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• A collection of subsets is a sigma-algebra iff it is a Dynkin system and closed under finite intersections
  1 KB (239 words) - 13:21, 17 December 2016
• The ring of sets generated by a semi-ring is the set containing the semi-ring and all finite disjoint unions
  ...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_{i
  7 KB (1,398 words) - 18:33, 19 August 2016
• Finite complement topology
  ...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
• Deterministic finite automaton
  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
• Deterministic finite acceptor automaton
  #REDIRECT [[Acceptor-type deterministic finite automaton]]
  93 B (9 words) - 22:15, 17 January 2018
• Non-deterministic finite automaton
  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

Page text matches

• Topology
  ...=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\in
  3 KB (543 words) - 09:28, 30 December 2016
• Compactness
  ...{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
• Product topology
  : '''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
• Tuple
  * Finite tuples
  610 B (97 words) - 16:30, 23 August 2015
• Function
  ...Mathematicians are lazy]]) especially if the number of undefined points is finite.
  4 KB (659 words) - 13:01, 19 February 2016
• Linear map
  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
• Span, linear independence, linear dependence, basis and dimension
  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 dependent
  2 KB (330 words) - 18:07, 25 April 2015
• Sequence
  ...>, <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 w
  2 KB (419 words) - 18:12, 13 March 2016
• Basis and coordinates
  ...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_{k
  9 KB (1,525 words) - 16:30, 23 August 2015
• Sigma-algebra
  ...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 pr
  8 KB (1,306 words) - 01:49, 19 March 2016
• Measure Theory
  ...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
• Additive function
  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
• Pre-measure
  *#* 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 countabl
  5 KB (782 words) - 01:49, 26 July 2015
• Measure
  ! Finite<ref name="MTH"/> * {{M|A}} is ''finite''
  6 KB (941 words) - 14:39, 16 August 2016
• Semi-ring of sets/Definition
  ...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
• Ring generated by
  ...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\subset
  2 KB (307 words) - 07:24, 27 April 2015
• Vector dot product
  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
• Hausdorff space
  * Add [[Example:The real line with the finite complement topology is not Hausdorff]] as an example of a familiar set with
  4 KB (679 words) - 22:52, 22 February 2017
• Addition of vector spaces
  !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 always
  ...'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