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- ...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|irrationa19 KB (2,948 words) - 10:07, 28 February 2024
- 12 bytes (1 word) - 08:16, 14 November 2007
- 87 bytes (12 words) - 05:18, 23 June 2008
- 389 bytes (39 words) - 12:37, 4 January 2009
- 460 bytes (62 words) - 19:24, 24 March 2008
Page text matches
- In mathematics, a [[complex number]] whose square is a negative real number, or (sometimes) more generally a non-real complex number.170 bytes (23 words) - 09:38, 1 January 2010
- Suppose ''x''<sub>1</sub>, ''x''<sub>2</sub>, ... is a [[sequence]] of [[Real number|real numbers]]. We say that the real number ''L'' is the ''limit'' of this sequence and we write771 bytes (122 words) - 09:45, 28 November 2007
- ...e difference of any two members of the set is an irrational number and any real number is the sum of a rational number and a member of the set.212 bytes (39 words) - 20:45, 4 September 2009
- The positive real number that, when multiplied by itself, gives the number 2.114 bytes (15 words) - 19:41, 4 September 2009
- {{r|Real number}}258 bytes (33 words) - 02:29, 8 February 2009
- the sum ''a''+''b''i of a real number ''a'' and an imaginary number ''b''i ...up>2</sup> = −''b''<sup>2</sup> of an imaginary number is a negative real number,3 KB (468 words) - 17:28, 1 January 2010
- #REDIRECT[[real number]]24 bytes (3 words) - 15:26, 3 February 2007
- #REDIRECT[[real number]]24 bytes (3 words) - 16:42, 10 July 2007
- {{r|Real number}}276 bytes (34 words) - 10:41, 21 April 2010
- Numbers of form a + bi + cj + dk, where a, b, c and d are [[real number|real]], and i<sup>2</sup> = −1, j<sup>2</sup> = −1 and k<sup>2</sup> =188 bytes (31 words) - 14:23, 8 March 2009
- In [[mathematics]], a '''normal number''' is a [[real number]] whose [[decimal expansion]] shows an equal proportion of each of the poss210 bytes (29 words) - 17:24, 7 February 2009
- An algebraic structure with operations generalising the familiar concepts of real number arithmetic.136 bytes (16 words) - 06:30, 1 January 2009
- **In [[mathematical analysis]], a domain is an [[open set]], usually in the [[real number|real]] or [[complex number]]s486 bytes (71 words) - 12:37, 31 May 2009
- A real number whose digits in some particular base occur equally often in the long run.123 bytes (19 words) - 13:17, 5 December 2008
- ...that for every real number <math>\epsilon>0</math> there exists a positive real number <math>T(\epsilon)</math> (note the dependence of ''T'' on <math>\epsilon</m ...nuity|continuous]] at ''t=0'' and with ''g(0)=0'', denotes that for every real number <math>\epsilon>0</math> there exists a [[topological space#Some topological2 KB (354 words) - 20:39, 20 February 2010
- ...addition]] and [[multiplication]] of [[integer]]s, [[rational number]]s, [[real number|real]] and [[complex number]]s. In this context commutativity is often ref695 bytes (102 words) - 19:40, 31 January 2009
- Constant real number equal to 2.71828 18284 59045 23536... that is the base of the natural logar138 bytes (16 words) - 15:13, 3 July 2008
- ...ch are mathematical constructs that generalize on the familiar concepts of real number arithmetic.194 bytes (25 words) - 13:32, 7 December 2008
- A [[differentiable function]] on the [[real number]]s is monotonic when its [[derivative]] is non-zero: this is a consequence In the case of [[real number|real]] sequences, a monotonic sequence converges if it is [[bounded set|bou1 KB (211 words) - 17:02, 7 February 2009
- ...]] ''f'' : ''A'' <math>\to</math> '''R''' from some [[set]] ''A'' to the [[Real number|real numbers]]680 bytes (101 words) - 21:28, 10 March 2008
- ...x-axis. The complex numbers left fixed by conjugation are precisely the [[real number]]s.906 bytes (139 words) - 13:16, 20 November 2008
- {{r|Real number}}1 KB (169 words) - 19:54, 11 January 2010
- A real number that cannot be expressed as a fraction, m / n, in which m and n are integer127 bytes (22 words) - 11:47, 29 November 2008
- ...> then the notation <math>f(t)=O(g(t))</math> indicates that there exist a real number ''T'' and a constant ''C'' such that <math>|f(t)|\leq C |g(t)|</math> for a ...solute value of another function, in that neigbourhood. For example, for a real number <math>t_0</math> the notation <math>f(t)=O(g(t-t_0))</math>, where ''g''('2 KB (283 words) - 06:18, 15 July 2008
- A real number and is the integer between 1 and -1, which signifies a value of nothing.122 bytes (19 words) - 02:51, 3 June 2008
- ...-ary operator, indicating the number of arguments it takes. In the case of real number addition, the operator is [[binary operation|binary]] because it takes two617 bytes (102 words) - 13:04, 12 December 2008
- {{r|Real number}}183 bytes (22 words) - 17:31, 1 January 2010
- {{r|Real number}}203 bytes (25 words) - 18:31, 26 October 2008
- Every cubic equation with [[real number]] [[coefficient]]s has at most three real roots, as dictated by the [[funda ...f a [[complex number]]. This is more difficult than finding the root of a real number, which is all that the quadratic formula requires. It is precisely this di3 KB (483 words) - 23:24, 17 December 2008
- {{r|Real number}}307 bytes (44 words) - 16:27, 26 July 2008
- ...|</math>. Then a set <math>A \subset X</math> is bounded if there exists a real number ''M'' > 0 such that <math>\|x\|\leq M</math> for all <math>x \in A</math>. Every bounded set of [[real number]]s has a [[supremum]] and an [[infimum]]. It follows that a [[monotonic seq1 KB (188 words) - 05:37, 29 December 2008
- {{r|Real number}}1 KB (146 words) - 16:32, 11 January 2010
- ...n defined on the set of [[positive integer]]s, usually with [[integer]], [[real number|real]] or [[complex number|complex]] values.1 KB (159 words) - 06:03, 15 June 2009
- 1 KB (191 words) - 17:30, 15 July 2009
- Suppose ''f''(''x'') is a [[real-valued function]] and ''a'' is a [[real number]]. The expression ...nterval]] containing ''a'' (except possibly at ''a'') and let ''L'' be a [[real number]].2 KB (285 words) - 05:41, 2 October 2010
- ...] is itself invertible: over a [[field (mathematics)|field]] such as the [[real number|real]] or [[complex number]]s, this is equivalent to specifying that the de1 KB (158 words) - 00:36, 18 April 2009
- {{r|real number}}224 bytes (27 words) - 11:52, 29 November 2008
- a real number (with the decimal expansion 0.000...), and a complex number (0+0i).2 KB (326 words) - 18:28, 17 July 2009
- {{r|Real number}}493 bytes (64 words) - 16:43, 11 January 2010
- {{r|Real number}}2 KB (247 words) - 17:28, 11 January 2010
- ...'d''=''b/a'' every rational or real number divides every other rational or real number.)3 KB (515 words) - 21:49, 22 July 2009
- ...n-commutative]] and [[Associative law|non-associative]] extension of the [[Real number|real numbers]]. They were were first discovered by John Graves, a friend of947 bytes (123 words) - 06:31, 14 September 2013
- {{r|Real number}}969 bytes (124 words) - 18:42, 11 January 2010
- {{r|Real number}}545 bytes (70 words) - 16:41, 16 July 2011
- '''0''' ('''zero''') is a [[real number]] and is the [[integer]] between [[1 (number)|1]] and [[-1 (number)|-1]], w1 KB (232 words) - 03:30, 6 November 2009
- {{r|Real number}}2 KB (206 words) - 19:38, 11 January 2010
- ...criptstyle \mathbb{Q}</math>. Then it can be shown that for an arbitrary [[real number]] ''a'' and desired accuracy <math>\scriptstyle \epsilon>0</math>, one can1 KB (232 words) - 15:27, 6 January 2009
- ...solve [[cubic equation|cubic equations]]. Even for equations with three [[real number|real]] solutions, the method they used sometimes required calculations wit4 KB (685 words) - 00:41, 6 May 2008
- '''Arithmetic''' is an elementary branch of [[mathematics]] in which [[real number]]s and relations among real numbers are studied and used to solve quantitat4 KB (562 words) - 18:28, 5 January 2010
- ...lds'' are algebraic structures that generalize on the familiar concepts of real number arithmetic. The set of rational numbers, the set of real numbers and the se3 KB (496 words) - 22:16, 7 February 2010
- ...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 and2 KB (385 words) - 19:06, 3 September 2008
- * The [[real number]]s form an ordered field in a unique way: the squares form the positive con2 KB (314 words) - 02:23, 23 November 2008
- * 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 the3 KB (379 words) - 13:22, 6 January 2013
- {{r|Real number}}237 bytes (29 words) - 08:06, 14 January 2009
- 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 poly3 KB (418 words) - 14:53, 4 March 2009
- More precisely, an α-quantile is a real number ''X''<sub>α</sub> and a real number <math>\alpha</math> (<math>0<\alpha<1</math>),3 KB (436 words) - 08:38, 21 January 2010
- {{r|Real number}}209 bytes (24 words) - 10:53, 6 November 2008
- ...ve, [[monotonic function|monotonic]] decreasing function of the positive [[real number|real]] variable ''x''. Suppose that the [[Laplace transform]]2 KB (362 words) - 16:05, 9 November 2008
- {{r|Real number}}942 bytes (125 words) - 18:29, 11 January 2010
- ...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''4 KB (629 words) - 16:46, 17 December 2008
- * The field '''R''' of [[real number]]s has only the identity automorphism. This is harder to prove, and relies3 KB (418 words) - 12:18, 20 December 2008
- ...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'' w2 KB (398 words) - 11:44, 15 June 2009
- {{r|Real number}}1 KB (136 words) - 11:36, 11 January 2010
- ...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 mult1 KB (225 words) - 22:09, 3 September 2010
- ...addition]] and [[multiplication]] of [[integer]]s, [[rational number]]s, [[real number|real]] and [[complex number]]s. In this context associativity is often ref2 KB (295 words) - 14:56, 12 December 2008
- ...a [[set]] that does not contain its boundary. Simplest examples include [[real number|real]] intervals without endpoints (commonly referred to as ''open interval1 KB (172 words) - 19:16, 24 March 2008
- ...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 va975 bytes (166 words) - 15:27, 6 January 2009
- ...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 operation2 KB (240 words) - 10:48, 21 September 2013
- ...and ''Y''. A [[complex number]] may be expressed as an ordered pair of [[real number]]s, the real and imaginary parts respectively.1 KB (213 words) - 07:01, 21 January 2009
- {{r|Real number}}449 bytes (60 words) - 20:34, 11 January 2010
- ...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 solution6 KB (951 words) - 05:01, 8 December 2009
- ...''', 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 comple8 KB (1,360 words) - 16:44, 17 December 2008
- ...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]].9 KB (1,446 words) - 08:52, 30 May 2009
- * '''Pseudocompact''' if every [[continuous function|continuous]] [[real number|real]]-valued [[function (mathematics)|function]] is bounded.2 KB (331 words) - 07:47, 30 December 2008
- {{r|Real number}}505 bytes (65 words) - 21:20, 11 January 2010
- 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 expansion10 KB (1,462 words) - 17:24, 25 August 2013
- 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 expansion10 KB (1,462 words) - 17:25, 25 August 2013
- {{r|Real number}}681 bytes (87 words) - 18:24, 11 January 2010
- ...'''characteristic function''' of any [[probability distribution]] on the [[real number|real]] line is given by the following formula, where ''X'' is any [[random2 KB (242 words) - 02:01, 2 February 2009
- {{r|Real number}}689 bytes (88 words) - 17:15, 11 January 2010
- ...heorem''' characterises the [[compact space|compact]] [[subset]]s of the [[real number]]s.2 KB (381 words) - 08:54, 29 December 2008
- 6 KB (1,077 words) - 19:25, 29 September 2020
- In [[mathematics]], an '''irrational number''' is any [[real number]] that is not a [[rational number]], i.e. it cannot be expressed as a [[fra4 KB (666 words) - 11:23, 3 October 2009
- {{r|Real number}}681 bytes (91 words) - 18:06, 11 January 2010
- ...nce of positive real numbers to [[limit of a sequence|converge]] against a real number4 KB (680 words) - 05:33, 2 February 2010
- {{r|Real number}}774 bytes (100 words) - 18:05, 11 January 2010
- ...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 number7 KB (1,160 words) - 07:41, 22 December 2008
- * 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 0623 bytes (95 words) - 00:59, 19 February 2009
- ...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 tr5 KB (924 words) - 16:35, 11 December 2008
- {{r|Real number}}837 bytes (109 words) - 16:27, 11 January 2010
- ...(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 (&thet3 KB (451 words) - 23:53, 20 February 2010
- '''e''' is a [[constant]] [[real number]] equal to 2.71828 18284 59045 23536.... [[Irrational number|Irrational]] a3 KB (527 words) - 12:19, 16 March 2008
- 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,7 KB (1,077 words) - 17:18, 10 January 2009
- ...]] coefficients. In this article, it is assumed that all polynomials have real number coefficients. See the [[polynonial equation/Advanced|"Advanced"]] subpage4 KB (647 words) - 16:35, 22 December 2008
- ...the complex numbers the series will have a radius of convergence ''R'', a real number with the property4 KB (785 words) - 14:27, 14 March 2021
- ...sts of [[row vector]]s <math>(x_1, \ldots, x_n)</math> with <math>n</math> real number entries.)3 KB (464 words) - 19:45, 1 December 2008
- * The set of all [[Borel set|Borel subsets]] of the [[real number|real line]] is a sigma-algebra.2 KB (314 words) - 16:35, 27 November 2008
- 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 with4 KB (604 words) - 23:44, 30 November 2010
- ...For the rest of the present article, all polynomials considered will have real number coefficients.8 KB (1,242 words) - 02:01, 10 November 2009
- .... Further let A<sub>1</sub> denote ''A'' itself. Let ''z'' be a positive real number and ''P''(''z'') denote the product of the primes in ''P'' which are ≤ '3 KB (473 words) - 15:39, 9 December 2008