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- In the following, we state two equivalent forms of the theorem, and show their equivalence. Later, we prove the theorem. This is done in the following steps: ...23 KB (4,033 words) - 16:33, 26 November 2007
- This is an example on how to design proofs. ==The square root of 2 is irrational theorem== ...2 KB (324 words) - 08:04, 22 December 2007
- The claim is made that −div is adjoint to ''d'': Proof of the above statement: ...3 KB (537 words) - 01:15, 9 November 2007
- * '''Claim:''' The volume of a conic solid whose base has area ''b'' and whose height is ''h'' is <math> ...ath>. Let <math> \vec v </math> be the vertex point, outside of the plane of <math> \vec \alpha </math>. ...5 KB (915 words) - 02:26, 2 December 2007
- <center><math>(x - h)^2 = 4p(y - k)</math></center> and that the vertex of this parabola is (''h'',''k'') |(4) Line ''l'', which is represented by the equation <math>y =k - p</math> ...4 KB (725 words) - 02:28, 2 December 2007
- ...>AC^2 + BC^2 = AB^2</math>, or <math>a^2 + b^2 = c^2</math> where ''c'' is the hypotenuse. This proof uses the following: ...3 KB (501 words) - 02:32, 2 December 2007
- ... if and only if ''x'' = ''y'' (''identity of indiscernibles'') ...s omitted and one just writes ''M'' for a metric space if it is clear from the context what metric is used. ...4 KB (787 words) - 01:17, 9 November 2007
- [[Image:Matrix.png|thumb|200px|right|Organization of a matrix]] ...th> where A = {1,2...m} [[w:Cartesian product|×]] {1,2...n} and F is the field under consideration. ...5 KB (956 words) - 01:07, 9 November 2007
- ==Lemma for the eigenspace== All eigenvectors of the linear transformation ''A'' that correspond to the eigenvalue λ form a subspace ''L''<sup>(λ)</sup> <math>\scriptstyle\subset< ...2 KB (343 words) - 15:48, 29 February 2008
- ...identities involving the [[totient function]] <math>\varphi(k)</math> and the [[Möbius function]] <math>\mu(k)</math>. ==Sum of integers relatively prime to and less than or equal to ''n''== ...13 KB (2,257 words) - 17:19, 16 December 2007
- ...oofs relating to prime numbers. Because the definitions are quite similar, proofs relating to irreducible numbers will also go on this page. == Definition of Prime == ...1 KB (202 words) - 08:27, 3 January 2008
- ==Definition of divisibility== If <math> a | b</math> and 0 < a < b then a is called a proper divisor of b. The notation <math> a^k || b</math> is used to indicate that <math> a^k | b</ma ...7 KB (1,201 words) - 18:36, 2 February 2008
- ==Property of R. Bryant's parametrization== ...the functions ''g<sub>1</sub>'', ''g<sub>2</sub>'', and ''g<sub>3</sub>'' of ''z'' are left unchanged. ...13 KB (2,087 words) - 18:38, 22 December 2007
Page text matches
- ...oofs relating to prime numbers. Because the definitions are quite similar, proofs relating to irreducible numbers will also go on this page. == Definition of Prime == ...1 KB (202 words) - 08:27, 3 January 2008
- ... if and only if ''x'' = ''y'' (''identity of indiscernibles'') ...s omitted and one just writes ''M'' for a metric space if it is clear from the context what metric is used. ...4 KB (787 words) - 01:17, 9 November 2007
- This is an example on how to design proofs. ==The square root of 2 is irrational theorem== ...2 KB (324 words) - 08:04, 22 December 2007
- The claim is made that −div is adjoint to ''d'': Proof of the above statement: ...3 KB (537 words) - 01:15, 9 November 2007
- ==Section 2.1 - Proofs== ...n output. There are three types of proofs depending on which is easiest to the student. ...7 KB (1,162 words) - 19:37, 9 January 2008
- [[Image:Matrix.png|thumb|200px|right|Organization of a matrix]] ...th> where A = {1,2...m} [[w:Cartesian product|×]] {1,2...n} and F is the field under consideration. ...5 KB (956 words) - 01:07, 9 November 2007
- ...lity, the statistician uses it to build models, but what is mathematics to the mathematician? ...ore interesting than others. For instance, if we were to redefine equality of numbers so that any two numbers were equal, we would have a well defined sy ...3 KB (573 words) - 00:26, 4 December 2007
- {{Navigate|Book=Geometry for elementary school|Prev=Lines|Curr=Constructing equilateral tri ...quilateral" mean? It simply means that all three sides of the triangle are the same length.<br/> ...6 KB (980 words) - 01:47, 20 December 2007
- ...ble (let us call this ''y''), and one or more [[w:derivative|derivatives]] of ''y'' with respect to ''x''. For example: ...f change. Using differential equations you can work from that equation to the equation you really want. Differential equations reflect changing patterns ...4 KB (716 words) - 05:15, 29 October 2007
- ==Definition of divisibility== If <math> a | b</math> and 0 < a < b then a is called a proper divisor of b. The notation <math> a^k || b</math> is used to indicate that <math> a^k | b</ma ...7 KB (1,201 words) - 18:36, 2 February 2008
- <noinclude>{{Mathematical Proof/navigation}}</noinclude> ...ader of what notation means. This section is to introduce the notation to the reader and explain its usage. ...12 KB (2,194 words) - 01:44, 5 April 2007
- ...h some aspects of the book. It seeks to maintain a simple approach but the proofs being correct, in some cases however it was necessary to make recourse to s ...roofs. It will be proved in a graphical manner utilising only the concepts of elementary geometry. Pythagoras’ proof will not be quoted being very comple ...16 KB (2,833 words) - 22:25, 29 May 2007
- ...the very beginning. A very good place to start" - ''[[Wikipedia:The Sound of Music | do-re-mi]]'' Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning. ...13 KB (2,270 words) - 21:29, 12 October 2007
- ...the concept of distance, though this will not be immediately apparent for the novice student. Topology generalises many distance related concepts, such a For an overview of the subject of topology, please see the Wikipedia [http://en.wikipedia.org/wiki/Topology entry]. ...6 KB (786 words) - 12:28, 30 January 2008
- ''Preimages'' are configurations in the past that lead in one step to the present configuration. == Reversing the direction of time == ...14 KB (2,322 words) - 23:39, 21 June 2006
- ...between linear transformations and matrices is very important in the study of linear transformations. ...is vectors y<sub>1</sub>, y<sub>2</sub>, y<sub>3</sub>, ..., y<sub>n</sub> of a vector space Y. ...15 KB (2,557 words) - 22:24, 16 December 2007
- ...defined as an unordered collection of distinct elements. That is, elements of a set can be listed in any order and elements occurring more than once are ...this book will only include numbers, but this is only a technique to make the topic less abstract. ...7 KB (1,215 words) - 21:53, 17 February 2008
- ...Equations|ordinary differential equations]] and at least have a basic idea of what a [[Modern_Physics:Math:Partial_Derivatives|partial derivative]] is. ...few chapters are built to be especially simple to understand so that, say, the interested engineering undergraduate can benefit; however later on importan ...8 KB (1,342 words) - 13:35, 22 October 2007
- ...s independent from Zermelo-Fraenkel set theory axioms. Thus, the addition of Choice to ZF enables work not previously possible. Zorn's Lemma, as usually stated, takes the form: ...7 KB (1,305 words) - 22:00, 12 October 2007
- In the following, we state two equivalent forms of the theorem, and show their equivalence. Later, we prove the theorem. This is done in the following steps: ...23 KB (4,033 words) - 16:33, 26 November 2007