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...of a given [[Complex number|complex valued]] function of <var>2n</var> [[real number|real]] [[variable]]s to be a [[Holomorphic function|holomorphic one]]. They

Let A=[0,1}, a proper subset of the [[real number]]s '''R'''.

...ns]] '''H''' is a [[division ring]] with [[centre of a ring|centre]] the [[real number]]s '''R'''. It may thus be regarded as an '''R'''-algebra.

...e the square of any real number is nonnegative, <math>i</math> cannot be a real number. At first glance, it is not even clear whether such an object exists and ca ...solve [[cubic equation|cubic equations]]. Even for equations with three [[real number|real]] solutions, the method they used sometimes required calculations wit

...2, experiment 3 ... , where the outcome of each experiment will generate a real number. If the probability that this sequence will converge to a given real number ''a'' equals 1, then we say the original sequence of stochastic variables

...the field of [[complex number]]s '''C''' is an extension of the field of [[real number]]s '''R'''.

* ordering (e.g., [[e (mathematics)|e]] is smaller than [[pi]] in the [[real number]] set), and # The [[real number]]s (<math> \scriptstyle \mathbb{R} </math>) find applications in measuremen

...an infinite series representation of a [[periodic function]] ''ƒ'' of a [[real number|real]] variable &xi;, of period ''P'':

...purely imaginary number, i.e., the [[product (mathematics)|product]] of a real number and <math>i</math> ). A real number may be either [[rational number|rational]] or [[irrational number|irrationa

** A continuous [[real number|real]]-valued function on a compact space is [[bounded set|bounded]] and at

.... Further let A₁ denote ''A'' itself. Let ''z'' be a positive real number and ''P''(''z'') denote the product of the primes in ''P'' which are &le; '

...n as well. For example, we know how to add vectors and multiply them by [[real number]]s ([[scalar]]s) in <font style = "vertical-align: 20%"><math>\mathbb{R}^3< ...eal numbers, ''x''_''k''+''y''_''k'' is a well-defined real number.

...rd Euclidean space of ''n'' dimensions as an [[affine space]] built on a [[real number|real]] [[vector space]] '''R'''^''n'' then the translations are t

...onvert a real number to an integer. One way is called ''rounding'', when a real number is rounded down if its fractional part less than 5, and up if more than or

...bit unfamiliar properties not shared by the more common polynomials with [[real number]] coefficients. Polynomials with coefficients in an arbitrary ring form a ...similarly to polynomials with real number coefficients. Polynomials with real number coefficients are discussed on the main [[polynomial]] page. This "advanced

...e the square of any real number is nonnegative, <math>i</math> cannot be a real number. At first glance, it is not even clear whether such an object exists and ca ...solve [[cubic equation|cubic equations]]. Even for equations with three [[real number|real]] solutions, the method they used sometimes required calculations wit

**The [[rational number|rational]], [[real number|real]] and [[complex number|complex]] numbers each form commutative rings.

The height of an individual is a real number that in principle may take on any value.

...istance between points ''O'' and ''P''. Each vector can be multiplied by a real number, which scales the length of the vector. In Figure 1, <font style = "vertic

...ations. Quadratic equations occurring in applications typically involve [[real number]] [[coefficient]]s. ...mmon case, where a polynomial has [[integer]] coefficients but one desires real number solutions. If, instead, one demands solutions of the same type as the poly

...pes of exponents, including [[negative integer]]s, [[rational number]]s, [[real number]]s, [[complex number]]s, and even [[matrix|matrices]], [[set (mathematics)|

...p> + ''Y''² = 1 defined over the [[field (algebra)|field]] of [[real number]]s. The point

...or the material. For homogeneous and isotropic materials the tensor is a real number &sigma;₀ times a 3&times;3 [[identity matrix]]. The scalar &sig

In a [[linear order|linearly ordered]] set, such as the [[real number]]s, any two elements ''x'' and ''y'' are comparable. We suppose for defini

...x_1,x_2,\ldots</math> of elements in ''X'' is a Cauchy sequence if for any real number <math>\epsilon>0</math> there exists a positive integer <math>N(\epsilon)</

A measure space (''X'',Σ,''μ'') is called finite if ''μ''(''X'') is a finite real number (rather than ∞). It is called ''σ-finite'' if ''X'' can be decomposed i ...r union is the entire real line. Alternatively, consider the same set of [[real number]]s with the [[counting measure]], which assigns to each finite set of reals

...ous linear functional on ''K'', if ''f'' maps all elements of ''K'' onto a real number (''f'', &phi;) such that

...tions of addition, multiplication, taking reciprocals and multiplying by a real number and b) the polynomial <math>x^2 + 1</math> are left unchanged. This two ele ...an group, but it is not cyclic. There is no single element such that every real number is some integral multiple of that element (if you suppose that there is suc

...h in turn is a part of [[mathematics]]. It studies the approximations of [[real number]]s by [[rational number]]s. This article presents an elementary introductio '''Theorem'''&nbsp; Let <math>\ a</math>&nbsp; be an arbitrary real number. Then

...[[Many Worlds Interpretation]] as used by Deutsch). It must of course be a real number, as the mean value of the observable as the number of measurements of that

In plane [[analytical geometry]], '''Cartesian coordinates''' are two [[real number]]s specifying a [[point (geometry)|point]] in a [[Euclid|Euclidean]] plane

...y algebra]]''', in which the properties of operations on the [[real number|real number system]] are recorded using symbols as "place holders" to denote [[constant ...st step to a systematic exploration of the properties of the [[real number|real number system]].

*<math>\mathbb{R}</math>, the set of [[real number|real numbers]] *The set consisting of all tuples (a,b), where a is any real number and ditto for b. This set is known as {{nowrap|ℝ'''×'''ℝ}} or {{nowra

...math>x</math>, there is no defined value of <math>f(x)</math> within the [[real number]]s &mdash; but using [[complex number]]s a value can be found, as will be d

...ote that log(''x'') is defined only for positive ''x'', but takes on all [[real number|real]] values.

...b>A</b>) • <b>B</b>= <b>A</b> • (c<b>B</b>)=c(<b>A</b> • <b>B</b>) for any real number c

...with the classical notion is that you can easily break up the digits of a real number to map it bijectively to two (or ''d'') real numbers. The example of space Let ''d'' be a non-negative real number and ''S'' ⊂ ''X'' a subset of a metric space (''X'',''ρ''). The ''d''-d

...y more than one solution. The graph of the Lambert ''W'' function in the [[real number]]s looks as follows: ...the correct branch. To calculate real values on the principal branch, any real number above <math>-1</math> will work, but faster convergence is obtained by taki

...cle was [[free particle|free]], its energy would be allowed to take on any real number. Once inside the box though, only a specific [[discrete]] set of energy ei ...L}</math>, where <math>\varphi</math> is some overall [[quantum phase]] (a real number).

{{r|Real number}}

...indicates value <math>N=2^q</math>; where <math>q</math> is assumed to be real number.

...also a real linear space (the latter ''underlies'' the former), since each real number is also a complex number. Linear operations, given in a linear space by def

...ite and the Hamiltonian ''H'' is Hermitian. In that case ''E''[&Phi;] is a real number. The boundary condition in electronic structure theory is the vanishing of ...ionians in quantum mechanics have a lower bound, that is there is a finite real number ''B'' such that

...al plane can be represented by two [[Cartesian coordinates]], which are [[real number]]s: '''r''' = (''x'', ''y''). These numbers are the projections of '''r''' ...is real; in that case, the values of the functions sin and cos are also [[real number]]s. However, the definition above can be used for [[complex number]]s too.

...its cubic root. More formally, for every real number ''x'' there exists a real number ''y'' such that <math> y^3 = x. </math> Symbolically, <math> \forall x \in

...r of this article, "positive" will be understood to mean either a positive real number or a complex number with positive real part.</ref>

...of [[Taylor series]] to show that the following identities hold for all [[real number]]s ''x'': ...finite series]] can be developed from the foundations of the [[real number|real number system]], independent of any geometric considerations. The [[differentiabil

...tions to algebraic equations of all degrees. He considered all kinds of [[real number]]s on an equal footing—[[natural number]]s, roots (the majority of which

...nts. Further the unit of time is undetermined and hence we scale time by a real number &omega;. In total the trial function is

...number systems, such as the [[integer]]s, the [[rational number]]s, the [[real number]]s, and the [[complex number]]s under addition, as well as the non-zero rat

...number]]s|| [[Whole number]]s|| [[Integer]]s || [[Rational number]]s || [[Real number]]s || [[Complex number]]s

where the quantity between round brackets is a Wigner [[3j-symbol]], a real number depending on the quantum numbers shown in the symbol. The proportionality f

...magnetic permeability of the substance, mentioned above. One can assign a real number (&mu;) to the permeability. When &mu; is much larger than one, say a thousa

...X \sim N(\mu, \sigma^2)</math> and <math>a</math> and <math>b</math> are [[real number]]s, then <math>a X + b \sim N(a \mu + b, (a \sigma)^2)</math> (see [[expect

...efined, quantitative, meanings in physics, and both can be measured with a real number as outcome. The physics definitions are inspired by, but differ somewhat fr

...ctor '''p''' is parallel to the vector '''E''', i.e., &alpha; is a single real number, a scalar. It can happen that the two vectors (cause and effect) are non-pa

Each body is attributed some positive [[real number]] called [[mass]]. The mass of each body determines, how the body reacts t

...al Instrument Digital Interface)|MIDI]] standard to map a frequency ƒ to a real number ''n'' as follows

...nly six can be easily recognized. Moreover there is no consensus about the real number of species to be accepted, according to the reference this number varies an

...devised with an infinite number of "degrees of truth", represented by a [[real number]] between 0 and 1. [[Bayesian probability]] can be interpreted as a system