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• Injection
  {{Requires work|grade=A* For a [[Function|function]] <math>f:X\rightarrow Y</math> every element of <math>
  3 KB (463 words) - 21:50, 8 May 2018
• Open ball
  Given a [[metric space]] {{M|(X,d)}} the ''open ball centred at {{M|x_0\in X}} of r ...{x\in X\vert\ d(x,x_0)<r\} }} - that is all the points of {{M|X}} that are a distance (given by {{M|d}}) strictly less than {{M|r}} from {{M|x_0}}
  4 KB (842 words) - 02:00, 29 November 2015
• Continuous map
  {{Refactor notice|grade=A}} ...are a few different conditions for continuity, there's also continuity at a point. This diagram is supposed to show how they relate to each other.
  6 KB (972 words) - 01:44, 14 October 2016
• Surjection
  {{Requires work|grade=A*|msg=See [[Injection]]'s requires-work box [https://wiki.unifiedmathematics ...element of <math>B</math> is mapped onto from at least one thing in <math>A</math>
  2 KB (263 words) - 21:56, 8 May 2018
• The relationship between logical implication and the subset relation
  ...f B") if and only if every element of <math>A</math> also belongs to <math>B</math> That is: <math>[A\subseteq B]\iff\forall x[x\in A\implies x\in B]</math><ref>Definition 3.10 (p10) - Introduction to Set Theory, Third Editi
  776 B (136 words) - 17:36, 16 January 2017
• Basis for a topology
  {{Refactor notice|grade=A|msg=Updating with findings. * Need to add: [[A function is continuous if and only if the pre-image of every basis element
  5 KB (802 words) - 18:35, 17 December 2016
• Homomorphism
  {{Refactor notice|grade=B}} ** [[Homomorphism (vector space)]] - {{AKA}}: [[linear map]] - instance of a [[module homomorphism]]
  4 KB (532 words) - 22:04, 19 October 2016
• The set of all open balls of a metric space are able to generate a topology and are a basis for that topology
  ...n Apr 2015 when [[Template:Theorem]] was moved to [[Template:Theorem Of]]. A very old page indeed!}} ...M|X}} be a [[set]], let {{M|d:X\times X\rightarrow\mathbb{R}_{\ge 0} }} be a [[metric]] on that set and let {{M|(X,d)}} be the resulting [[metric space]
  4 KB (814 words) - 22:16, 16 January 2017
• Triangle inequality
  ...[Metric space|metric space]]) of which <math>|x-z|\le|x-y|+|y-z|</math> is a special case. ...is <math>|a+b|\le |a|+|b|</math>, notice if we set {{M|1=a=x-y}} and {{M|1=b=y-z}} then we get <math>|x-y+y-z|\le|x-y|+|y-z|</math> which is just <math>
  3 KB (546 words) - 13:05, 19 February 2016
• Product topology
  {{Refactor notice|grade=A|As a part of the topology patrol}} {{Requires references|grade=A|msg=Check Munkres and Topological Manifolds}}
  5 KB (871 words) - 20:32, 23 September 2016
• Function
  A function {{M|f}} is a special kind of [[Relation|relation]] ...]<ref name="API">Analysis - Part 1: Elements - Krzysztof Maurin</ref>, for a relation:
  4 KB (659 words) - 13:01, 19 February 2016
• Set theory axioms
  ...posed to provide some discussion for the axioms (for example "there exists a set with no elements" doesn't really deserve its own page) ...eory axioms|motivation for set theory axioms page]], note that "R" denotes a result. Only "major" results are shown, they are covered in the motivation
  3 KB (619 words) - 10:25, 11 March 2015
• Motivation for set theory axioms
  This assumes you have some "general idea" of what a set is. For example you are happy that {{M|\{1,2,3\}=\{2,1,3\} }} and that ...can say "from these axioms, we know this set exists" - for example we use a letter (<math>\emptyset</math>) to denote the empty set, what if there are
  3 KB (584 words) - 23:03, 28 February 2015
• Implies
  ...th>A\implies B</math> or <math>B\impliedby A</math> where {{M|A\text{ and }B}} are statements of some sort means<ref>https://en.wikipedia.org/w/index.ph ! A
  681 B (111 words) - 13:36, 16 June 2015
• Editing guide
  | rowspan="2" | A shame, because a black-board style {{M|1}} would be a great [[indicator function]] ...ome letters can be difficult to identify, for example {{M|\mathscr{I} }} - a {{C|J}} right? ''Wrong'' - an {{C|I}}}}
  5 KB (759 words) - 18:48, 24 September 2016
• Ordered pair
  ...dered pair <math>(a,b)=\{\{a\},\{a,b\}\}</math>, this way <math>(a,b)\ne(b,a)</math>. Suppose we are given <math>a,b</math> (so we can be sure they exist).
  2 KB (327 words) - 07:22, 27 April 2015
• Todo list
  | Proof that a function is invertible {{M|\iff}} it is one-to-one (Jech, Set Theory -p25) ...oof that <math>B^A</math> - the set of all functions from {{M|A}} into {{M|B}} exists
  464 B (76 words) - 16:54, 10 June 2015
• Ordering
  ...g|Proof that <math>\le</math> is a partial ordering <math>\iff <</math> is a strict ordering]] ...special kind of [[Relation|relation]], we can define an order uniquely as a partial or strict ordering. That is the two are equivalent.
  5 KB (1,006 words) - 13:21, 1 January 2016
• Equivalence relation
  A [[relation]], {{M|\sim}}, in {{M|X}}<ref group="Note">This terminology mean ...ss]] is the name given to the set of all things which are equivalent under a given equivalence relation.
  3 KB (522 words) - 15:18, 12 February 2019
• Linear map
  | What we'd call linear map, it's just a map {{M|T:(V,F)\rightarrow(W,F)}} where {{M|1=T(\alpha u+\beta v)=\alpha T( | A linear transform into the same space as the domain, that is {{M|T:(V,F)\rig
  3 KB (512 words) - 16:30, 23 August 2015