Search results

From Maths
Jump to: navigation, search

Create the page "C Definitions" on this wiki! See also the search results found.

  • Nabla
    ...ok (Vector Analysis and Cartesian Tensors - Third Edition - D E Borune & P C Kendall - which is a good book) distinguishbetween the <math>\nabla</math>s ...actually come across the need for this. Which is why I list the first two definitions. I write this to show I have considered alternatives and why I do not use t
    1 KB (245 words) - 18:35, 13 February 2015
  • Connected (topology)
    There are equivalent definitions, some are given below. Note also, that by this convention the [[emptyset|{{ There are equivalent definitions, some are given below.
    5 KB (866 words) - 01:52, 1 October 2016
  • Ordering
    | <math>\forall a\in A\forall b\in A\forall c\in A([aRb\wedge bRc]\implies aRc)</math> ...=\mathbb{N} }} then <math>a\le b\wedge b\le c\iff a\le b\le c\implies a\le c</math>
    5 KB (1,006 words) - 13:21, 1 January 2016
  • Basis and coordinates
    ===Formal definitions=== Rather than working out the transform from {{M|C}} to {{M|S'}} or whatever we can simply notice:
    9 KB (1,525 words) - 16:30, 23 August 2015
  • Sigma-algebra
    ===Note on Alternative Definitions=== ...sigma|algebra}}, the definition above is actually equivalent to the longer definitions one might see around.<br/> The two properties above give rise to all the ot
    8 KB (1,306 words) - 01:49, 19 March 2016
  • Ring
    | <math>\forall a,b,c\in R[(a+b)+c=a+(b+c)]</math> | Now writing {{M|a+b+c}} isn't ambiguous
    7 KB (1,248 words) - 05:02, 16 October 2016
  • Tangent space
    <math>\omega\in T_p(\mathbb{R}^n)\iff \omega:C^\infty(\mathbb{R}^n)\rightarrow\mathbb{R} </math> is a [[Derivation|derivat ...ghtarrow\mathbb{R}</math> which satisfies the [[Leibniz rule]]. Recall {{M|C^\infty(M)}} is the set of all [[Smooth function|smooth functions]] on our [
    6 KB (1,190 words) - 19:27, 14 April 2015
  • Derivation
    If {{M|a\in\mathbb{R}^n}}, we say that a map, {{M|\alpha:C^\infty(\mathbb{R}^n)\rightarrow\mathbb{R} }} is a '''''derivation at {{M|a} * Given {{M|f,g\in C^\infty(\mathbb{R}^n)}} we have:
    2 KB (325 words) - 18:08, 14 October 2015
  • Smooth
    '''Note:''' there are many definitions of smooth and it changes a lot between books - I shall be consistent in thi ...Second Edition</ref> <math>F:U\rightarrow V</math> is '''smooth''', <math>C^\infty</math> or ''infinitely differentiable'' if:
    870 B (148 words) - 06:38, 7 April 2015
  • Motivation for tangent space definitions
    ...nts, and going between manifolds. THIS page will talk about the reason for definitions. Like a study guide. So far on [[Smooth manifold|smooth manifolds]] all we have are the following definitions:
    4 KB (790 words) - 22:25, 12 April 2015
  • Hausdorff space
    ===Equivalent definitions=== ...q A}} and {{M|D\subseteq B}} then if {{M|A\cap B\eq\emptyset}} we have {{M|C\cap D\eq\emptyset}} - this could be worth factoring out
    4 KB (679 words) - 22:52, 22 February 2017
  • Addition of vector spaces
    ==Definitions== '''Operations:''' (given {{M|u_i,v_i\in V_i}} and {{M|c}} is a scalar in {{M|F}})
    4 KB (804 words) - 18:02, 18 March 2016
  • Limit
    ...>\forall C>0\exists N\in\mathbb{N}\forall n\in\mathbb{N}[n> N\implies a_n> C]</math> ...>\forall C<0\exists N\in\mathbb{N}\forall n\in\mathbb{N}[n> N\implies a_n< C]</math>
    2 KB (310 words) - 18:23, 8 January 2016
  • Site projects:Patrolling measure theory/Task list
    * [[Dynkin system/Proof that definitions 1 and 2 are equivalent]] '''DONE''' [[User:Alec|Alec]] ([[User talk:Alec|ta ...S is in A for every S in G|A map from two sigma-algebras, A and B,...]] {{C|Needs minor work}}
    5 KB (645 words) - 11:40, 21 August 2016
  • Bounded set
    ...\forall a,b\in A[d(a,b)<C]}} - where {{M|C}} is real<ref group="Note">{{M|C\in\mathbb{R}_{\ge 0} }} should do as {{M|0}} could be a bound, I suppose on This follows right from the definitions, the {{M|K}} is the bound.
    2 KB (409 words) - 23:31, 29 October 2016
  • Dynkin system
    ==Proof of equivalence of definitions== '''[[Dynkin system/Proof that definitions 1 and 2 are equivalent|Claim]]: ''' Definition 1 {{M|\iff}} Definition 2
    1 KB (184 words) - 01:54, 19 March 2016
  • Borel sigma-algebra
    ...hcal{B} }} itself) - some are listed here. First here are some non-obvious definitions: ! {{M|1=\mathcal{B}^n=\sigma(\mathcal{C})}} - closed<ref name="MIM"/>
    5 KB (854 words) - 09:25, 6 August 2015
  • Dynkin system/Proof that definitions 1 and 2 are equivalent
    The following definitions are the same: :#* Note that {{M|1=A-B=(A^c\udot B)^c}} (this is not true in general, it requires {{M|B\subseteq A}}{{Note|Includ
    2 KB (326 words) - 05:09, 22 August 2015
  • Cone (category theory)
    ...ontrast each other well, see the page [[cone and cocone compared]] for the definitions compared side by side ...category theory)|objects]] {{M|A}}, {{M|B}} in a [[category]] {{M|\mathscr{C} }}, a ''cone''{{rAITCTHS2010}} is:
    1 KB (197 words) - 22:27, 28 February 2016
  • Cocone (category theory)
    ...ontrast each other well, see the page [[cone and cocone compared]] for the definitions compared side by side ...category theory)|objects]] {{M|A}}, {{M|B}} in a [[category]] {{M|\mathscr{C} }}, a ''cocone''{{rAITCTHS2010}} is:
    1 KB (182 words) - 22:28, 28 February 2016
  • Product and coproduct compared
    ...ory theory)|coproduct]] pages make it hard to see just how similar the two definitions are. As a result I shall steal the format from{{rAITCTHS2010}} and do a two ...pair {{M|A}}, {{M|B}} of [[object|objects]] in a [[category]] {{M|\mathscr{C} }} a:
    2 KB (351 words) - 16:59, 1 March 2016
  • Site projects:Measure theory plan
    The plan is to stick pretty close to what Halmos does but introduce definitions found elsewhere, for example Measures, Integrals and Martingales introduces ! {{M|\mathcal{C} }}
    2 KB (309 words) - 15:31, 27 March 2016
  • Notes:Types of retractions
    ==Definitions== * {{C|"The key is that if one want a continuous function r:X-->I ,then r can not
    6 KB (1,008 words) - 11:56, 2 June 2016
  • Notes:Differential (manifolds)
    ==Definitions== * '''Smoothness of a map ({{AKA}}: {{M|C^\infty}}''' - a map, {{M|f:U\subseteq\mathbb{R}^n\rightarrow V\subseteq\mat
    4 KB (716 words) - 14:24, 16 May 2016
  • Types of set algebras/Type table
    ...e that {{M|1=A-B=A\cap B^c=(A^c\cup B)^c}} - or that {{M|1=A-B=(A^c\cup B)^c}} - so we see that being closed under union and complement means we have cl ...under complements, so {{M|\emptyset^c\in\mathcal{A} }} and {{M|1=\emptyset^c=\Omega\in\mathcal{A} }}</ref>
    4 KB (573 words) - 20:00, 19 August 2016
  • Editing guide/Templates/Page categorisation
    | To categorise definitions | {{C|<nowiki>{{Definition|</nowiki>Subject<sub>1</sub><nowiki>|...|Subject</nowi
    653 B (80 words) - 10:11, 8 September 2016
  • Doctrine:Homotopy terminology
    Before we can define terms, here are the definitions we work with: ...ans continuous with continuous first and second derivatives, so forth, {{M|C^\infty}} means [[smooth]].
    3 KB (535 words) - 09:01, 31 October 2016
  • Closed map
    * {{M|1=\forall U\in C(X,\mathcal{J})[f(U)\in C(Y,\mathcal{K})]}} - that is, that the {{link|image|map|s}} (under {{M|f}}) ** {{M|C(X,\mathcal{J})}} denotes the set of all {{plural|closed set|s}} of the [[to
    1 KB (246 words) - 19:59, 26 September 2016
  • Every surjective map gives rise to an equivalence relation
    ...page|grade=C|msg=Flesh out, check existing content then demote to grade {{C|F}}}} ...2\in X[x_1\sim x_2\iff f(x_1)=f(x_2)]}} (for the "and only if" part, see [[definitions and iff]])
    2 KB (315 words) - 13:54, 8 October 2016
  • Dense
    ...definitions to here, as they're like... "easy equivalent" and may well be definitions, not like ... a proposition of equivalence. ...p="Note">These are not just logically equivalent to density, they could be definitions for density, and may well be in some books.</ref>
    6 KB (1,097 words) - 04:15, 1 January 2017
  • Notes:Homology
    ==Definitions== & & z \ar@/_.5pc/[uu]^c \ar@/_2pc/[uu]_d
    6 KB (897 words) - 07:30, 15 October 2016
  • Invariant of an equivalence relation
    ...invariant of ''{{M|\sim}}" if<ref group="Note" name="definition">See "''[[definitions and iff]]''"</ref>: ...al{P}(S)}}, such that there [[exists a unique]] {{M|c\in C}} such that {{M|c\sim s}}
    3 KB (478 words) - 18:58, 9 November 2016
  • Notes:Dual to dual vector space
    ** {{MM|A:v\mapsto\left(\begin{array}{c}:V^*\rightarrow\mathbb{F}\\:f^*\mapsto\ (???)\end{array}\right)}} in some w * After faffing about with the definitions and getting a "feel" for what was going on, I realised:
    2 KB (318 words) - 05:34, 8 December 2016
  • List of topological properties
    ...)}} is a [[topological space]] or {{M|(X,d)}} is a [[metric space]] in the definitions. ...C}(X)\ \big\vert\ A\subseteq C\right\} }}{{rFAVIDMH}} - where {{M|\mathcal{C}(X)}} denotes the set of {{plural|closed set|s}} of {{M|X}}
    4 KB (630 words) - 19:33, 16 February 2017
  • Index of notation for sets of continuous maps/Index
    ...C(X,Y)}}]] - for [[topological spaces]] {{Top.|X|J}} and {{Top.|Y|K}}, {{M|C(X,Y)}} is the [[set]] of all [[continuous maps]] between them. # [[C(I,X)|{{M|C(I,X)}}]] - {{M|I:\eq[0,1]\subset\mathbb{R} }}, set of all {{link|path|topol
    2 KB (463 words) - 06:20, 1 January 2017
  • Exercises:Saul - Algebraic Topology - 3/Exercise 3.2
    ...[[Delta-complex|{{M|\Delta}}-complex]] structure. Show, directly from the definitions (Hatcher, of course...) that {{M|H^\Delta_0(X)\cong\mathbb{Z} }} ...the Abelian groups that usually have a {{M|C}} in them and how he used {{M|C}}.
    13 KB (2,312 words) - 06:33, 1 February 2017
  • Doctrine:K
    : See also: [[Doctrine:Index]] for implicit definitions like these, conventions (like {{M|i}} for an index or {{M|f}} for a functio ...ither [[the reals|{{M|\mathbb{R} }}]] or [[the complex numbers|{{M|\mathbb{C} }}]]
    617 B (92 words) - 18:42, 16 February 2017
  • Real projective space
    * Demote to grade C once charts and definition 1 is in place [[User:Alec|Alec]] ([[User talk:Al Let {{M|n\in\mathbb{N}_{\ge 1} }} be given. There are 2 common definitions for {{M|\mathbb{RP}^n}} that we encounter. We will use definition 1 unless
    2 KB (289 words) - 09:08, 18 February 2017
  • Unique lifting property
    {{Requires work|grade=C|msg={{Warning|What follows is VERY messy.}} I was distracted when writing i Let us make the following definitions:
    13 KB (2,510 words) - 16:23, 2 March 2017
  • Contractible topological space
    * {{M|\exists c\in X\big[(:x\mapsto c)\simeq \text{Id}_X\big]}} ...case {{M|(:X\rightarrow X)}} by {{M|(:x\mapsto c)}} for some constant {{M|c}}) that is [[homotopic maps|homotopic to]] {{M|\text{Id}_X:X\rightarrow X}}
    3 KB (544 words) - 20:00, 24 April 2017
  • Logical workings of the Enigma machines
    We make the following definitions for the [[permutations]] applied, these are taken in the context of [[Group * {{M|A,B,C,D,E\in S_I}} represent the permutations of the rotors, there may only be 3
    4 KB (696 words) - 15:24, 15 December 2017
  • Notes:Reflection of ray given normal
    * {{M|\ell_1}} by {{M|y:\eq mx+c}} and * {{M|\ell_2}} by {{M|y:\eq m'x+c'}}
    2 KB (444 words) - 21:02, 2 January 2018
Retrieved from "https://wiki.unifiedmathematics.com/index.php?title=Special:Search"