User:Paulmiko

Contributions

User:Paulmiko/vector.css

Notes

• User:Paulmiko/Testpage
• User:Paulmiko/Testpage/box-header
• User:Paulmiko/Testpage/box-footer
• User:Paulmiko/Testpage/box-footer-empty
• User:Paulmiko/Testpage/Intro
• User:Paulmiko/Testpage/Random portal component

To-Do

• Group Theory
• Computational complexity of mathematical operations
• Function (mathematics)

Interesting Pages

• http://en.wikipedia.org/wiki/Wikipedia:Unusual_articles
• http://en.wikipedia.org/wiki/Kim_Peek
• http://en.wikipedia.org/wiki/Abigail_and_Brittany_Hensel
• http://en.wikipedia.org/wiki/Paul_Erdős
• http://en.wikipedia.org/wiki/Chaos_magic
• http://en.wikipedia.org/wiki/Boolean_algebra
• http://en.wikipedia.org/wiki/School_shooting
• http://en.wikipedia.org/wiki/Reign_of_Terror
• http://en.wikipedia.org/wiki/Akashic_records
• http://en.wikipedia.org/wiki/The_Sleep_of_Reason_Produces_Monsters
• http://copybot.wordpress.com/2009/04/07/the-50-most-interesting-articles-on-wikipedia/
• http://copybot.wordpress.com/2009/09/29/50-more-of-wikipedias-most-interesting-articles/
• http://en.wikipedia.org/wiki/Michael_Malloy
• http://en.wikipedia.org/wiki/Georgia_Guidestones
• http://en.wikipedia.org/wiki/EnCase
• http://en.wikipedia.org/wiki/TEMPEST

Important style guides and useful help

Important Style guides and useful help

• meta:Help:Formula - for TeX markup in Wikipedia
• Wikipedia:Manual of Style (mathematics)
• Wikipedia:Manual of Style (China-related articles)
• Wikipedia:Userboxes
• Wikipedia:Template messages
• Wikipedia:Duplicate articles - use {{merge|OTHER ARTICLE}}
• Wikipedia:Administrator intervention against vandalism - to block
• Wikipedia:Requests for expansion
• Wikipedia:WikiProject Stub sorting and Wikipedia:WikiProject Stub sorting/Stub types
• Wikipedia:Footnotes - If citing something, put <ref> Reference </ref> after it. *If citation is missing, put {{fact}} for
  1. "{{dubious}}" for ""
  2. {{Citation needed}} for
• Wikipedia:Refactoring talk pages
• Help:Interlanguage links en de fi etc.; Help:Interwiki linking one scope step further
• Category:Wikipedia maintenance templates
• Category:Disambiguation and redirection templates
• Category:Templates using ParserFunctions and m:ParserFunctions and m:Help:Magic words
• mw:Manual:Extensions, mw:Manual:Extensions and mw:Category:All extensions for useful markup extensions such as <source lang="php">
• Wikipedia:NavFrame and Wikipedia:Collapsible tables - frankly speaking, I love 'em
• How to find the deletion discussion of an article:
  • the awkward way: look in the Deletion log to obtain date and time of a deletion, then look at Wikipedia:Archived delete debates near that time to see which edit regards the unlisting of the page, then view the previous version.
  • the probably not always working easier way: directly go to Wikipedia:Articles for deletion/ARTICLENAME
• Wikipedia:WikiProject Inline Templates

WIP

Relations Chart

Heterogeneous Relations

				Uniqueness				Totality
Relations	Left-Unique (Injective Relation)		Right-Unique (Functional Relation) (Right-Definite) (Partial Function)		Left-Total (Multivalued Function) (Total)		Right-Total (Surjective Relation)
	Left and Right Unique (Injective Partial Function) (One-to-One Relation)				Left and Right Total (Correspondence Relation)
			Right-Unique and Right-Total (Surjective Partial Function)	<------------------>			Right-Unique and Right-Total (Surjective Partial Function)
	Functions			Right-Unique and Left-Total Function (Total Function)
		Left and Right Unique, Left-Total Injective Function (One-to-One Function)
				Right-Unique, Left and Right Total Surjective Function (Correspondence Function) (Onto Function)
		Left and Right Unique, Left and Right Total Bijective Function (Injective and Surjective Function) (One-to-One and Correspondence Relation)

Equivalence Relation Example

An Equivalence Relation Partitions a set into Collectively Exhaustive and Mutually Exclusive subsets called Equivalence Classes.

Original Set

$\{a,b,c,d,e,f,g,h\}\,$

Partition

${\Big \{}{\color {RoyalBlue}\{a,b,c\}},\ {\color {BrickRed}\{d,e\}},\ {\color {ForestGreen}\{f,g\}},\ {\color {Orange}\{h\}}{\Big \}}$

Graph

${\begin{aligned}\{&{\color {RoyalBlue}(a,a),(a,b),(a,c),(b,a),(b,b),(b,c),(c,a)(c,b)(c,c),}\\&{\color {BrickRed}(d,d),(d,e),(e,e),(e,d),\ }{\color {ForestGreen}(f,f),(f,g),(g,g),(g,f),\ }{\color {Orange}(h,h)}\}\\\end{aligned}}$

Directed Graph

Equivalence Classes form "Squares" in Matrices.

Matrix

${\begin{bmatrix}{\color {RoyalBlue}1}&{\color {RoyalBlue}1}&{\color {RoyalBlue}1}&0&0&0&0&0\\{\color {RoyalBlue}1}&{\color {RoyalBlue}1}&{\color {RoyalBlue}1}&0&0&0&0&0\\{\color {RoyalBlue}1}&{\color {RoyalBlue}1}&{\color {RoyalBlue}1}&0&0&0&0&0\\0&0&0&{\color {BrickRed}1}&{\color {BrickRed}1}&0&0&0\\0&0&0&{\color {BrickRed}1}&{\color {BrickRed}1}&0&0&0\\0&0&0&0&0&{\color {ForestGreen}1}&{\color {ForestGreen}1}&0\\0&0&0&0&0&{\color {ForestGreen}1}&{\color {ForestGreen}1}&0\\0&0&0&0&0&0&0&{\color {Orange}1}\\\end{bmatrix}}$

Set Union can be used to test for Collectively Exhaustive (Union of all Equivalence Classes = Original Set) and Set Intersection for Mutually Exclusive (zero for any Intersection).