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1 KB (239 words) - 13:21, 17 December 2016
- ...written {{M|R(\mathcal{F})}} is exactly the set {{M|\mathcal{F} }} and all finite [[union|unions]] of elements of {{M|\mathcal{F} }}{{rMIAMRLS}}. #*** As {{M|S_i,T_j\in\mathcal{F} }} we know there exists a finite [[sequence]] of elements of {{M|\mathcal{F} }}, say {{MSeq|W_{ijk}|k|1|n_{i7 KB (1,398 words) - 18:33, 19 August 2016
- ...ere is a [[topology]], {{M|\mathcal{J} }}, we can give {{M|X}} called "the finite complement topology", such that {{M|(X,\mathcal{J})}} is a [[topological sp ...if {{M|U\eq\emptyset}} or the [[complement]] of {{M|U}} in {{M|X}} has ''[[finite]]'' [[cardinality]].1 KB (233 words) - 09:21, 30 December 2016
- A ''deterministic finite automaton'' or ''DFA'' is a [[tuple]] of 4 items: ** {{M|Q}} is a [[finite set]] of "states",2 KB (373 words) - 03:23, 21 January 2018
- #REDIRECT [[Acceptor-type deterministic finite automaton]]93 B (9 words) - 22:15, 17 January 2018
- A ''non-deterministic-finite-automaton'' is a [[tuple]] of 4-items, {{M|A}}, for: ** {{M|Q}} is a [[finite set]] of states - ''just as in a [[DFA]]''3 KB (541 words) - 22:22, 17 January 2018
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- ...=1}^nU_i\in\mathcal{J} }} too - {{M|\mathcal{J} }} is [[closed]] under ''[[finite]]'' [[intersection]]. ...teq\mathcal{J} }} is ''any'' collection of elements of {{M|\mathcal{J} }} (finite, [[countable]], [[uncountable]] or otherwise) then {{M|1=\bigcup_{\alpha\in3 KB (543 words) - 09:28, 30 December 2016
- ...{M|X}}, {{M|\{U_\alpha\}_{\alpha\in I}\subseteq\mathcal{J} }} contains a ''finite'' [[sub-cover]] ...[[covering]] by sets [[open set|open]] in {{M|X}} of {{M|S}} contains a ''finite'' [[sub-cover]]5 KB (828 words) - 15:59, 1 December 2015
- : '''Note: ''' for finite collections of topological spaces the product and [[box topology]] agree. I ...e basis set contains all the products of open sets where the product has a finite number of elements that are not the entirety of their space.5 KB (871 words) - 20:32, 23 September 2016
- * Finite tuples610 B (97 words) - 16:30, 23 August 2015
- ...Mathematicians are lazy]]) especially if the number of undefined points is finite.4 KB (659 words) - 13:01, 19 February 2016
- Because linear maps can often (always if {{M|U}} and {{M|V}} are finite dimensional) be represented as a [[Matrix|matrix]] sometimes the notation <3 KB (512 words) - 16:30, 23 August 2015
- It is very important that only finite linear combinations are in the span. ...y dependent if for any '''finite''' collection of elements of {{M|E}} that finite collection is linearly dependent2 KB (330 words) - 18:07, 25 April 2015
- ...>, <math>f:\mathbb{N}\rightarrow S</math> where {{M|S}} is some set. For a finite sequence it is simply <math>f:\{1,...,n\}\rightarrow S</math>. Now we can w2 KB (419 words) - 18:12, 13 March 2016
- ...near independence, linear dependence, basis and dimension#Basis|Basis]], a finite one, <math>\{b_1,...,b_n\}</math>, a point {{M|p}} is given by <m>\sum^n_{k9 KB (1,525 words) - 16:30, 23 August 2015
- ...we only know {{M|\mathcal{A} }} is closed under ''countable'' union, not ''finite'' (2) union. so we cannot know {{M|A^C\cup B\in\mathcal{A} }}, thus this pr8 KB (1,306 words) - 01:49, 19 March 2016
- ...h> may well just be 1, this intuition is correct, but we're staying in the finite ...e above we can see that anything in this ring is the union of some (indeed finite) amount of sets in <math>\mathcal{J}^n</math>4 KB (733 words) - 01:41, 28 March 2015
- This is a separate property, while given additivity we can get finite additivity, but we cannot get countable additivity from just additivity. If <math>f(0)=0</math> or <math>\mu(\emptyset)=0</math> then given a finite set <math>\{a_i\}_{i=1}^n</math> we can define an infinite set <math>\{b_n\6 KB (971 words) - 18:16, 20 March 2016
- *#* Where {{M|1=(A_i)_{i=1}^n\subseteq\mathcal{A} }} is a [[Sequence|finite sequence]] ...tuitive to define it as a property we want. We are assured of closed-under-finite-union already, so we can measure over that. We then extend this to countabl5 KB (782 words) - 01:49, 26 July 2015
- ! Finite<ref name="MTH"/> * {{M|A}} is ''finite''6 KB (941 words) - 14:39, 16 August 2016
- ...joint} }}]]{{M|1=[S-T=\bigudot_{i=1}^m S_i]}}<ref group="Note">Usually the finite [[sequence]] {{MSeq|S_i|i|m|in=\mathcal{F} }} being pairwise disjoint is im ...'t require {{M|S-T\in\mathcal{F} }} note, it only requires that their be a finite collection of disjoint elements whose union is {{M|S-T}}.<noinclude>2 KB (337 words) - 17:25, 18 August 2016
- ...A}} is any class of sets, then every set in {{M|R(A)}} can be covered by a finite union of sets in {{M|A}} The class of all sets which may be covered by a finite union of sets in {{M|A}} is a ring! (call it {{M|R_f}}) Since {{M|A\subset2 KB (307 words) - 07:24, 27 April 2015
- Given two vectors in a finite vector space {{M|a,b\in V}} where {{M|v_i}} denotes the {{M|i^\text{th} }}534 B (96 words) - 02:04, 29 March 2015
- * Add [[Example:The real line with the finite complement topology is not Hausdorff]] as an example of a familiar set with4 KB (679 words) - 22:52, 22 February 2017
- !colspan="3" | Finite ...htarrow\bigcup_{i\in K}V_i\right|f(i)\in V_i\ \forall i\in K,\ f\text{ has finite support}\right\}</math>4 KB (804 words) - 18:02, 18 March 2016
- ...'Almost everywhere''' or '''Almost all'' are phrases that mean ''all but a finite number''<ref>Algebra - Serge Lang - Revised Third Edition - GTM</ref> *: The set {{M|\{x\vert f(x)\ge 10\} }} is finite (assuming that ''f'' runs over natural numbers, of course)694 B (115 words) - 21:44, 19 March 2016