles and order-indiscernibles in the Gödel constructible universe. It is often encode
U-bit
In quantum mechanics, the u-bit or ubit is a proposed theoretical entity which arises in attempts to reformulate wave functions using only real numbers instead of the complex numbers conventionally us
Construction of the real numbers
In mathematics, there are several equivalent ways of defining the real numbers. One of them is that they form a complete ordered field that does not contain any smaller complete ordered field. Such a
Function of several real variables
In mathematical analysis and its applications, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables. Th
Decidability of first-order theories of the real numbers
In mathematical logic, a first-order language of the real numbers is the set of all well-formed sentences of first-order logic that involve universal and existential quantifiers and logical combinatio
Tarski's axiomatization of the reals
In 1936, Alfred Tarski set out an axiomatization of the real numbers and their arithmetic, consisting of only the 8 axioms shown below and a mere four primitive notions: the set of reals denoted R, a
Number line
In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a
Real number
In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature. Here, continuous means that values can have arb
Rational zeta series
In mathematics, a rational zeta series is the representation of an arbitrary real number in terms of a series consisting of rational numbers and the Riemann zeta function or the Hurwitz zeta function.
Cantor–Dedekind axiom
In mathematical logic, the Cantor–Dedekind axiom is the thesis that the real numbers are order-isomorphic to the linear continuum of geometry. In other words, the axiom states that there is a one-to-o
Quotient
In arithmetic, a quotient (from Latin: quotiens 'how many times', pronounced /ˈkwoʊʃənt/) is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics,
Dedekind cut
In mathematics, Dedekind cuts, named after German mathematician Richard Dedekind but previously considered by Joseph Bertrand, are а method of construction of the real numbers from the rational number
Function of a real variable
In mathematical analysis, and applications in geometry, applied mathematics, engineering, and natural sciences, a function of a real variable is a function whose domain is the real numbers , or a subs
Fuzzy number
A fuzzy number is a generalization of a regular, real number in the sense that it does not refer to one single value but rather to a connected set of possible values, where each possible value has its
Absolute difference
The absolute difference of two real numbers and is given by , the absolute value of their difference. It describes the distance on the real line between the points corresponding to and . It is a speci
Commensurability (mathematics)
In mathematics, two non-zero real numbers a and b are said to be commensurable if their ratio a/b is a rational number; otherwise a and b are called incommensurable. (Recall that a rational number is
Completeness of the real numbers
Completeness is a property of the real numbers that, intuitively, implies that there are no "gaps" (in Dedekind's terminology) or "missing points" in the real number line. This contrasts with the rati