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...g with very small and very large numbers, though it is applicable to any [[real number]]. A number in scientific notation is expressed as a number between -10 and

* The [[real number]]s form an ordered field in a unique way: the squares form the positive con

* The connected subsets of the [[real number]]s with the Euclidean metric topology are the [[interval]]s. In conjunctions with the statement above, that the connected subsets of the [[real number]]s with the Euclidean metric topology are the [[interval]]s, this gives the

{{r|Real number}}

Quadratic equations occurring in applications typically involve [[real number]] [[coefficient]]s. However, one can algebraically manipulate polynomial e ...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

More precisely, an &alpha;-quantile is a real number ''X''_&alpha; and a real number <math>\alpha</math> (<math>0<\alpha<1</math>),

{{r|Real number}}

...ve, [[monotonic function|monotonic]] decreasing function of the positive [[real number|real]] variable ''x''. Suppose that the [[Laplace transform]]

{{r|Real number}}

...t)=\langle x+t e^{i\phi(x,y)} y, x+te^{i\phi(x,y)} y\rangle</math> for any real number ''t'' and notice that, by the properties of a complex inner product, ''f''

* The field '''R''' of [[real number]]s has only the identity automorphism. This is harder to prove, and relies

...mplex numbers the series will have an [[abscissa of convergence]] ''S'', a real number with the property that the series converges for all complex numbers ''s'' w

{{r|Real number}}

...calculations involving [[real numbers]], since a computer can only store a real number up to a finite number of [[significant figures]]. These errors can be mult

...addition]] and [[multiplication]] of [[integer]]s, [[rational number]]s, [[real number|real]] and [[complex number]]s. In this context associativity is often ref

...a [[set]] that does not contain its boundary. Simplest examples include [[real number|real]] intervals without endpoints (commonly referred to as ''open interval

...tric space. A set <math>A \subset X</math> is totally bounded if for any [[real number]] ''r''>0 there exists a finite number ''n''(''r'') (that depends on the va

...number systems, such as the [[integer]]s, the [[rational number]]s, the [[real number]]s, and the [[complex number]]s are abelian groups with the group operation

...and ''Y''. A [[complex number]] may be expressed as an ordered pair of [[real number]]s, the real and imaginary parts respectively.

{{r|Real number}}

...on those values. For example, <math>x+y = y+x</math> is an identity for [[real number]]s, since it is true for all real values of ''x'' and ''y''. ...(namely, <math>x=\sqrt{2}</math> and <math>x=-\sqrt{2}</math>) among the [[real number]]s, and it has only one solution

...''', involving no operation more advanced than taking the square root of a real number. ...lex number]]s even when every other part of the problem deals only with [[real number]]s. Looking at the quadratic formula, we see that the roots will be comple

...hen rational numbers are considered to be [[p-adic number]]s rather than [[real number]]s. Conversely, if the expansion of a number for one base is periodic, it i A [[real number]] that is not a rational number is called an [[irrational number]].

* '''Pseudocompact''' if every [[continuous function|continuous]] [[real number|real]]-valued [[function (mathematics)|function]] is bounded.

{{r|Real number}}

Since any real number between 0 and 1 can be written as a decimal number, To show this, we construct a real number ''r'' with a decimal expansion

Since any real number between 0 and 1 can be written as a decimal number, To show this, we construct a real number ''r'' with a decimal expansion

{{r|Real number}}

...'''characteristic function''' of any [[probability distribution]] on the [[real number|real]] line is given by the following formula, where ''X'' is any [[random

{{r|Real number}}

...heorem''' characterises the [[compact space|compact]] [[subset]]s of the [[real number]]s.

In [[mathematics]], an '''irrational number''' is any [[real number]] that is not a [[rational number]], i.e. it cannot be expressed as a [[fra

{{r|Real number}}

...nce of positive real numbers to [[limit of a sequence|converge]] against a real number

{{r|Real number}}

...of the entities <math>i</math>, <math>j</math> or <math>k</math> can be a real number. At first glance, it is not even clear whether such objects can exist in an Like a real number can be interpreted as a point in 1-dimensional space, and a complex number

* The subset <math>\{0\} \cup \{ 1/n : n =1,2,\ldots \}</math> of the [[real number]]s with the usual topology is a door space. Any set containing the point 0

...Fundamental Theorem of Algebra is that every nonconstant polynomial with [[Real number|real]] coefficients must have at least one complex root. Since it is not tr

{{r|Real number}}

...(the ''pole'') and a given line (the ''polar axis'') through ''O''. One [[real number]] (''r'' ) gives the distance of ''P'' to ''O'' and another number (&thet

'''e''' is a [[constant]] [[real number]] equal to 2.71828 18284 59045 23536.... [[Irrational number|Irrational]] a

Some, say ''r'', of these embeddings will actually have image in the [[real number]]s, and the remaining embeddings will occur in [[complex conjugate]] pairs,

...]] coefficients. In this article, it is assumed that all polynomials have real number coefficients. See the [[polynonial equation/Advanced|"Advanced"]] subpage

...the complex numbers the series will have a radius of convergence ''R'', a real number with the property

...sts of [[row vector]]s <math>(x_1, \ldots, x_n)</math> with <math>n</math> real number entries.)

* The set of all [[Borel set|Borel subsets]] of the [[real number|real line]] is a sigma-algebra.

where <math>U=U(x, t)</math> and <math>F=F(x, t)</math> are [[real number|real]]-valued functions of <math>n</math> spatial variables, <math>x=(x_1, (where <math>i=\sqrt{-1}</math> and <math>\omega</math> is a real number), the wave equation is reduced to the inhomogeneous Helmholtz equation with

...For the rest of the present article, all polynomials considered will have real number coefficients.

.... 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; '