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  • Imaginary number/Definition
    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
  • Limit of a sequence
    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 write
    771 bytes (122 words) - 09:45, 28 November 2007
  • Vitali set/Definition
    ...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
  • Square root of two/Definition
    The positive real number that, when multiplied by itself, gives the number 2.
    114 bytes (15 words) - 19:41, 4 September 2009
  • Number/Related Articles
    {{r|Real number}}
    258 bytes (33 words) - 02:29, 8 February 2009
  • Imaginary number
    the sum ''a''+''b''i of a real number ''a'' and an imaginary number ''b''i ...up>2</sup> = &minus;''b''<sup>2</sup> of an imaginary number is a negative real number,
    3 KB (468 words) - 17:28, 1 January 2010
  • Real numbers
    #REDIRECT[[real number]]
    24 bytes (3 words) - 15:26, 3 February 2007
  • Real line
    #REDIRECT[[real number]]
    24 bytes (3 words) - 16:42, 10 July 2007
  • Complex number/Related Articles
    {{r|Real number}}
    276 bytes (34 words) - 10:41, 21 April 2010
  • Quaternions/Definition
    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
  • Normal number
    In [[mathematics]], a '''normal number''' is a [[real number]] whose [[decimal expansion]] shows an equal proportion of each of the poss
    210 bytes (29 words) - 17:24, 7 February 2009
  • Field (mathematics)/Definition
    An algebraic structure with operations generalising the familiar concepts of real number arithmetic.
    136 bytes (16 words) - 06:30, 1 January 2009
  • Domain (disambiguation)
    **In [[mathematical analysis]], a domain is an [[open set]], usually in the [[real number|real]] or [[complex number]]s
    486 bytes (71 words) - 12:37, 31 May 2009
  • Normal number/Definition
    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
  • Little o notation
    ...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 topological
    2 KB (354 words) - 20:39, 20 February 2010
  • Commutativity
    ...addition]] and [[multiplication]] of [[integer]]s, [[rational number]]s, [[real number|real]] and [[complex number]]s. In this context commutativity is often ref
    695 bytes (102 words) - 19:40, 31 January 2009
  • E (mathematics)/Definition
    Constant real number equal to 2.71828 18284 59045 23536... that is the base of the natural logar
    138 bytes (16 words) - 15:13, 3 July 2008
  • Field theory (mathematics)/Definition
    ...ch are mathematical constructs that generalize on the familiar concepts of real number arithmetic.
    194 bytes (25 words) - 13:32, 7 December 2008
  • Monotonic function
    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|bou
    1 KB (211 words) - 17:02, 7 February 2009
  • Optimization (mathematics)
    ...]] ''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
  • Complex conjugation
    ...x-axis. The complex numbers left fixed by conjugation are precisely the [[real number]]s.
    906 bytes (139 words) - 13:16, 20 November 2008
  • Rational number/Related Articles
    {{r|Real number}}
    1 KB (169 words) - 19:54, 11 January 2010
  • Irrational number/Definition
    A real number that cannot be expressed as a fraction, m / n, in which m and n are integer
    127 bytes (22 words) - 11:47, 29 November 2008
  • Big O notation
    ...> 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
  • 0 (number)/Definition
    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
  • Operation (mathematics)
    ...-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 two
    617 bytes (102 words) - 13:04, 12 December 2008
  • Imaginary number/Related Articles
    {{r|Real number}}
    183 bytes (22 words) - 17:31, 1 January 2010
  • Exponent/Related Articles
    {{r|Real number}}
    203 bytes (25 words) - 18:31, 26 October 2008
  • Cubic equation
    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 di
    3 KB (483 words) - 23:24, 17 December 2008
  • Cantor's diagonal argument/Related Articles
    {{r|Real number}}
    307 bytes (44 words) - 16:27, 26 July 2008
  • Bounded set
    ...|</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 seq
    1 KB (188 words) - 05:37, 29 December 2008
  • Field (mathematics)/Related Articles
    {{r|Real number}}
    1 KB (146 words) - 16:32, 11 January 2010
  • Arithmetic function
    ...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
  • Finite and infinite
    1 KB (191 words) - 17:30, 15 July 2009
  • Limit of a function
    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
  • Matrix inverse
    ...] 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 de
    1 KB (158 words) - 00:36, 18 April 2009
  • Irrational number/Related Articles
    {{r|real number}}
    224 bytes (27 words) - 11:52, 29 November 2008
  • Zero (mathematics)
    a real number (with the decimal expansion 0.000...), and a complex number (0+0i).
    2 KB (326 words) - 18:28, 17 July 2009
  • Fundamental Theorem of Algebra/Related Articles
    {{r|Real number}}
    493 bytes (64 words) - 16:43, 11 January 2010
  • Integer/Related Articles
    {{r|Real number}}
    2 KB (247 words) - 17:28, 11 January 2010
  • Divisibility
    ...'d''=''b/a'' every rational or real number divides every other rational or real number.)
    3 KB (515 words) - 21:49, 22 July 2009
  • Octonions
    ...n-commutative]] and [[Associative law|non-associative]] extension of the [[Real number|real numbers]]. They were were first discovered by John Graves, a friend of
    947 bytes (123 words) - 06:31, 14 September 2013
  • Multiplication/Related Articles
    {{r|Real number}}
    969 bytes (124 words) - 18:42, 11 January 2010
  • Mathematical notation/Related Articles
    {{r|Real number}}
    545 bytes (70 words) - 16:41, 16 July 2011
  • 0 (number)
    '''0''' ('''zero''') is a [[real number]] and is the [[integer]] between [[1 (number)|1]] and [[-1 (number)|-1]], w
    1 KB (232 words) - 03:30, 6 November 2009
  • Polynomial/Related Articles
    {{r|Real number}}
    2 KB (206 words) - 19:38, 11 January 2010
  • Denseness
    ...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 can
    1 KB (232 words) - 15:27, 6 January 2009
  • Complex number/Advanced
    ...solve [[cubic equation|cubic equations]]. Even for equations with three [[real number|real]] solutions, the method they used sometimes required calculations wit
    4 KB (685 words) - 00:41, 6 May 2008
  • Arithmetic
    '''Arithmetic''' is an elementary branch of [[mathematics]] in which [[real number]]s and relations among real numbers are studied and used to solve quantitat
    4 KB (562 words) - 18:28, 5 January 2010
  • Field (mathematics)
    ...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 se
    3 KB (496 words) - 22:16, 7 February 2010
  • Scientific notation
    ...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
    2 KB (385 words) - 19:06, 3 September 2008
  • Ordered field
    * The [[real number]]s form an ordered field in a unique way: the squares form the positive con
    2 KB (314 words) - 02:23, 23 November 2008
  • Connected space
    * 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
    3 KB (379 words) - 13:22, 6 January 2013
  • Logarithm/Related Articles
    {{r|Real number}}
    237 bytes (29 words) - 08:06, 14 January 2009
  • Linear equation/Advanced
    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
    3 KB (418 words) - 14:53, 4 March 2009
  • Quantile
    More precisely, an &alpha;-quantile is a real number ''X''<sub>&alpha;</sub> and a real number <math>\alpha</math> (<math>0<\alpha<1</math>),
    3 KB (436 words) - 08:38, 21 January 2010
  • Power law/Related Articles
    {{r|Real number}}
    209 bytes (24 words) - 10:53, 6 November 2008
  • Wiener-Ikehara theorem
    ...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
  • Metric space/Related Articles
    {{r|Real number}}
    942 bytes (125 words) - 18:29, 11 January 2010
  • Cauchy-Schwarz inequality
    ...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
  • Field automorphism
    * The field '''R''' of [[real number]]s has only the identity automorphism. This is harder to prove, and relies
    3 KB (418 words) - 12:18, 20 December 2008
  • Dirichlet series
    ...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
    2 KB (398 words) - 11:44, 15 June 2009
  • Calculus/Related Articles
    {{r|Real number}}
    1 KB (136 words) - 11:36, 11 January 2010
  • Numerical analysis
    ...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
    1 KB (225 words) - 22:09, 3 September 2010
  • Associativity
    ...addition]] and [[multiplication]] of [[integer]]s, [[rational number]]s, [[real number|real]] and [[complex number]]s. In this context associativity is often ref
    2 KB (295 words) - 14:56, 12 December 2008
  • Open set
    ...a [[set]] that does not contain its boundary. Simplest examples include [[real number|real]] intervals without endpoints (commonly referred to as ''open interval
    1 KB (172 words) - 19:16, 24 March 2008
  • Totally bounded set
    ...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
    975 bytes (166 words) - 15:27, 6 January 2009
  • Abelian group
    ...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
    2 KB (240 words) - 10:48, 21 September 2013
  • Ordered pair
    ...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
  • Square root of two/Related Articles
    {{r|Real number}}
    449 bytes (60 words) - 20:34, 11 January 2010
  • Equation (mathematics)
    ...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
    6 KB (951 words) - 05:01, 8 December 2009
  • Quadratic equation
    ...''', 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
    8 KB (1,360 words) - 16:44, 17 December 2008
  • Rational number
    ...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
  • Compactness axioms
    * '''Pseudocompact''' if every [[continuous function|continuous]] [[real number|real]]-valued [[function (mathematics)|function]] is bounded.
    2 KB (331 words) - 07:47, 30 December 2008
  • Uniform space/Related Articles
    {{r|Real number}}
    505 bytes (65 words) - 21:20, 11 January 2010
  • Countable set
    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
    10 KB (1,462 words) - 17:25, 25 August 2013
  • Countable set/Citable Version
    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
    10 KB (1,462 words) - 17:24, 25 August 2013
  • Measure (mathematics)/Related Articles
    {{r|Real number}}
    681 bytes (87 words) - 18:24, 11 January 2010
  • Characteristic function
    ...'''characteristic function''' of any [[probability distribution]] on the [[real number|real]] line is given by the following formula, where ''X'' is any [[random
    2 KB (242 words) - 02:01, 2 February 2009
  • Homeomorphism/Related Articles
    {{r|Real number}}
    689 bytes (88 words) - 17:15, 11 January 2010
  • Heine–Borel theorem
    ...heorem''' characterises the [[compact space|compact]] [[subset]]s of the [[real number]]s.
    2 KB (381 words) - 08:54, 29 December 2008
  • Complex analysis
    6 KB (1,077 words) - 19:25, 29 September 2020
  • Irrational number
    In [[mathematics]], an '''irrational number''' is any [[real number]] that is not a [[rational number]], i.e. it cannot be expressed as a [[fra
    4 KB (666 words) - 11:23, 3 October 2009
  • Limit of a sequence/Related Articles
    {{r|Real number}}
    681 bytes (91 words) - 18:06, 11 January 2010
  • Necessary and sufficient
    ...nce of positive real numbers to [[limit of a sequence|converge]] against a real number
    4 KB (680 words) - 05:33, 2 February 2010
  • Limit (mathematics)/Related Articles
    {{r|Real number}}
    774 bytes (100 words) - 18:05, 11 January 2010
  • Quaternions
    ...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
    7 KB (1,160 words) - 07:41, 22 December 2008
  • Door space
    * 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
    623 bytes (95 words) - 00:59, 19 February 2009
  • Fundamental Theorem of Algebra
    ...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
    5 KB (924 words) - 16:35, 11 December 2008
  • Exponential function/Related Articles
    {{r|Real number}}
    837 bytes (109 words) - 16:27, 11 January 2010
  • Polar coordinates
    ...(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
    3 KB (451 words) - 23:53, 20 February 2010
  • E (mathematics)
    '''e''' is a [[constant]] [[real number]] equal to 2.71828 18284 59045 23536.... [[Irrational number|Irrational]] a
    3 KB (527 words) - 12:19, 16 March 2008
  • Algebraic number field
    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
  • Polynomial equation
    ...]] coefficients. In this article, it is assumed that all polynomials have real number coefficients. See the [[polynonial equation/Advanced|"Advanced"]] subpage
    4 KB (647 words) - 16:35, 22 December 2008
  • Power series
    ...the complex numbers the series will have a radius of convergence ''R'', a real number with the property
    4 KB (785 words) - 14:27, 14 March 2021
  • Basis (linear algebra)
    ...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
  • Sigma algebra
    * 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
  • Inhomogeneous Helmholtz equation
    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
    4 KB (604 words) - 23:44, 30 November 2010
  • Polynomial
    ...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
  • Selberg sieve
    .... 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 &le; '
    3 KB (473 words) - 15:39, 9 December 2008
  • Cauchy-Riemann equations
    ...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
    6 KB (874 words) - 03:45, 7 October 2013
  • Discrete probability distribution
    Let A=[0,1}, a proper subset of the [[real number]]s '''R'''.
    4 KB (590 words) - 09:17, 26 September 2007
  • Algebra over a field
    ...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.
    1 KB (155 words) - 15:55, 23 December 2008
  • Complex number
    ...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
    18 KB (3,028 words) - 17:12, 25 August 2013
  • Stochastic convergence
    ...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
    11 KB (1,680 words) - 19:57, 29 September 2020
  • Field extension
    ...the field of [[complex number]]s '''C''' is an extension of the field of [[real number]]s '''R'''.
    3 KB (435 words) - 22:38, 22 February 2009
  • Number
    * 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
    11 KB (1,701 words) - 20:07, 1 July 2021
  • Fourier series
    ...an infinite series representation of a [[periodic function]] ''ƒ'' of a [[real number|real]] variable &xi;, of period ''P'':
    7 KB (1,088 words) - 10:11, 11 June 2012
  • Real number
    ...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
    19 KB (2,948 words) - 10:07, 28 February 2024
  • Compact space
    ** A continuous [[real number|real]]-valued function on a compact space is [[bounded set|bounded]] and at
    4 KB (652 words) - 14:44, 30 December 2008
  • Turan sieve
    .... 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 &le; '
    3 KB (494 words) - 15:55, 29 October 2008
  • Vector space
    ...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''<sub>''k''</sub>+''y''<sub>''k''</sub> is a well-defined real number.
    15 KB (2,506 words) - 05:16, 11 May 2011
  • Rigid motion
    ...rd Euclidean space of ''n'' dimensions as an [[affine space]] built on a [[real number|real]] [[vector space]] '''R'''<sup>''n''</sup> then the translations are t
    3 KB (392 words) - 14:42, 28 November 2008
  • Integer
    ...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
    10 KB (1,566 words) - 08:34, 2 March 2024
  • Polynomial/Advanced
    ...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
    10 KB (1,741 words) - 10:04, 3 January 2009
  • Complex number/Citable Version
    ...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
    20 KB (3,304 words) - 17:11, 25 August 2013
  • Continuous probability distribution
    The height of an individual is a real number that in principle may take on any value.
    3 KB (390 words) - 07:22, 26 September 2007
  • Ring (mathematics)
    **The [[rational number|rational]], [[real number|real]] and [[complex number|complex]] numbers each form commutative rings.
    10 KB (1,667 words) - 13:47, 5 June 2011
  • Vector (mathematics)
    ...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
    4 KB (632 words) - 10:13, 6 January 2010
  • Quadratic equation/Advanced
    ...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
    10 KB (1,580 words) - 08:52, 4 March 2009
  • Exponent
    ...pes of exponents, including [[negative integer]]s, [[rational number]]s, [[real number]]s, [[complex number]]s, and even [[matrix|matrices]], [[set (mathematics)|
    8 KB (1,297 words) - 14:49, 12 December 2008
  • Generic point
    ...p> + ''Y''<sup>2</sup> = 1 defined over the [[field (algebra)|field]] of [[real number]]s. The point
    1 KB (240 words) - 20:00, 7 February 2009
  • Ohm's law
    ...or the material. For homogeneous and isotropic materials the tensor is a real number &sigma;<sub>0</sub> times a 3&times;3 [[identity matrix]]. The scalar &sig
    1 KB (225 words) - 02:06, 24 October 2009
  • Extreme value
    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
    3 KB (538 words) - 18:17, 17 January 2010
  • Cauchy sequence
    ...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)</
    1 KB (240 words) - 12:30, 4 January 2009
  • Measure (mathematics)
    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
    14 KB (2,350 words) - 17:37, 10 November 2007
  • Distribution (mathematics)
    ...ous linear functional on ''K'', if ''f'' maps all elements of ''K'' onto a real number (''f'', &phi;) such that
    5 KB (786 words) - 21:28, 19 February 2010
  • Group theory
    ...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
    15 KB (2,535 words) - 20:29, 14 February 2010
  • Number theory/Signed Articles/Elementary diophantine approximations
    ...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
    35 KB (5,836 words) - 08:40, 15 March 2021
  • Observable (quantum computation)
    ...[[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
    3 KB (562 words) - 00:00, 17 February 2010
  • Cartesian coordinates
    In plane [[analytical geometry]], '''Cartesian coordinates''' are two [[real number]]s specifying a [[point (geometry)|point]] in a [[Euclid|Euclidean]] plane
    4 KB (679 words) - 03:09, 8 March 2024
  • Algebra
    ...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]].
    18 KB (2,669 words) - 08:38, 17 April 2024
  • Set (mathematics)
    *<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
    17 KB (2,828 words) - 10:37, 24 July 2011
  • Logarithm
    ...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
    19 KB (3,039 words) - 12:51, 7 March 2023
  • Function (mathematics)
    ...ote that log(''x'') is defined only for positive ''x'', but takes on all [[real number|real]] values.
    15 KB (2,342 words) - 06:26, 30 November 2011
  • Dot product
    ...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
    3 KB (575 words) - 12:41, 14 February 2011
  • Hausdorff dimension
    ...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
    15 KB (2,549 words) - 09:18, 17 February 2012
  • Lambert W function
    ...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
    14 KB (2,354 words) - 21:43, 25 September 2011
  • Particle in a box
    ...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).
    16 KB (2,810 words) - 11:31, 5 April 2011
  • Computer/Related Articles
    {{r|Real number}}
    3 KB (441 words) - 12:55, 13 November 2014
  • DCTIII
    ...indicates value <math>N=2^q</math>; where <math>q</math> is assumed to be real number.
    8 KB (1,204 words) - 18:09, 8 September 2020
  • Space (mathematics)
    ...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
    28 KB (4,311 words) - 08:36, 14 October 2010
  • Rayleigh-Ritz method
    ...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
    12 KB (1,893 words) - 04:51, 25 March 2010
  • Sine
    ...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.
    19 KB (3,106 words) - 09:53, 10 October 2013
  • Proof assistant
    ...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
    21 KB (3,291 words) - 16:07, 3 November 2013
  • Gamma function
    ...r of this article, "positive" will be understood to mean either a positive real number or a complex number with positive real part.</ref>
    32 KB (5,024 words) - 12:05, 22 December 2008
  • Trigonometric function
    ...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
    33 KB (5,179 words) - 08:26, 4 June 2010
  • Simon Stevin
    ...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
    8 KB (1,266 words) - 03:23, 27 April 2010
  • Harmonic oscillator (classical)
    ...nts. Further the unit of time is undetermined and hence we scale time by a real number &omega;. In total the trial function is
    11 KB (1,757 words) - 11:17, 11 September 2021
  • Group (mathematics)
    ...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
    19 KB (3,074 words) - 11:11, 13 February 2009
  • Mathematics
    ...number]]s|| [[Whole number]]s|| [[Integer]]s || [[Rational number]]s || [[Real number]]s || [[Complex number]]s
    30 KB (4,289 words) - 16:03, 20 January 2023
  • Crystal field theory
    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
    15 KB (2,390 words) - 10:11, 5 February 2010
  • Magnetism
    ...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
    7 KB (1,065 words) - 11:42, 12 October 2011
  • Normal distribution
    ...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
    46 KB (6,956 words) - 07:01, 9 June 2009
  • Work (physics)
    ...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
    17 KB (2,892 words) - 23:00, 26 May 2010
  • Polarizability
    ...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
    12 KB (1,839 words) - 10:43, 5 October 2009
  • Classical mechanics
    Each body is attributed some positive [[real number]] called [[mass]]. The mass of each body determines, how the body reacts t
    27 KB (4,192 words) - 17:33, 19 August 2020
  • Pitch (music)
    ...al Instrument Digital Interface)|MIDI]] standard to map a frequency ƒ to a real number ''n'' as follows
    32 KB (5,025 words) - 10:07, 28 February 2024
  • Heterotaxis
    ...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
    22 KB (3,143 words) - 14:30, 19 March 2023
  • Logic
    ...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
    32 KB (4,979 words) - 21:47, 12 November 2011
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