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• Relation
  # The ''identity relation''<ref name="APIKM"/>, {{M|1=\text{id}_X:=\text{id}:=\{(x,y)\in X\t | Every element is related to itself (example, equality)
  4 KB (762 words) - 20:07, 20 April 2016
• Basis and coordinates
  ...ese matrices (which I simply cannot be bothered to write) you will get the identity matrix, that is <math>([L]_S^{S'}[K]_{S'}^S)(x,y)=(x,y)</math> ===L is actually the identity===
  9 KB (1,525 words) - 16:30, 23 August 2015
• Group
  ...(G,*)</math> (or sometimes {{M|(G,*,e_G)}} where {{M|e_G}} is the identity element of the group), often just "Let {{M|G}} be a group" with the implicit operat | {{M|*}} has an [[Identity element|identity element]]
  7 KB (1,332 words) - 07:17, 16 October 2016
• Subgroup
  # There exists an identity element <math>\in H</math>. # Every element has an inverse <math>\in H</math>
  2 KB (364 words) - 17:35, 15 March 2015
• Ring
  | Additive identity If {{M|(S,+,\times)}} is a ring, and every element of {{M|S}} is also in {{M|R}} (for another ring {{M|(R,+,\times)}}) and the
  7 KB (1,248 words) - 05:02, 16 October 2016
• The fundamental group
  * Identity element
  3 KB (393 words) - 16:10, 4 November 2016
• Monoid
  * Has identity element - that is <math>\exists e\in S\forall x\in S[ex=xe=x]</math>
  735 B (131 words) - 07:48, 27 April 2015
• Kernel
  ...}} and {{M|Y}} of the same type of space (which is imbued with an identity element), the kernel of {{M|f:X\rightarrow Y}} (where {{M|f}} is a [[Function|funct ...th>\text{Ker}(f)=\{x\in X|f(x)=e\}</math> where <math>e</math> denotes the identity of {{M|Y}}
  2 KB (376 words) - 19:53, 10 May 2015
• Generated subgroup
  A [[Cyclic subgroup|cyclic subgroup]] is a group generated by a single element. ...}} the result of the operation on the empty list is {{M|e}} - the identity element of {{M|G}}''
  2 KB (404 words) - 12:39, 12 May 2015
• Group action
  ** {{M|1=\forall x\in X[1\cdot x=x]}} (where {{M|1}} is the identity element of {{M|(G,*)}} group) and
  2 KB (320 words) - 23:28, 21 July 2016
• Abstract Algebra (subject)
  ...certain properties, for example, associativity, or an element (called the identity) which does nothing.
  2 KB (328 words) - 10:53, 20 February 2016
• Group/New page
  ...of {{M|G}}<ref group="Note">At this point we do not know that the identity element is unique, there could be more than one such {{M|e}} - but one exists. In f ...in G\exists h\in G[g*h=h*g=e]}} - for each element there exists an inverse element in {{M|G}}<ref group="Note">Again, we do not know there is a unique inverse
  2 KB (326 words) - 11:38, 2 July 2016
• Free monoid generated by
  * The identity element of the monoid is: ...ated by]] {{M|X}}<ref group="Note">We do this because the semigroup has no identity (in fact, is considered as the set of all tuples of length greater than or
  2 KB (419 words) - 16:20, 20 July 2016
• Notes:Topology - Munkres/Section 68
  ...a\implies G_\alpha\cap G_\beta=\{e\}]}} where {{M|e}} denotes the identity element of {{M|G}}
  1,008 B (160 words) - 11:57, 9 August 2016
• Notes:Advanced Linear Algebra - Roman/Chapter 1
  ...lusion]], with smallest element {{M|\{0\} }} (the zero vector) and largest element {{M|V}} itself. The meet and join are defined as follows<ref group="Note">A ...rwise disjoint (not counting the identity, so the intersection is only the identity)}} this isn't hard to see, if you take, for example:
  8 KB (1,463 words) - 14:35, 13 August 2016
• Notes:Modules
  ...}} then {{M|1=p(\tau)=i+2\tau+\tau^3}} where {{M|i:V\rightarrow V}} is the identity map, and {{M|\tau^3}} is the threefold [[function composition]] {{M|\tau\ci ...operations of addition and multiplication of an element of {{M|V}} with an element of {{M|F[x]}}!
  4 KB (808 words) - 17:18, 11 October 2016
• Ring/New page
  ...\forall a\in R[e\oplus a=a\oplus e=a]}} - existence of [[identity element|identity]], on the [[group]] page we show it is unique<ref group="Note">there is onl ...age we show it is unique<ref group="Note">there is only one inverse for an element</ref>. Denoted by {{M|-a}} as we're using [[additive notation]]<ref group="
  4 KB (728 words) - 16:29, 19 October 2016
• Proof that the fundamental group is actually a group/Proof
  # Existence of an identity element in {{M|(\pi_1(X,b),\overline{*})}} # For each element of {{M|\pi_1(X,b)}} the existence of an inverse element in {{M|(\pi_1(X,b),\overline{*})}}
  3 KB (459 words) - 11:44, 8 November 2016
• Absolute value (object)
  ...\vert x\vert_v\eq 0)\iff(x\eq 0)]}} where {{M|0}} is the additive identity element of the field.
  2 KB (350 words) - 05:25, 21 November 2016
• Symmetric group
  ...tarrow\{1,\ldots,k\} }} which acts as so: {{M|e:i\mapsto i}} - this is the identity permutation, it does nothing. ...gma}} considered as a [[function]] and thing below it is the image of that element under {{M|\sigma}}
  3 KB (425 words) - 12:21, 30 November 2016
• Example:Permutation (group theory) of S5/Body
  ...3\ 5\ 4)(2)}} if you do not take the "implicit identity" part. That is any element not in a cycle stays the same
  1 KB (177 words) - 12:11, 30 November 2016
• Trivial
  ...ightarrow\{e\})}} is called the [[trivial group]], {{M|e}} is the identity element and {{M|e*e\eq e}} is the only operation
  1 KB (171 words) - 13:29, 16 February 2017
• Trivial group
  We use {{M|e}} for the object as it is the identity element of the group # {{M|e}} is the identity element of the group.
  2 KB (268 words) - 13:41, 16 February 2017
• Exercises:Saul - Algebraic Topology - 7/Exercise 7.6
  ...beta)-\partial_1(\beta)}}, then we see {{M|\partial_1(c)}} is the identity element, {{M|0}}, so cannot be in a basis set for obvious reasons, and {{M|\partial ...y to the identity, couple this with the domain of {{M|\partial_n}} has one element and the result follows.
  10 KB (1,664 words) - 12:43, 1 March 2017
• Floor function
  ...subseteq\mathbb{N}_0\subseteq\mathbb{R}_{\ge 0} }} - note that the maximum element is defined as {{M|T_x}} is always finite. ...}_0} }} - its {{link|restriction|function}} to {{M|\mathbb{N}_0}} is the [[identity map]] on {{M|\mathbb{N}_0}}
  2 KB (377 words) - 21:20, 21 January 2018