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- Given an [[Equivalence relation]] {{M|\sim}} the equivalence class of {{M|a}} is denoted as follows: An equivalence class may be denoted by {{M|[a]}} where {{M|a}} is the ''representative'' of it.1 KB (160 words) - 20:00, 14 November 2015
- The [[Equivalence class|equivalence class]] of {{M|\alpha}} is denoted (as is usual) by {{M|[\alpha]}}2 KB (316 words) - 02:37, 17 April 2015
- * [[Class of sets closed under set-subtraction properties]]1 KB (165 words) - 20:50, 15 June 2015
- The ''class of all [[smooth]], [[real-valued function|real-valued]], [[function|functio ==[[Class of smooth real-valued functions on R-n/Structure|Structure]]==2 KB (259 words) - 23:41, 21 October 2015
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636 B (103 words) - 23:43, 21 October 2015
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102 B (13 words) - 14:11, 23 August 2016
Page text matches
- {| class="wikitable" border="1"2 KB (268 words) - 13:37, 20 April 2016
- {| class="wikitable" border="1"6 KB (972 words) - 01:44, 14 October 2016
- {| class="wikitable" border="1"4 KB (532 words) - 22:04, 19 October 2016
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- {| class="wikitable" border="1"3 KB (619 words) - 10:25, 11 March 2015
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- {| class="wikitable" border="1" {| class="wikitable" border="1"5 KB (1,006 words) - 13:21, 1 January 2016
- {| class="wikitable" border="1" * An [[equivalence class]] is the name given to the set of all things which are equivalent under a g3 KB (522 words) - 15:18, 12 February 2019
- {| class="wikitable" border="1" {| class="wikitable" border="1"3 KB (512 words) - 16:30, 23 August 2015
- {| class="wikitable" border="1"4 KB (682 words) - 15:44, 16 June 2015
- {| class="wikitable" border="1"6 KB (1,026 words) - 20:33, 9 April 2017
- {| class="wikitable" border="1"589 B (108 words) - 20:15, 21 April 2015
- {| class="wikitable" border="1" {| class="wikitable" border="1"9 KB (1,490 words) - 06:13, 1 January 2017
- {| class="wikitable" border="1" {| class="wikitable" border="1"9 KB (1,525 words) - 16:30, 23 August 2015
- {| class="wikitable" border="1" {| class="wikitable" border="1"2 KB (410 words) - 16:35, 9 March 2015
- {| class="wikitable" border="1" {| class="wikitable" border="1"7 KB (1,332 words) - 07:17, 16 October 2016
- An class {{M|R}} of sets is an ''Algebra of sets'' if<ref>p21 - Halmos - Measure The3 KB (507 words) - 18:43, 1 April 2016
- A non-empty class of sets {{M|S}} is a {{sigma|ring}} if<ref>Measure Theory, p24 - Halmos - G728 B (125 words) - 15:34, 13 March 2015
- : See [[Class of sets closed under set-subtraction properties|Properties of a class of sets closed under set subtraction]] * [[Class of sets closed under set-subtraction properties|Properties of a class of sets closed under set subtraction]]8 KB (1,306 words) - 01:49, 19 March 2016
- {| class="wikitable" border="1"4 KB (733 words) - 01:41, 28 March 2015
- {| class="wikitable" border="1"409 B (62 words) - 15:49, 13 March 2015
- {| class="wikitable" border="1"2 KB (396 words) - 16:07, 13 March 2015
- ...on is simply a [[Function|function]] with a domain of definition that is a class of sets<ref>Halmos - Measure Theory - p30 - Springer - Graduate Texts in Ma355 B (54 words) - 16:10, 13 March 2015
- ...ra Maths}}A ''[[real valued function|real valued]]'' [[set function]] on a class of [[set|sets]], {{M|\mathcal{A} }}, {{M|f:\mathcal{A}\rightarrow\mathbb{R}6 KB (971 words) - 18:16, 20 March 2016
- {| class="wikitable" border="1" {| class="wikitable" border="1"6 KB (941 words) - 14:39, 16 August 2016
- Given any class of sets {{M|A}}, there exists a unique ring {{M|R_0}} such that {{M|E\subse If {{M|A}} is any class of sets, then every set in {{M|R(A)}} can be covered by a finite union of s2 KB (307 words) - 07:24, 27 April 2015
- {| class="wikitable" border="1" {| class="wikitable" border="1"7 KB (1,248 words) - 05:02, 16 October 2016
- {|class="wikitable" border="1"4 KB (596 words) - 14:41, 20 March 2015
- {| class="wikitable" border="1" {| class="wikitable" border="1"2 KB (338 words) - 22:55, 2 May 2015
- {| class="wikitable" border="1"6 KB (1,190 words) - 19:27, 14 April 2015
- Germs are an [[Equivalence class]] of an [[Equivalence relation]], rather than the usual way of denoting equ A germ is an [[Equivalence class|equivalence class]] of an [[Equivalence relation|equivalence relation]] defined as follows:2 KB (285 words) - 01:36, 5 April 2015
- Given an [[Equivalence relation]] {{M|\sim}} the equivalence class of {{M|a}} is denoted as follows: An equivalence class may be denoted by {{M|[a]}} where {{M|a}} is the ''representative'' of it.1 KB (160 words) - 20:00, 14 November 2015
- We could define a smooth structure as an [[Equivalence class]] of smooth atlases however it is far easier to use the second option2 KB (246 words) - 07:10, 7 April 2015
- {| class="wikitable" border="1" ...s {{M|p:(x,y)\mapsto[(x,y)]}} where {{M|[(x,y)]}} denotes an [[Equivalence class]] - as usual.4 KB (681 words) - 10:33, 7 April 2015
- {| class="wikitable" border="1"2 KB (267 words) - 18:08, 10 April 2015
- {| class="wikitable" border="1"6 KB (975 words) - 00:18, 11 April 2015
- * <math>\pi_1(X,x_0)</math> denotes the set of [[Homotopy class|homotopy classes]] of [[Paths and loops in a topological space|loops]] base See [[Homotopy class]] for these properties3 KB (393 words) - 16:10, 4 November 2016
- {| class="wikitable" border="1"403 B (61 words) - 18:10, 16 April 2015
- Using a bit of abstract algebra it is not hard to see that the [[Equivalence class|equivalence classes]] are exactly the [[Coset|cosets]] of {{M|\mathbb{Z} }} ...en {{M|a,b\in [t]}} we know {{M|a\sim b}} as {{M|[t]}} is an [[Equivalence class]]3 KB (592 words) - 16:57, 11 May 2015
- The [[Equivalence class|equivalence class]] of {{M|\alpha}} is denoted (as is usual) by {{M|[\alpha]}}2 KB (316 words) - 02:37, 17 April 2015
- {| class="wikitable" border="1"4 KB (804 words) - 18:02, 18 March 2016
- {| class="wikitable" border="1" ! Class2 KB (310 words) - 18:23, 8 January 2016
- {| class="wikitable" border="1"2 KB (272 words) - 11:43, 28 April 2015
- {| class="wikitable" border="1"1 KB (187 words) - 08:53, 21 May 2015
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- {{Extra Maths}}In this table the class of sets {{M|\mathcal{A} }} is a collection of subsets from another set {{M| {| class="wikitable" border="1"3 KB (449 words) - 20:06, 19 August 2016
- {| class="wikitable" border="1"2 KB (360 words) - 20:43, 15 June 2015
- * [[Class of sets closed under set-subtraction properties]]1 KB (165 words) - 20:50, 15 June 2015
- Suppose {{M|\mathcal{A} }} is an arbitrary class of [[set|sets]] with the property that: If {{M|\mathcal{A} }} is a class of subsets of {{M|\Omega}} such that<ref name="PTACC">Probability Theory -3 KB (490 words) - 11:38, 21 August 2016
- {| class="wikitable" border="1"627 B (98 words) - 18:44, 28 August 2015
- {| class="wikitable" border="1"1 KB (173 words) - 14:51, 18 June 2015
- * [[Class of sets closed under set-subtraction properties]] - '''DONE''' [[User:Alec| * [[Class of sets closed under complements properties]]5 KB (645 words) - 11:40, 21 August 2016
- {| class="wikitable sortable" border="1" ! class="unsortable" | {{M|A}}964 B (165 words) - 20:55, 22 June 2015
- {| class="wikitable sortable" border="1" {| class="wikitable sortable" border="1"3 KB (616 words) - 08:37, 1 July 2015
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- {| class="wikitable" border="1"1 KB (214 words) - 14:52, 12 July 2015
- {| class="wikitable" border="1" | Class3 KB (612 words) - 21:06, 29 February 2016
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- {| class="wikitable" border="1" {| class="wikitable" border="1"10 KB (1,899 words) - 18:48, 23 September 2015
- ...ass]] of ''objects'' {{M|\mathcal{X} }}<ref group="Note">Munkres calls the class of objects {{M|X}} and uses {{M|X}} for specific objects. Not sure why, so ...|f\in\hom(W,X)}} and {{M|g\in\hom(X,Y)}} where {{M|W}} and {{M|Y}} are any class of ''objects''2 KB (347 words) - 00:36, 27 September 2015
- template<class T> class DeleteWhenDone; template<class T>31 KB (3,827 words) - 14:42, 28 September 2015
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- * ''Of class {{M|C^k}}'' or {| class="wikitable" border="1"3 KB (632 words) - 20:32, 16 October 2015
- * [[Class of smooth real-valued functions on R-n|The class of smooth real-valued functions on {{M|\mathbb{R}^n}}]] * [[Class of k-differentiable real-valued functions on R-n|The class of {{M|k}}-differentiable real-valued functions on {{M|\mathbb{R}^n}}]]807 B (117 words) - 23:15, 21 October 2015
- The ''class of all [[smooth]], [[real-valued function|real-valued]], [[function|functio ==[[Class of smooth real-valued functions on R-n/Structure|Structure]]==2 KB (259 words) - 23:41, 21 October 2015
- * Then {{M|\frac{X}{\sim} }} denotes the "[[equivalence class|equivalence classes]]" of {{M|~}} {| class="wikitable" border="1"3 KB (588 words) - 09:38, 24 November 2015
- Here {{M|[v]}} denotes the equivalence class of {{M|v}} under {{M|\sim}}, that is: {| class="wikitable" border="1"5 KB (879 words) - 23:09, 1 December 2016
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- {| class="wikitable" border="1"! colspan="8" | Range517 B (56 words) - 23:18, 12 February 2016
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- ...=1}} and such as [[mathematicians are lazy]]) and denote the [[equivalence class|equivalence classes]] as {{M|[(a_n)]}} or even just {{M|[a_n]}} (provided t1 KB (153 words) - 21:05, 20 April 2016
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- {| class="wikitable" border="1" * [[Class of smooth real-valued functions on R-n|The class of smooth real-valued functions on {{M|\mathbb{R}^n}}]]2 KB (351 words) - 05:26, 1 January 2017
- ...editary {{sigma|ring}} {{M|\mathcal{H} }} and if {{M|\mathcal{S} }} is the class of all {{M|\mu^*}}-measurable sets, ''then {{M|\mathcal{S} }} is a [[ring o ...|\mu}} to {{M|\sigma_R(\mathcal{R})}} is identical with {{M|\mu^*}} on the class of all {{M|\mu^*}}-measurable sets4 KB (674 words) - 19:46, 3 April 2016
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- * [[Homotopy class]]4 KB (404 words) - 21:36, 30 September 2016
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- ...sends each {{M|x\in X}} to {{M|[x]}} (the [[equivalence class|equivalence class containing {{M|x}}]]) which we denote here as {{M|\pi:X\rightarrow\frac{X}{1 KB (213 words) - 14:36, 25 April 2016
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- ...using {{M|\bar{\mu}^*}} as the measure induced by an outer measure on the class of all outer-measurable sets. So on this page: * '''Theorem A:''' if {{M|\bar{S} }} is the class of all outer-measurable sets then {{M|\bar{S} }} is a [[ring of sets]]6 KB (1,067 words) - 22:19, 23 May 2016
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- ...} \in}} [[Classes of continuously differentiable functions|{{M|C^1}} - the class of functions with continuous partial derivatives]]. Let {{M|1=x=(x_1,\ldots3 KB (529 words) - 08:07, 4 June 2016
- ...g, and that isn't far from the truth, we can define it on ''at least'' the class of maps that are at least once differentiable. (There are in fact more as w4 KB (713 words) - 20:55, 20 June 2016
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- {| class="wikitable" border="1" {| class="wikitable" border="1"4 KB (654 words) - 23:06, 10 July 2016
- ...an [[equivalence relation]], {{M|X/\sim}} denotes the set of [[equivalence class|equivalence classes]] of {{M|\sim}}.1 KB (220 words) - 16:56, 12 July 2016
- {| class="wikitable" border="1" style="overflow:hidden;" {| class="wikitable" border="1" style="width:80%;"7 KB (1,195 words) - 22:55, 3 December 2016
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- ...ch component by that scalar I am happy that this is a vector space. It's a class [[product (category theory)]]}}8 KB (1,463 words) - 14:35, 13 August 2016
- {| class="wikitable" border="1"267 B (41 words) - 14:09, 16 August 2016
- ...al{R} }} to a [[measure]] is not trivial. For example, to find the biggest class of sets we can extend a pre-measure to is different to what this page shows2 KB (257 words) - 17:27, 17 August 2016
- </noinclude>A Ring of sets is a non-empty class {{M|R}}<ref>Page 19 -[[Books:Measure Theory - Paul R. Halmos|Measure Theory390 B (69 words) - 17:21, 18 August 2016
- {| class="wikitable" border="1" ...p}}-closed}} also<ref group="Theorem" name="\-closed-consequences">Using [[Class of sets closed under set-subtraction properties]] we know that if {{M|\math4 KB (573 words) - 20:00, 19 August 2016
- </noinclude>{| class="wikitable" border="1"559 B (79 words) - 20:05, 19 August 2016
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- {| class="wikitable" border="1" style="text-align:center;min-width:12em;" {| class="wikitable" border="1" style="text-align:center;"2 KB (369 words) - 07:46, 11 September 2016
- </noinclude>{| class="wikitable" border="1" style="font-size:0.8em;"2 KB (327 words) - 16:09, 13 September 2016
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- {| class="wikitable" border="1" style="overflow:hidden;margin-top:0px;"2 KB (262 words) - 22:45, 25 September 2016
- # '''Homotopy class''' - [[equivalence classes]] of maps under the homotopy relation.3 KB (535 words) - 09:01, 31 October 2016
- ...apsto[x]}} where {{M|1=[x]:=\{y\in X\ \vert x\sim y\} }}, an [[equivalence class]]2 KB (315 words) - 13:54, 8 October 2016
- {| class="wikitable" border="1" style="overflow:hidden;margin-top:0px;margin-left:0.6 KB (897 words) - 07:30, 15 October 2016
- ...given by {{M|\pi:x\mapsto [x]}} where {{M|[x]}} denotes the [[equivalence class]] of {{M|x}} ...} we have {{M|1=\pi(x)=[x]=\{x\} }}, that is that the {{plural|equivalence class|es}} are singletons. So if {{M|1=\pi(x)=\pi(y)}} we must have {{M|1=\pi(y)=9 KB (1,732 words) - 23:26, 11 October 2016
- {| class="wikitable" border="1" style="margin:0px;"248 B (40 words) - 20:38, 8 October 2016
- ...given by {{M|\pi:x\mapsto [x]}} (where {{M|[x]}} denotes the [[equivalence class]] of {{M|x}}) is a [[function]].697 B (107 words) - 22:33, 8 October 2016
- {| class="wikitable" border="1" style="max-width:15em;margin:0px;"261 B (38 words) - 22:54, 8 October 2016
- ...given by {{M|\pi:x\mapsto [x]}} where {{M|[x]}} denotes the [[equivalence class]] containing {{M|x}}</ref> to {{underline|yield a unique [[injective]]}} ma6 KB (1,097 words) - 20:24, 9 October 2016
- ...given by {{M|\pi:x\mapsto [x]}} where {{M|[x]}} denotes the [[equivalence class]] containing {{M|x}}</ref> to {{underline|yield a [[bijective]]}} map<ref>[2 KB (339 words) - 12:57, 9 October 2016
- #REDIRECT [[equivalence class]]74 B (8 words) - 00:23, 15 October 2016
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- {| class="wikitable" border="1" {| class="wikitable" border="1" style="max-width:50%;"3 KB (464 words) - 11:57, 19 October 2016
- </noinclude>{| class="wikitable" border="1" style="margin:0px;overflow:hidden;max-width:27em;"868 B (120 words) - 21:01, 19 October 2016
- {| class="wikitable" border="1" style="overflow:hidden;margin:0px;max-width:30em;"607 B (83 words) - 13:52, 20 October 2016
- We denote the ''homology class'' of {{M|x\in\text{Ker}(\partial_n)}} by {{M|1=\text{cls }z:=z+\text{Im}(\p3 KB (440 words) - 17:15, 20 October 2016
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- ...better written symbolically using {{M|[\ell]}} to denote the [[equivalence class]] of {{M|\ell}} under (equivalence) [[relation]] of [[end point preseriving3 KB (462 words) - 09:21, 6 November 2016
- {| class="wikitable" border="1"267 B (42 words) - 09:49, 11 November 2016
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- ...im}:\eq\{[x]\ \vert\ x\in X\} }} where {{M|[x]}} denotes the [[equivalence class]] of {{M|x}}.2 KB (295 words) - 14:16, 13 November 2016
- ...ke sure to prove the requirements}} e.g. that {{M|[x]}}, the [[equivalence class]] containing {{M|x}} makes sense. As if I use a property like:2 KB (388 words) - 14:36, 13 November 2016
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- * '''Germ: ''' The [[equivalence class]] of {{M|(f,U)}} is called the '''Germ''' of {{M|f}} at {{M|p}}5 KB (910 words) - 14:07, 1 December 2016
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- ...as it doesn't matter whuch {{M|f}} we take to represent the [[equivalence class] {{M|[f]}}.8 KB (1,475 words) - 07:35, 14 December 2016
- ...{Caveat|Remember that {{M|[f]}} means {{M|f}} represents the [[equivalence class]] - this definition must be "[[well-defined]]" for whichever {{M|f}} we use3 KB (442 words) - 04:28, 14 December 2016
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- {| class="wikitable" border="1" ! Class so far17 KB (3,132 words) - 12:03, 18 January 2017
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- ...his notation is unambiguous, {{M|[c]}} represents an arbitrary equivalence class of the quotient (as this is first year work I will not elaborate any furthe13 KB (2,312 words) - 06:33, 1 February 2017
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- Books:Introduction To Set Theory - Third Edition, Revised and Expanded - Karel Hrbacek & Thomas Jech{| class="wikitable" border="1"267 B (44 words) - 12:54, 3 February 2017
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- {| class="wikitable" border="1" ...\ast}} is the point in {{M|X_1\vee\cdots\vee X_n}} that is the equivalence class which the {{M|p_i}} are sent to (in this case the {{M|p_i}} are all joined10 KB (1,664 words) - 12:43, 1 March 2017
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- The ''axiom schema of replacement'' posits that if {{M|F}} is some [[class function]] then for all sets {{M|X}}, {{M|F(X)}} - the {{link|image|functio2 KB (390 words) - 15:28, 5 April 2017
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- ...'' project folder, and {{C|wxStaticWrappedText}} (my class, not a {{C|wx}} class) {| class="wikitable" border="1"2 KB (371 words) - 16:38, 23 April 2017
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