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  • 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
  • Cyclic subgroup
    This is a subgroup, and is Abelian (for finite groups - not sure about infinite)
    580 B (94 words) - 14:12, 12 May 2015
  • Greatest common divisor
    Using the [[Well-ordered principle]] (given the set of divisors is a finite set, the set has a maximum element, and the maximum is the same as the {{M|
    1 KB (252 words) - 08:33, 21 May 2015
  • Span
    It is very important that only finite linear combinations are in the span. ===Span of a finite set of vectors===
    1,013 B (173 words) - 17:09, 28 May 2015
  • External direct sum
    ===Finite=== Given a ''finite'' family of [[Vector space|vector spaces]] ''over the same [[Field|field]]
    3 KB (613 words) - 13:12, 9 June 2015
  • Notes:Vector space operations
    | All finite sums from the union of the family of subspaces (inline with Lang's sum) | {{M|\boxplus}} (finite)
    3 KB (489 words) - 20:27, 1 June 2015
  • Notes:Tensor product
    There are two. First of all is an arbitrary (finite?) operation {{M|\otimes}} where we define:
    2 KB (460 words) - 10:08, 12 June 2015
  • Index of abbreviations
    * "Continuous AA" - means finite no. discontinuities * "Continuous AA" - means finite no. discontinuities
    954 B (158 words) - 22:18, 11 July 2015
  • Semi-ring of half-closed-half-open intervals
    ...teq B\big]}}</ref> and {{MSeq|b_i|i|1|n|in=\mathbb{R}|pre=b:=}} be two ''[[finite]]'' {{plural|sequence|s}} of the same length (namely {{M|n\in\mathbb{N} }})
    4 KB (680 words) - 00:23, 20 August 2016
  • Index of properties
    ...the ''adjective in the property'', for example: {{Sigma|finite}} is under "finite". ...information, so {{Sigma|finite}} is under finite, but specifically {{Sigma|finite}}
    2 KB (360 words) - 20:43, 15 June 2015
  • De Morgan's laws
    ...eck my books - I'm sure it's more general than this (this statement is for finite)}}
    364 B (69 words) - 13:14, 16 June 2015
  • Site projects:Patrolling measure theory/Task list
    ...n of subsets is a sigma-algebra iff it is a Dynkin system and closed under finite intersections]]
    5 KB (645 words) - 11:40, 21 August 2016
  • Pre-measure/Properties in common with measure
    {{Todo|Be bothered, note the significance of the finite-ness of {{M|A}} - see [[Extended real value]]}}
    1 KB (201 words) - 22:30, 30 March 2016
  • Conditions for a Dynkin system to be a sigma-algebra
    ...n of subsets is a sigma-algebra iff it is a Dynkin system and closed under finite intersections|A Dynkin system, {{M|\mathcal{D} }} is a {{sigma|algebra}} ''
    782 B (123 words) - 22:56, 2 August 2015
  • D-system
    ...n of subsets is a sigma-algebra iff it is a Dynkin system and closed under finite intersections|A collection of subsets of {{M|X}}, {{M|\mathcal{A} }} is a {
    538 B (84 words) - 15:32, 28 August 2015
  • Notes:Lambda calculus
    * ''Atomic constants'': a sequence of expressions again, that may also be finite or empty
    4 KB (832 words) - 21:22, 11 August 2015
  • Compactness/Uniting covers proof
    * Every [[Covering|cover]] by sets open in {{M|X}} has a finite subcover. }} ...every covering consisting of open sets of {{M|(X,\mathcal{J})}} contains a finite subcover.
    7 KB (1,411 words) - 19:44, 15 August 2015
  • The (pre-)measure of a set is no more than the sum of the (pre-)measures of the elements of a covering for that set
    Suppose that {{MSeq|A_i|i|1|n|in=\mathcal{R} }} is a finite [[sequence]], in this case we shall consider the ''[[countably infinite]]'' ...rove the statement for infinite sequences (as we implicitly associate each finite sequence with the corresponding infinite sequence by the above construction
    4 KB (688 words) - 21:03, 31 July 2016
  • P-system
    ...ubsets of {{M|X}}, {{M|P\subseteq\mathcal{P}(X)}} where it is closed under finite intersections<ref name="PAS"/>, that is to say: ...n of subsets is a sigma-algebra iff it is a Dynkin system and closed under finite intersections|A collection of subsets of {{M|X}}, {{M|\mathcal{A} }} is a {
    960 B (158 words) - 15:43, 28 August 2015
  • Notes:Spherical coordinates
    .... You can do it in less, but 4 is a very natural number. Notice also it is finite. This means we can do it on a computer!
    10 KB (1,899 words) - 18:48, 23 September 2015
  • Linear independence
    * For all finite sums {{M|\sum_i a_iv_i}} with ''distinct'' {{M|v_i\in S}} we have that {{M| * If for all finite sums {{M|\sum_i a_iv_i}} with {{M|v_i\in S}} we have that {{M|1=\sum_i a_iv
    3 KB (605 words) - 21:11, 2 November 2015
  • Topological space/Definition
    ..._\alpha\in\mathcal{J}</math> - that is it is closed under union (infinite, finite, whatever - "closed under ''arbitrary'' union") # For the collection <math>\{U_i\}^n_{i=1}\subseteq\mathcal{J}</math> (any ''finite'' collection of members of the topology) that <math>\cap^n_{i=1}U_i\in\math
    1 KB (227 words) - 18:09, 20 April 2016
  • Totally bounded
    * {{M|1=\forall\epsilon>0}} there exists a finite collection of [[open balls]], each of radius {{M|\epsilon}}, such that the
    626 B (101 words) - 19:44, 27 May 2016
  • Every sequence in a compact space is a lingering sequence/Proof
    ...o a set]] we see that $\ne\aleph_0$ means showing that the intersection is finite, or: ...er {{M|X}} is [[compact]] by assumption, this means every open cover has a finite subcover. Thus:
    2 KB (452 words) - 16:46, 6 December 2015
  • Combinatorics (subject)
    ...inations (or permutations) there are of doing things. For example, given 2 finite sets, how many [[function|functions]] are there from 1 to the other? This i
    708 B (88 words) - 15:05, 26 February 2016
  • Product
    ...topology]] - a very similar concept that is identical when the product is finite
    489 B (67 words) - 00:03, 7 August 2016
  • Limsup and liminf (sequence of sets)
    ...the set that contains {{M|x\in X}} given that {{M|x}} is in all ''but'' a finite number of elements of {{M|(A_n)}}. One may think to "not be in a finite number of elements" is "to be in an infinite number of elements" and conclu
    2 KB (386 words) - 22:17, 19 April 2016
  • Notes:Halmos measure theory skeleton/Old page
    * ''Theorem: '' if {{M|\mu}} is a {{sigma|finite}} measure on a {{sigma|ring}} {{M|\mathbb{R} }} and if {{M|\mu^*}} is the o
    4 KB (674 words) - 19:46, 3 April 2016
  • The (pre-)measure of a set is no more than the sum of the (pre-)measures of the elements of a covering for that set/Statement
    ...r all {{M|A\in\mathcal{R} }} and for all ''[[countably infinite]]'' or ''[[finite]]'' [[sequence|sequences]] {{M|(A_i)\subseteq\mathcal{R} }} we have:
    801 B (129 words) - 20:44, 31 July 2016
  • Extending pre-measures to outer-measures
    #*#** Given a set {{M|A}} and a [[countably infinite]] or [[finite]] ''[[sequence]]'' of sets, {{M|(A_i)}} such that {{M|A\subseteq\bigcup_i A
    11 KB (1,921 words) - 16:59, 17 August 2016
  • Lebesgue number lemma
    ** {{M|\exists}} a ''finite'' subcover of {{M|1=\{B_{\frac{1}{2}\epsilon_x}(x)\ \vert\ x\in X\} }}, cal
    2 KB (333 words) - 10:11, 10 May 2016
  • Notes:First order language
    * '''Expression''' - any finite sequence of symbols of a language.
    6 KB (1,088 words) - 09:22, 28 August 2016
  • Notes:Outer-measures to measures
    ...C: ''' If a set {{M|E\in\mathcal{H}_{\sigma R}(\mathcal{R})}} has {{sigma|finite}} ''outer'' measure then: ...{M|\bar{\mu}:\mathcal{R}\rightarrow\bar{\mathbb{R} }_{\ge 0} }} is {{sigma|finite}} then so are the measures {{M|\bar{\mu}^*}} on {{M|\sigma(\mathcal{R})}} a
    6 KB (1,067 words) - 22:19, 23 May 2016
  • Notes:The set of all mu*-measurable sets is a ring
    # I'm uncomfortable jumping from a finite sum to an infinite ...mu^*(A-F_n)}} (this is okay because {{M|\mathcal{S} }} is a ring, thus the finite union, {{M|F_n\in\mathcal{S} }}.)
    4 KB (828 words) - 03:11, 30 May 2016
  • The real numbers
    * Be sure to include [[Example:The real line with the finite complement topology is not Hausdorff]]}}
    1 KB (200 words) - 21:31, 26 February 2017
  • Notes:Diff algorithm
    * Given a finite string formed of symbols from an infinite or finite alphabet, {{M|A}} and * another finite string of the same or different length, from the same alphabet, {{M|B}}
    12 KB (2,041 words) - 00:50, 27 June 2016
  • Free monoid generated by
    * The elements of {{M|F}} are all the finite [[tuple|tuples]], {{M|(x_1,\ldots,x_n)}} (where {{M|x_i\in X}}) * The finite [[tuple|tuples]] of {{M|F}} are sometimes called "words".
    2 KB (419 words) - 16:20, 20 July 2016
  • Permutation of a set
    ...mmetric group]] is a special case of the permutation group when the set is finite.
    870 B (134 words) - 23:59, 21 July 2016
  • Linear combination
    '''Note: ''' A ''linear combination'' is ''always'' a finite sum<ref name="FAVIDMH"/><ref group="Note">This is because in a [[vector spa
    1 KB (200 words) - 07:37, 29 July 2016
  • Notes:Generalising the limit
    ...es {{M|U\cap V}} - '''PROVED''' - remember that a topology is closed under finite intersection so this is applicable.
    6 KB (1,118 words) - 11:34, 30 July 2016
  • Notes:Dual basis
    Let {{M|(V,\mathcal{K})}} be a ''finite dimensional'' [[vector space]] over the [[field]], {{M|\mathcal{K} }}, supp
    5 KB (1,020 words) - 08:43, 12 August 2016
  • Notes:Advanced Linear Algebra - Roman/Chapter 1
    * The set of all finite sums of vectors from the [[union]] {{MM|1=\bigcup_{\alpha\in I} S_\alpha}} ...of {{M|\alpha\in I}}'', that is if the [[cardinality]] of the support is [[finite]] (or {{M|\in\mathbb{N} }}).
    8 KB (1,463 words) - 14:35, 13 August 2016
  • Notes:Basis for a topology/McCarty
    ...is an arbitrary family of sets then {{M|\mathcal{B} }} - the family of all finite intersections of elements of {{M|\mathcal{A} }}<ref group="Note">Note that # For each member of {{M|\mathcal{J} }} the member is the union of (finite intersections of elements of {{M|\mathcal{A} }})
    3 KB (467 words) - 16:58, 16 August 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
  • Distributivity of intersections across unions
    ...finite disjoint unions]], the theorem is easy and routine, at least in the finite cases}}
    730 B (128 words) - 23:19, 18 August 2016
  • A pre-measure on a semi-ring may be extended uniquely to a pre-measure on a ring
    * The ring generated by a semi-ring is exactly the set of all finite disjoint unions of elements from that semiring. ...thcal{F}) }} can be written as {{M|1=A=\bigudot_{i=1}^n A_i}} for some ''[[finite]]'' [[sequence]] of [[pariwise disjoint]] sets, {{MSeq|A_i|i|1|n|in=\mathca
    2 KB (390 words) - 22:16, 19 August 2016
  • Types of set algebras/Type table
    ...} is {{M|\backslash}}-closed<ref group="Note" name="\-closed">Closed under finite [[Set subtraction]]</ref> ...l{A} }} is {{M|\cup}}-closed<ref group="Note" name="U-closed">Closed under finite [[Union]]</ref>
    4 KB (573 words) - 20:00, 19 August 2016
  • Notes:Infinity notation
    ** Does this mean all ''finite'' tuples, or does it include {{M|X^\mathbb{N} }}?
    2 KB (350 words) - 15:23, 21 October 2016
  • A subset of a topological space is open if and only if it is a neighbourhood to all of its points
    ...collection of things in {{M|\mathcal{J} }} is in {{M|\mathcal{J} }}) and ''finite'' [[intersection]].
    8 KB (1,529 words) - 00:27, 6 September 2016
  • Domain (FOL)
    # Define some sort of pre-cursor "finite" set theory and "bootstrap" formal logic with it, to then develop "real" se ...e that these sets, {{M|\mathcal{F} }} and {{M|\mathcal{R} }} could also be finite, as in (most?) {{plural|first order language|s}} there are only finitely ma
    4 KB (672 words) - 06:42, 10 September 2016
  • Demonstrating why category arrows are best thought of as arrows and not functions
    ...ory]], {{M|\mathscr{C} }}, whose {{link|object|category theory|s}} are ''[[finite]]'' {{plural|set|s}} and whose {{link|arrow|category theory|s}}, {{M|\xymat
    2 KB (275 words) - 12:29, 15 September 2016
  • Path
    * [[Path (graph)]] - a path in a [[graph]] or [[digraph]] is a possibly finite sequence of edges such that the final node of each edge is the initial node
    917 B (146 words) - 23:47, 14 October 2016
  • The image of a compact set is compact
    ...mathcal{U} }} be an [[open cover]] of {{M|f(A)}} and then showing it has a finite subcover
    2 KB (332 words) - 17:20, 18 December 2016
  • Notes:Modules
    ...tion doesn't matter if the vector spaces are finite (or if just {{M|V}} is finite {{caution|I would have thought}})</ref> be given. Then for any [[polynomial
    4 KB (808 words) - 17:18, 11 October 2016
  • Pasting lemma
    # A [[finite]] ''[[closed set|closed]]'' [[cover]] of {{M|X}}
    1 KB (193 words) - 07:07, 14 October 2016
  • Exercises:Measure Theory - 2016 - 1/Section B/Problem 1
    ...t\mathbb{N})}} - where {{M|\mathcal{P} }} denotes the [[power set]] of the finite set {{M|\{1,\ldots,n\} }} - which is a portion of {{M|\mathbb{N} }} - the n
    10 KB (1,844 words) - 14:09, 23 October 2016
  • Invariant of an equivalence relation
    * [[Complete system of invariants]] - a finite set of complete invariants really.
    3 KB (478 words) - 18:58, 9 November 2016
  • Total derivative
    ...} are finite {{link|dimension|vector space|al}} then recall [[all norms on finite dimensional vector spaces are equivalent]] and thus the choice of norm does * '''''See: '''[[For finite dimensional vector spaces the derivative at a point is independent of the n
    2 KB (313 words) - 01:27, 15 November 2016
  • Characteristic property of the tensor product/Statement
    ...,\mathbb{F})\big)_{i\eq 1}^k}} be a family of ''[[dimension (vector space)|finite dimensional]]'' [[vector spaces]] over {{M|\mathbb{F} }}. Let {{M|(W,\mathb
    2 KB (268 words) - 22:07, 20 December 2016
  • Basis for the tensor product/Statement
    ...,\mathbb{F})\big)_{i\eq 1}^k}} be a family of ''[[dimension (vector space)|finite dimensional]]'' [[vector spaces]]. Let {{M|n_i:\eq\text{Dim}(V_i)}} and {{M
    972 B (177 words) - 23:56, 6 December 2016
  • Notes:Dual to dual vector space
    Let {{M|(V,\mathbb{F})}} be a finite dimensional [[vector space]]. Let {{M|V^*}} denote the [[dual vector space]
    2 KB (318 words) - 05:34, 8 December 2016
  • Notes:Free group
    '''Words''' in the "''alphabet''" {{M|Y}} are ''[[finite]]'', but possibly empty, [[sequences]] of elements of {{M|Y}}. ...lication is [[concatenation]]<ref group="Note">Obviously, concatenation of finite sequences {{M|a:\eq(a_1,\ldots,a_\ell)}} and {{M|b:\eq(b_1,\ldots,b_m)}} is
    3 KB (544 words) - 20:36, 10 December 2016
  • Formal linear combination/Definition
    ...ert\in\mathbb{N} }} '''doesn't hold'''}} as the set of even numbers is not finite.</ref><sup>, </sup><ref group="Note">Zero here denotes the "additive identi *** That is to say {{M|f}} takes non-zero values a finite number of times only, it is zero "''[[almost everywhere]]''"
    3 KB (615 words) - 15:36, 24 December 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
  • CW-complex
    ...ndary (topology)|{{M|\partial\overline{\mathbb{B}^n} }}]] is mapped into a finite [[union]] of [[open n-cell|open {{N|cells}}]] of dimension strictly less th
    1 KB (187 words) - 14:14, 20 January 2017
  • Notes:CW-Complex
    ...injection" - I mention this here to record Munkres' exact phrasing</ref> a finite union of open cells, each of dimension (strictly) less than {{M|m}} We build an "attaching space" called a (finite) cell complex inductively from the following recipe:
    10 KB (1,736 words) - 01:00, 23 January 2017
  • Exercises:Saul - Algebraic Topology - 2/Exercise 2.5
    ...lian group if you will. Then any {{M|B\in\mathcal{P}(A)}} where {{M|B}} is finite must be a linearly independent set (and obviously doesn't contain {{M|0\in\
    4 KB (713 words) - 12:22, 25 January 2017
  • Basis (linear algebra)
    ...})}} be a [[vector space]] and let {{M|(b_i)_{i\eq 1}^n\subseteq V }} be a finite set of vectors of {{M|V}}. Then {{M|(b_i)_{i\eq 1}^n}} is a ''basis'' for {
    1 KB (251 words) - 13:17, 26 January 2017
  • Span (linear algebra)
    * {{M|\text{Span}(v_1,\ldots,v_k)}} for a finite collection For a [[finite]] collection, {{M|\{v_1,\ldots,v_k\} }} this simplifies to:
    3 KB (486 words) - 13:51, 26 January 2017
  • The ell p spaces
    ...M|\mathbb{R}^n}} and {{M|\mathbb{C}^n}} we also have the p-norm, just as a finite sum rather than an infinite one as shown above. It is claimed that{{RW2014L
    2 KB (296 words) - 14:30, 26 January 2017
  • Simplicial complex
    ...polyhedron]]'' - but some topologists reserve this for the polytope of a ''finite'' simplicial complex * [[If a simplicial complex is finite then it is compact]]
    4 KB (681 words) - 15:12, 31 January 2017
  • Notes:Delta complex/Formal attempt
    **** As {{M|\mathbb{R}^{m+1} }} is finite dimensional we see that {{M|L_f'}} is a [[continuous map]], so forth. As wo
    5 KB (966 words) - 14:36, 6 February 2017
  • Vertex scheme of an abstract simplicial complex/Definition
    ...ere so {{M|n}} may be zero, we are expressing our interest in only those ''finite'' members of {{M|\mathcal{P}(V_K)}} here, and that are non-empty.
    1 KB (224 words) - 11:51, 19 February 2017
  • Exercises:Saul - Algebraic Topology - 8/Exercise 8.5
    ...- note that this is [[open set|open]] in {{M|N}} as the intersection of a finite number (2) of sets is open in a [[topology]]
    7 KB (1,330 words) - 15:25, 7 March 2017
  • Path-connected topological space
    * The [[n-torus]], {{M|\mathbb{T}^n}} is path connected as it is a finite product of [[circle|circles]]
    2 KB (249 words) - 12:52, 23 February 2017
  • Graph (graph theory)
    : {{Caveat|Here we describe a finite graph;}} infinite graphs are a thing, but they require special handling<ref * {{M|V}} be a [[finite set]] whose elements we shall call ''vertices'' (singular: ''vertex'') or '
    2 KB (319 words) - 22:15, 13 January 2018
  • Digraph
    ...rmal languages and automata hardbook by my bed, deal with later.</ref> for finite set of vertices {{M|V}} and {{M|E}} are edges of the form {{M|(v_i,v_j)}} -
    903 B (155 words) - 22:18, 13 January 2018
  • Weighted average
    ...ues'', for {{M|V}} a ???; and let {{M|\big(w_i\big)_{i\eq 1}^n\in W}} be a finite collection of ''weights'', for {{M|W}} a ???.
    2 KB (417 words) - 04:47, 6 September 2017
  • Example:Joint probability distribution
    ...\eq\bigcup_{V\in U}Z^{-1}(V) }} - which is a finite union. As {{M|S}} is a finite set in this example, we see that {{M|\sigma(S)\eq\mathcal{P}(S)}}, which gi ...asurable, both the {{link|codomain|function|s}} of {{M|X}} and {{M|Y}} are finite, thus they're both measurable</ref>
    7 KB (1,100 words) - 19:36, 13 September 2017
  • Law of total probability
    ...be a [[probability space]], let {{M|(U_i)_{i\eq 1}^n\subseteq\Omega}} be a finite collection of [[measurable set|{{M|\mathbb{P} }}-measurable sets]] such tha
    2 KB (398 words) - 01:50, 7 October 2017
  • Alec's taxonomy of units
    #* As any total order (aka [[linear order]]) that is finite is (obviously) in some sense "isomorphic" to a subset of the [[natural numb
    4 KB (592 words) - 07:29, 11 December 2017
  • Floor function
    ...ge 0} }} - note that the maximum element is defined as {{M|T_x}} is always finite.
    2 KB (377 words) - 21:20, 21 January 2018
  • 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
  • Alphabet (formal languages)
    ...FA]] and so forth, typically denoted {{M|\Sigma}} (capital "sigma") is a [[finite set]] of "symbols" used in the {{link|sentences|formal languages}} or {{lin * {{link|String|formal languages|s}} - ''[[finite]]'' [[tuples]] of symbols from an alphabet.
    1 KB (153 words) - 00:37, 13 January 2018
  • DFA
    #REDIRECT [[Deterministic finite automaton]]
    79 B (8 words) - 00:32, 13 January 2018
  • NFA
    #REDIRECT [[Non-deterministic finite automaton]]
    83 B (8 words) - 00:33, 13 January 2018
  • NFAs
    #REDIRECT [[Non-deterministic finite automaton]]
    83 B (8 words) - 22:05, 13 January 2018
  • DFAs
    #REDIRECT [[Deterministic finite automaton]]
    79 B (8 words) - 14:40, 17 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
  • Combination
    A combination lock is the unfortunate term given to a device which has a finite and fixed number of wheels or dials with some number (usually the same for
    3 KB (506 words) - 16:32, 14 April 2018
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