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Create the page "C Definitions" on this wiki! See also the search results found.

• Nabla
  ...ok (Vector Analysis and Cartesian Tensors - Third Edition - D E Borune & P C Kendall - which is a good book) distinguishbetween the <math>\nabla</math>s ...actually come across the need for this. Which is why I list the first two definitions. I write this to show I have considered alternatives and why I do not use t
  1 KB (245 words) - 18:35, 13 February 2015
• Connected (topology)
  There are equivalent definitions, some are given below. Note also, that by this convention the [[emptyset|{{ There are equivalent definitions, some are given below.
  5 KB (866 words) - 01:52, 1 October 2016
• Ordering
  | <math>\forall a\in A\forall b\in A\forall c\in A([aRb\wedge bRc]\implies aRc)</math> ...=\mathbb{N} }} then <math>a\le b\wedge b\le c\iff a\le b\le c\implies a\le c</math>
  5 KB (1,006 words) - 13:21, 1 January 2016
• Basis and coordinates
  ===Formal definitions=== Rather than working out the transform from {{M|C}} to {{M|S'}} or whatever we can simply notice:
  9 KB (1,525 words) - 16:30, 23 August 2015
• Sigma-algebra
  ===Note on Alternative Definitions=== ...sigma|algebra}}, the definition above is actually equivalent to the longer definitions one might see around.<br/> The two properties above give rise to all the ot
  8 KB (1,306 words) - 01:49, 19 March 2016
• Ring
  | <math>\forall a,b,c\in R[(a+b)+c=a+(b+c)]</math> | Now writing {{M|a+b+c}} isn't ambiguous
  7 KB (1,248 words) - 05:02, 16 October 2016
• Tangent space
  <math>\omega\in T_p(\mathbb{R}^n)\iff \omega:C^\infty(\mathbb{R}^n)\rightarrow\mathbb{R} </math> is a [[Derivation|derivat ...ghtarrow\mathbb{R}</math> which satisfies the [[Leibniz rule]]. Recall {{M|C^\infty(M)}} is the set of all [[Smooth function|smooth functions]] on our [
  6 KB (1,190 words) - 19:27, 14 April 2015
• Derivation
  If {{M|a\in\mathbb{R}^n}}, we say that a map, {{M|\alpha:C^\infty(\mathbb{R}^n)\rightarrow\mathbb{R} }} is a '''''derivation at {{M|a} * Given {{M|f,g\in C^\infty(\mathbb{R}^n)}} we have:
  2 KB (325 words) - 18:08, 14 October 2015
• Smooth
  '''Note:''' there are many definitions of smooth and it changes a lot between books - I shall be consistent in thi ...Second Edition</ref> <math>F:U\rightarrow V</math> is '''smooth''', <math>C^\infty</math> or ''infinitely differentiable'' if:
  870 B (148 words) - 06:38, 7 April 2015
• Motivation for tangent space definitions
  ...nts, and going between manifolds. THIS page will talk about the reason for definitions. Like a study guide. So far on [[Smooth manifold|smooth manifolds]] all we have are the following definitions:
  4 KB (790 words) - 22:25, 12 April 2015
• Hausdorff space
  ===Equivalent definitions=== ...q A}} and {{M|D\subseteq B}} then if {{M|A\cap B\eq\emptyset}} we have {{M|C\cap D\eq\emptyset}} - this could be worth factoring out
  4 KB (679 words) - 22:52, 22 February 2017
• Addition of vector spaces
  ==Definitions== '''Operations:''' (given {{M|u_i,v_i\in V_i}} and {{M|c}} is a scalar in {{M|F}})
  4 KB (804 words) - 18:02, 18 March 2016
• Limit
  ...>\forall C>0\exists N\in\mathbb{N}\forall n\in\mathbb{N}[n> N\implies a_n> C]</math> ...>\forall C<0\exists N\in\mathbb{N}\forall n\in\mathbb{N}[n> N\implies a_n< C]</math>
  2 KB (310 words) - 18:23, 8 January 2016
• Site projects:Patrolling measure theory/Task list
  * [[Dynkin system/Proof that definitions 1 and 2 are equivalent]] '''DONE''' [[User:Alec|Alec]] ([[User talk:Alec|ta ...S is in A for every S in G|A map from two sigma-algebras, A and B,...]] {{C|Needs minor work}}
  5 KB (645 words) - 11:40, 21 August 2016
• Bounded set
  ...\forall a,b\in A[d(a,b)<C]}} - where {{M|C}} is real<ref group="Note">{{M|C\in\mathbb{R}_{\ge 0} }} should do as {{M|0}} could be a bound, I suppose on This follows right from the definitions, the {{M|K}} is the bound.
  2 KB (409 words) - 23:31, 29 October 2016
• Dynkin system
  ==Proof of equivalence of definitions== '''[[Dynkin system/Proof that definitions 1 and 2 are equivalent|Claim]]: ''' Definition 1 {{M|\iff}} Definition 2
  1 KB (184 words) - 01:54, 19 March 2016
• Borel sigma-algebra
  ...hcal{B} }} itself) - some are listed here. First here are some non-obvious definitions: ! {{M|1=\mathcal{B}^n=\sigma(\mathcal{C})}} - closed<ref name="MIM"/>
  5 KB (854 words) - 09:25, 6 August 2015
• Dynkin system/Proof that definitions 1 and 2 are equivalent
  The following definitions are the same: :#* Note that {{M|1=A-B=(A^c\udot B)^c}} (this is not true in general, it requires {{M|B\subseteq A}}{{Note|Includ
  2 KB (326 words) - 05:09, 22 August 2015
• Cone (category theory)
  ...ontrast each other well, see the page [[cone and cocone compared]] for the definitions compared side by side ...category theory)|objects]] {{M|A}}, {{M|B}} in a [[category]] {{M|\mathscr{C} }}, a ''cone''{{rAITCTHS2010}} is:
  1 KB (197 words) - 22:27, 28 February 2016
• Cocone (category theory)
  ...ontrast each other well, see the page [[cone and cocone compared]] for the definitions compared side by side ...category theory)|objects]] {{M|A}}, {{M|B}} in a [[category]] {{M|\mathscr{C} }}, a ''cocone''{{rAITCTHS2010}} is:
  1 KB (182 words) - 22:28, 28 February 2016