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• Group
  ...th groups we use "multiplicative notation", if the group is Abelian we use additive. This is (probably) motivated from linear algebra. Addition of matrices is ===Additive===
  7 KB (1,332 words) - 07:17, 16 October 2016
• Additive function
  Right now this defines an additive SET function, if you add an additive function (which way have meaning in say algebra), be sure to update the SET ...f:\mathcal{A}\rightarrow\mathbb{R} }} is called ''additive'' or ''finitely additive'' if{{rMT1VIB}}:
  6 KB (971 words) - 18:16, 20 March 2016
• Associative
  ...{M|\times}} the ''product'' (or indeed the ''sum'' if we're using additive notation)
  455 B (77 words) - 07:44, 27 April 2015
• Kernel
  ...near Algebra - Steven Roman - Third Edition - Springer GTM</ref> using the notation <math>Tv=T(v)</math> ...th>\text{Ker}(f)=\{x\in X|f(x)=0\}</math> where <math>0</math> denotes the additive identity of the vector space
  2 KB (376 words) - 19:53, 10 May 2015
• Pre-measure/New page
  ...non-negative) pre-measure'' is an ''[[extended real valued]]'' [[countably additive set function]], {{M|\bar{\mu}:\mathcal{R}\rightarrow\overline{\mathbb{R}_{\ ...\bar{\mu}(A_n)\right)\right]}}<ref group="Note">There is a slight abuse of notation here, by the nature of [[implies]] if the LHS is false, we do not care if t
  3 KB (422 words) - 21:25, 17 August 2016
• Notes:Measure theory plan
  This document is the ''plan'' for the measure theory notation and development on this site. ...{M|\bar{\mu} }}) - Introduce a (positive) extended real valued [[countably additive set function]], {{M|\bar{\mu} }} on that ring. This will be a pre-measure a
  4 KB (619 words) - 19:28, 24 May 2016
• Notes:Halmos measure theory skeleton/Old page
  * [[additive set function]] ...measure'', {{M|\mu}} - [[extended real valued]], non negative, [[countably additive set function]] defined on a [[ring of sets]]
  4 KB (674 words) - 19:46, 3 April 2016
• Notes:Boundary operator
  We often abuse notation and denote the elementary chain corresponding to {{M|\sigma}} by {{M|\sigma We can form an (additive) group of {{M|p}}-chains, by simply adding them pointwise. The resulting gr
  1 KB (257 words) - 00:29, 8 May 2016
• Outer splicing set
  ...mos, abuse notation quite a lot. For example Halmos gives a great abuse of notation here, by writing {{M|B\cap A'}} (where {{M|A'}} denotes the [[complement]] ...perty that that "splicing" together {{M|Y-X}} and {{M|Y\cap X}} is exactly additive on the [[outer-measure]] {{M|\mu^*}}. Be aware that traditionally such sets
  2 KB (378 words) - 22:09, 20 August 2016
• Ring/New page
  ...as we're using [[additive notation]]<ref group="Note">For [[multiplicative notation]] we'd use {{M|a^{-1} }}</ref>
  4 KB (728 words) - 16:29, 19 October 2016
• Polynomial u-ring
  ...- which is quite literally "there are finitely many elements that are the additive identity of {{M|R}}"</ref> Identity (of the [[abelian group|abelian]] additive [[group]]) and unity of the ring:
  3 KB (643 words) - 02:34, 20 November 2016
• Absolute value (object)
  ...uation''{{rAAPAG}}) on {{M|F}} is a [[mapping]], {{M|v}}, with the special notation defined as follows{{rAAPAG}}: ...M|\forall x\in F[(\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
• Formal linear combination/Definition
  ...is not finite.</ref>^,<ref group="Note">Zero here denotes the "additive identity" of the field, {{M|\mathbb{F} }}</ref> (where {{M|\big\vert\cdot\b ...m were formally defined to have meaning, we still use the usual [[abuse of notation]] when only finitely many elements of the summation are non-zero whereby {{
  3 KB (615 words) - 15:36, 24 December 2016
• Span (linear algebra)
  ...do this finitely many times ultimately. So we use the following [[abuse of notation]]: ...''finitely many'' non zero terms. We use the fact that zero vector is the additive identity (and thus {{M|0+v\eq v}}) to "pretend" we included them, they have
  3 KB (486 words) - 13:51, 26 January 2017