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- In [[mathematics]], a '''rational number''' is a number that can be expressed as a [[ratio]] of two [[integer]]s. N ...common [[divisor]]s except 1 (i.e., they are [[coprime]]). Every non-zero rational number has exactly one simplest form of this type with a positive denominator. A f9 KB (1,446 words) - 08:52, 30 May 2009
- 12 bytes (1 word) - 07:56, 14 November 2007
- 94 bytes (15 words) - 09:18, 1 June 2008
- Auto-populated based on [[Special:WhatLinksHere/Rational number]]. Needs checking by a human.1 KB (169 words) - 19:54, 11 January 2010
Page text matches
- #REDIRECT [[Rational number]]29 bytes (3 words) - 21:58, 10 May 2007
- ...equirement. An algebraic number must be a root of a [[polynomial]] with [[rational number|rational]] coefficients.1 KB (179 words) - 14:14, 10 December 2008
- {{r|Rational number}}258 bytes (33 words) - 02:29, 8 February 2009
- Auto-populated based on [[Special:WhatLinksHere/Rational number]]. Needs checking by a human.1 KB (169 words) - 19:54, 11 January 2010
- ...equivalently, it is not a root of any polynomial whose coefficients are [[rational number|rational]].875 bytes (130 words) - 12:27, 8 May 2008
- ...ers 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
- ...with respect to a given [[prime number]] ''p'', on the field '''Q''' of [[rational number]]s is a [[metric space|metric]] which is a [[valuation]] on the field. Every non-zero rational number may be written uniquely in the form <math>p^n.r/s</math> where ''r'' and ''1 KB (168 words) - 12:39, 4 January 2009
- ...ed accuracy <math>\scriptstyle \epsilon>0</math>, one can always find some rational number ''q'' such that <math>\scriptstyle |q-a|<\epsilon</math>. Hence the set of1 KB (232 words) - 15:27, 6 January 2009
- {{r|Rational number}}710 bytes (90 words) - 19:54, 11 January 2010
- ...atics]], an '''irrational number''' is any [[real number]] that is not a [[rational number]], i.e. it cannot be expressed as a [[fraction]] ''m'' / ''n'' in ...mber is frequently approximated by 22/7 = 3.142857142957... But 22/7 is a rational number, so this cannot be exact.4 KB (666 words) - 11:23, 3 October 2009
- {{r|Rational number}}1 KB (146 words) - 16:32, 11 January 2010
- ...tor''' refers to a number field regarded as an extension of the field of [[rational number]]s. There need not be a conductor for an extension: indeed, [[class field1 KB (177 words) - 01:07, 18 February 2009
- {{r|Rational number}}887 bytes (126 words) - 02:29, 22 December 2008
- ...e product of integral powers of prime numbers (and such factorization or a rational number corresponds to the unique [[lowest terms]] representation of the number as2 KB (371 words) - 00:36, 2 February 2009
- — "[[rational number|rational]]", "[[irrational number|irrational]]", and "[[real number|real]]"3 KB (468 words) - 17:28, 1 January 2010
- ...tive operations are [[addition]] and [[multiplication]] of [[integer]]s, [[rational number]]s, [[real number|real]] and [[complex number]]s. In this context commutat695 bytes (102 words) - 19:40, 31 January 2009
- In [[mathematics]], a '''rational number''' is a number that can be expressed as a [[ratio]] of two [[integer]]s. N ...common [[divisor]]s except 1 (i.e., they are [[coprime]]). Every non-zero rational number has exactly one simplest form of this type with a positive denominator. A f9 KB (1,446 words) - 08:52, 30 May 2009
- The [[rational number]] 22/7 is the most widely cited rational approximation to [[pi|π]]. It2 KB (219 words) - 15:08, 8 December 2009
- {{r|Rational number}}592 bytes (77 words) - 19:15, 11 January 2010
- ...since an automorphism must map the [[unit element]] 1 to itself, and every rational number may be obtained from 1 by field operations. which are preserved by automorp3 KB (418 words) - 12:18, 20 December 2008
- ...umber''' is a [[complex number]] that is a root of a [[polynomial]] with [[rational number|rational]] coefficients. * Rational numbers are algebraic and of degree <math>\ 1.</math> The rational number ''a'' has defining polynomial <math> x-a </math>. All non-rational algebrai7 KB (1,145 words) - 00:49, 20 October 2013
- {{r|Rational number}}2 KB (247 words) - 17:28, 11 January 2010
- ''zero'' is an integer, a rational number (the fraction 0/1),2 KB (326 words) - 18:28, 17 July 2009
- ...lve only small class of cubic equations, namely, those with at least one [[rational number|rational]] root. For such equations, all roots can be found by [[factor|fa3 KB (483 words) - 23:24, 17 December 2008
- When dealing with <math>\mathbb{Q}</math>, the set of [[rational number]]s, we notice several things:3 KB (496 words) - 22:16, 7 February 2010
- {{r|Rational number}}675 bytes (89 words) - 17:28, 11 January 2010
- {{r|Rational number}}942 bytes (125 words) - 18:29, 11 January 2010
- {{r|Rational number}}482 bytes (62 words) - 20:41, 11 January 2010
- Many common number systems, such as the [[integer]]s, the [[rational number]]s, the [[real number]]s, and the [[complex number]]s are abelian groups wi2 KB (240 words) - 10:48, 21 September 2013
- ...i.e. it is not solution of any [[polynomial]] having a finite number of [[rational number|rational]] coefficients.3 KB (527 words) - 12:19, 16 March 2008
- {{r|Rational number}}649 bytes (85 words) - 15:41, 11 January 2010
- The minimal poynomial of an [[algebraic number]] α is the [[rational number|rational]] [[polynomial]] of least [[degree of a polynomial|degree]] which4 KB (613 words) - 02:34, 4 January 2013
- ...not matter that — because the fractions are not reduced — each rational number appears infinitely often.10 KB (1,462 words) - 17:25, 25 August 2013
- ...not matter that — because the fractions are not reduced — each rational number appears infinitely often.10 KB (1,462 words) - 17:24, 25 August 2013
- .... In this article we treat quadratic extensions of the field '''Q''' of [[rational number]]s. ...is of the form <math>\mathbf{Q}(\sqrt d)</math> for a non-zero non-square rational number ''d''. Multiplying by a square integer, we may assume that ''d'' is in fac3 KB (453 words) - 17:18, 6 February 2009
- ...to zero. By division the set of integral numbers is augmented with the [[rational number]]s (quotients of two integral numbers).4 KB (562 words) - 18:28, 5 January 2010
- ...tive operations are [[addition]] and [[multiplication]] of [[integer]]s, [[rational number]]s, [[real number|real]] and [[complex number]]s. In this context associat2 KB (295 words) - 14:56, 12 December 2008
- Value <math>\ g(x)</math> is a rational number whenever ''x'' is rational. For instance, for ''x'' = ½:5 KB (743 words) - 13:10, 27 July 2008
- * The [[rational number]]s as a [[subspace]] of the [[real number]]s with the Euclidean metric topo3 KB (379 words) - 13:22, 6 January 2013
- * The [[rational number]]s form an ordered field in a unique way.2 KB (314 words) - 02:23, 23 November 2008
- ...yle k = 1, \ldots, 13 </math>. In each case, he found that the value is a rational number times <math> \scriptstyle \pi^{2k} </math> Later, he discovered a general7 KB (1,113 words) - 10:50, 4 October 2013
- # The [[rational number]]s (<math> \scriptstyle \mathbb{Q} </math>) are any number that can be repr ...2}</math> are both irrational. This set does not share any member with the rational number set.11 KB (1,701 words) - 20:07, 1 July 2021
- ...tably compact]]. But '''R''' is [[separable space|separable]] since the [[rational number]]s '''Q''' form a [[countability|countable]] [[dense set]], and this applie2 KB (381 words) - 08:54, 29 December 2008
- ...se "ordinary" integers, embedded in the [[field (mathematics)|field]] of [[rational number]]s, from other "integers" such as the [[algebraic integer]]s. ...ics)|field]]. The smallest field containing the integers is the field of [[rational number]]s. This process can be mimicked to form the [[field of fractions]] of any10 KB (1,566 words) - 08:34, 2 March 2024
- ...of [[mathematics]]. It studies the approximations of [[real number]]s by [[rational number]]s. This article presents an elementary introduction to diophantine approxi ...o this end we will not worry about the details of the difference between a rational number and a fraction (with integer numerator and denominator)—this will not35 KB (5,836 words) - 08:40, 15 March 2021
- A real number may be either [[rational number|rational]] or [[irrational number|irrational]]; either [[algebraic number|a ...94) completed the proof, and showed that π is not the square root of a rational number. [[Paolo Ruffini|Ruffini]] (1799) and [[Niels Henrik Abel|Abel]] (1842) bot19 KB (2,948 words) - 10:07, 28 February 2024
- **The [[rational number|rational]], [[real number|real]] and [[complex number|complex]] numbers eac10 KB (1,667 words) - 13:47, 5 June 2011
- ...ation <math>x^2=2</math> has no solutions if the domain is formed by the [[rational number]]s, it has two solutions (namely, <math>x=\sqrt{2}</math> and <math>x=-\sqr6 KB (951 words) - 05:01, 8 December 2009
- ...problem with polynomials over rings of usual numbers like [[integer]]s, [[rational number|rational]], [[real number|real]] or [[complex number|complex]] numbers. Sti10 KB (1,741 words) - 10:04, 3 January 2009
- ...gree [[field extension]] of the [[field (mathematics)|field]] '''Q''' of [[rational number]]s. The elements of ''K'' are thus [[algebraic number]]s. Let ''n'' = [''7 KB (1,077 words) - 17:18, 10 January 2009
- ...ps. These include familiar number systems, such as the [[integer]]s, the [[rational number]]s, the [[real number]]s, and the [[complex number]]s under addition, as we Consider the set of [[rational number]]s '''Q''', that is the set of numbers ''a''/''b'' such that19 KB (3,074 words) - 11:11, 13 February 2009
- ...s of a whole object, if the object is divided into five equal parts. Any [[rational number]] can be written as a fraction.21 KB (3,089 words) - 10:08, 28 February 2024
- is a fixed rational number whose square root is not rational.)27 KB (4,383 words) - 08:05, 11 October 2011
- ...to allow many other types of exponents, including [[negative integer]]s, [[rational number]]s, [[real number]]s, [[complex number]]s, and even [[matrix|matrices]], [[8 KB (1,297 words) - 14:49, 12 December 2008
- ...tity element is 1, since 1 × ''a'' = ''a'' × 1 = ''a'' for any rational number ''a''. The inverse of ''a'' is 1/''a'', since ''a'' × 1/''a'' = 1.18 KB (2,669 words) - 08:38, 17 April 2024
- thus being the basis for fractions and [[rational number]]s.16 KB (2,562 words) - 00:45, 13 October 2009
- *<math>\mathbb{Q}</math>, the set of [[rational number|rational numbers]]17 KB (2,828 words) - 10:37, 24 July 2011
- ...al function of <math>r</math> whenever <math>n</math> is an integer, and a rational number whenever <math>r</math> is rational.<ref>Assuming that no poles are encount32 KB (5,024 words) - 12:05, 22 December 2008
- ...The traditional Japanese mathematicians did not discriminate between the [[rational number|rational]] and the [[irrational number|irrational]] numbers, since they did15 KB (2,247 words) - 10:12, 28 February 2024
- ...y on <math>(0,1),</math> and <math>B</math> the event "<math>X</math> is a rational number"; what about <math>P(X=1/n|B)?</math>32 KB (5,149 words) - 15:48, 29 June 2009
- | [[Natural number]]s|| [[Whole number]]s|| [[Integer]]s || [[Rational number]]s || [[Real number]]s || [[Complex number]]s30 KB (4,289 words) - 16:03, 20 January 2023