Changes

16,517 bytes added , 22:28, 19 May 2007

add user workspace

==Formula Help==

* [http://meta.wikimedia.org/wiki/Help:Displaying_a_formula Mathematical formulas]
* [http://en.wikipedia.org/wiki/Wikipedia:Mathematical_symbols Mathematical symbols]

==Bytes & Parses==

{| style="width:50%"
| &isin;
| ∈
|-
| &epsilon;
| ε
|-
| <nowiki><math>\in</math></nowiki>
| <math>\in</math>
|-
| <nowiki><math>\in\!</math></nowiki>
| <math>\in\!</math>
|-
| <nowiki><math>\epsilon</math></nowiki>
| <math>\epsilon</math>
|-
| <nowiki><math>\epsilon\!</math></nowiki>
| <math>\epsilon\!</math>
|-
| <nowiki><math>\varepsilon</math></nowiki>
| <math>\varepsilon</math>
|-
| <nowiki><math>\varepsilon\!</math></nowiki>
| <math>\varepsilon\!</math>
|}
 

{| style="width:50%"
| &eta;
| η
|-
| <nowiki><math>\eta</math></nowiki>
| <math>\eta</math>
|-
| <nowiki><math>\eta\!</math></nowiki>
| <math>\eta\!</math>
|}
 

{| style="width:50%"
| &theta;
| θ
|-
| <nowiki><math>\theta</math></nowiki>
| <math>\theta</math>
|-
| <nowiki><math>\theta\!</math></nowiki>
| <math>\theta\!</math>
|-
| <nowiki><math>\vartheta</math></nowiki>
| <math>\vartheta</math>
|-
| <nowiki><math>\vartheta\!</math></nowiki>
| <math>\vartheta\!</math>
|}
 

{| style="width:50%"
| &chi;
| χ
|-
| <nowiki><math>\chi</math></nowiki>
| <math>\chi</math>
|-
| <nowiki><math>\chi\!</math></nowiki>
| <math>\chi\!</math>
|}
 

''x'' = ''x''''J'' = ¢(''J'') = ''J''¢ = ''J'' ¢ = ''J''¢ = ''J'' ¢

''x'' = ''x''''J'' = ¢(''J'') = ''J''¢ = ''J'' ¢ = ''J''¢ = ''J'' ¢

==Display==

===New===

:{| cellpadding=1 style="height:40px"
| '''W'''
| :
| (
| [
| '''B'''''n''
| ]
| →
| [
| '''B'''''k''
| ]
| )
|  
| →
|  
| (
| [
| '''B'''''n''
| ×
| '''D'''''n''
| ]
| →
| [
| '''B'''''k''
| ×
| '''D'''''k''
| ]
| )
| .
|}

:{| style="height:80px; text-align:center; width:90%"
| align=left width=20%| Concrete type
| width=8% | <math>\epsilon</math>
| :
| (
| ''U''•
| →
| ''X''•
| )
| width=16% | →
| (
| E''U''•
| →
| ''X''•
| )
|-
| align=left width=20%| Abstract type
| width=8% | <math>\epsilon</math>
| :
| (
| ['''B'''''n'']
| →
| ['''B'''''k'']
| )
| width=16% | →
| (
| ['''B'''''n'' × '''D'''''n'']
| →
| ['''B'''''k'']
| )
|}

:{| style="height:80px; text-align:center; width:90%"
| align=left width=20%| Concrete type
| width=8% | W
| :
| (
| ''U''•
| →
| ''X''•
| )
| width=16% | →
| (
| E''U''•
| →
| d''X''•
| )
|-
| align=left width=20%| Abstract type
| width=8% | W
| :
| (
| ['''B'''''n'']
| →
| ['''B'''''k'']
| )
| width=16% | →
| (
| ['''B'''''n'' × '''D'''''n'']
| →
| ['''D'''''k'']
| )
|}

:{| style="height:80px; text-align:center; width:90%"
| width=6% | <math>\epsilon</math>''F''
| width=2% | :
| width=2% | (
| width=8% | E''U''•
| width=4% | →
| width=8% | ''X''•
| width=4% | &sube;
| width=8% | E''X''•
| width=2% | )
| width=4% | <math>\cong</math>
| width=2% | (
| width=16% | ['''B'''''n'' × '''D'''''n'']
| width=4% | →
| width=8% | ['''B'''''k'']
| width=4% | &sube;
| width=16% | ['''B'''''k'' × '''D'''''k'']
| width=2% | )
|-
| width=6% | W''F''
| width=2% | :
| width=2% | (
| width=8% | E''U''•
| width=4% | →
| width=8% | d''X''•
| width=4% | &sube;
| width=8% | E''X''•
| width=2% | )
| width=4% | <math>\cong</math>
| width=2% | (
| width=16% | ['''B'''''n'' × '''D'''''n'']
| width=4% | →
| width=8% | ['''D'''''k'']
| width=4% | &sube;
| width=16% | ['''B'''''k'' × '''D'''''k'']
| width=2% | )
|}

===Old===

:{| cellpadding=1 style="height:40px"
| '''W'''
| :
| (
| [
| '''B'''''n''
| ]
| →
| [
| '''B'''''k''
| ]
| )
|  
| →
|  
| (
| [
| '''B'''''n''
| ×
| '''D'''''n''
| ]
| →
| [
| '''B'''''k''
| ×
| '''D'''''k''
| ]
| )
| .
|}

:{| style="height:80px; text-align:center; width:90%"
| align=left width=20%| Concrete type
| width=4% | <math>\epsilon</math>
| width=2% | :
| width=2% | (
| width=8% | ''U''•
| width=4% | →
| width=8% | ''X''•
| width=2% | )
| width=8% | →
| width=2% | (
| width=16% | E''U''•
| width=4% | →
| width=8% | ''X''•
| width=2% | )
|-
| align=left width=20%| Abstract type
| width=4% | <math>\epsilon</math>
| width=2% | :
| width=2% | (
| width=8% | ['''B'''''n'']
| width=4% | →
| width=8% | ['''B'''''k'']
| width=2% | )
| width=8% | →
| width=2% | (
| width=16% | ['''B'''''n'' × '''D'''''n'']
| width=4% | →
| width=8% | ['''B'''''k'']
| width=2% | )
|}

:{| style="height:80px; text-align:center; width:90%"
| align=left width=20%| Concrete type
| width=4% | W
| width=2% | :
| width=2% | (
| width=8% | ''U''•
| width=4% | →
| width=8% | ''X''•
| width=2% | )
| width=8% | →
| width=2% | (
| width=16% | E''U''•
| width=4% | →
| width=8% | d''X''•
| width=2% | )
|-
| align=left width=20%| Abstract type
| width=4% | W
| width=2% | :
| width=2% | (
| width=8% | ['''B'''''n'']
| width=4% | →
| width=8% | ['''B'''''k'']
| width=2% | )
| width=8% | →
| width=2% | (
| width=16% | ['''B'''''n'' × '''D'''''n'']
| width=4% | →
| width=8% | ['''D'''''k'']
| width=2% | )
|}

:{| style="height:80px; text-align:center; width:90%"
| width=6% | <math>\epsilon</math>''F''
| width=2% | :
| width=2% | (
| width=8% | E''U''•
| width=4% | →
| width=8% | ''X''•
| width=4% | &sube;
| width=8% | E''X''•
| width=2% | )
| width=4% | <math>\cong</math>
| width=2% | (
| width=16% | ['''B'''''n'' × '''D'''''n'']
| width=4% | →
| width=8% | ['''B'''''k'']
| width=4% | &sube;
| width=16% | ['''B'''''k'' × '''D'''''k'']
| width=2% | )
|-
| width=6% | W''F''
| width=2% | :
| width=2% | (
| width=8% | E''U''•
| width=4% | →
| width=8% | d''X''•
| width=4% | &sube;
| width=8% | E''X''•
| width=2% | )
| width=4% | <math>\cong</math>
| width=2% | (
| width=16% | ['''B'''''n'' × '''D'''''n'']
| width=4% | →
| width=8% | ['''D'''''k'']
| width=4% | &sube;
| width=16% | ['''B'''''k'' × '''D'''''k'']
| width=2% | )
|}

==Epitext==

{| cellpadding=12 style="height:100px; width:100%; text-align:left"
|-
| '''''Rosebud'''''
|}

{| cellpadding=12 style="height:100px; width:100%; text-align:center"
|-
| '''''Rosebud'''''
|}

{| cellpadding=12 style="height:100px; width:100%; text-align:right"
|-
| '''''Rosebud'''''
|}

==Gallery==

<center>
’

`´

′

‹ ›

〈〉

( )

( , )
</center>

{| border=1 cellpadding=10 cellspacing=2 width=100%
| A = {''a''''i''} = {''a''1, …, ''a''''n''}
|-
| ''A'' = 〈A〉 = 〈''a''1, …, ''a''''n''〉= {‹''a''1, …, ''a''''n''›}
|-
| ''A''^ = (''A'' → '''B''')
|-
| ''A''• = [A] = [''a''1, …, ''a''''n'']
|}
 

{| border=1 cellpadding=10 cellspacing=2 width=100%
| dA = {d''a''''i''} = {d''a''1, …, d''a''''n''}
|-
| d''A'' = 〈dA〉 = 〈d''a''1, …, d''a''''n''〉= {‹d''a''1, …, d''a''''n''›}
|-
| d''A''^ = (d''A'' → '''B''')
|-
| d''A''• = [dA] = [d''a''1, …, d''a''''n'']
|}
 

{| border=1 cellpadding=10 cellspacing=2 width=100%
| EA = A ∪ dA = {''a''''i''} ∪ {d''a''''i''} = {''a''1, …, ''a''''n'', d''a''1, …, d''a''''n''}
|-
| E''A'' = 〈EA〉 = 〈''a''1, …, ''a''''n'', d''a''1, …, d''a''''n''〉= {‹''a''1, …, ''a''''n'', d''a''1, …, d''a''''n''›}
|-
| E''A''^ = (E''A'' → '''B''')
|-
| E''A''• = [EA] = [''a''1, …, ''a''''n'', d''a''1, …, d''a''''n'']
|}
 

{| border=1 cellpadding=10 cellspacing=2 width=100%
| X = {''x''''i''} = {''x''1, …, ''x''''n''}
|-
| ''X'' = 〈X〉 = 〈''x''1, …, ''x''''n''〉= {‹''x''1, …, ''x''''n''›}
|-
| ''X''^ = (''X'' → '''B''')
|-
| ''X''• = [X] = [''x''1, …, ''x''''n'']
|}
 

{| border=1 cellpadding=10 cellspacing=2 width=100%
| dX = {d''x''''i''} = {d''x''1, …, d''x''''n''}
|-
| d''X'' = 〈dX〉 = 〈d''x''1, …, d''x''''n''〉= {‹d''x''1, …, d''x''''n''›}
|-
| d''X''^ = (d''X'' → '''B''')
|-
| d''X''• = [dX] = [d''x''1, …, d''x''''n'']
|}
 

{| border=1 cellpadding=10 cellspacing=2 width=100%
| X = {''x''''i''} = {''x''1, …, ''x''''n''}
|-
| ''X'' = 〈X〉 = 〈''x''1, …, ''x''''n''〉= {‹''x''1, …, ''x''''n''›}
|-
| ''X''^ = (''X'' → '''B''')
|-
| ''X''• = [X] = [''x''1, …, ''x''''n'']
|}
 

''f'' : '''B'''''k'' → '''B'''

''f'' : '''B'''''n'' → '''B'''

''f''–1

Pow(''X'') = 2''X''

{| cellpadding=6
| Arbitrary
| →
| '''B'''''n'' → '''B'''
| ''X'' → '''B'''
|-
| Basic
| '''¸>'''
| '''B'''''n'' '''¸>''' '''B'''
| ''X'' '''¸>''' '''B'''
|-
| Linear
| '''+>'''
| '''B'''''n'' '''+>''' '''B'''
| ''X'' '''+>''' '''B'''
|-
| Positive
| '''¥>'''
| '''B'''''n'' '''¥>''' '''B'''
| ''X'' '''¥>''' '''B'''
|-
| Singular
| '''××>'''
| '''B'''''n'' '''××>''' '''B'''
| ''X'' '''××>''' '''B'''
|}

The ''linear propositions'', {hom : '''B'''''n'' → '''B'''} = ('''B'''''n'' '''+>''' '''B'''), may be expressed as sums of the following form:

: <math>\textstyle \sum_{i=1}^n e_i = e_1 + \ldots + e_n \ \mbox{where} \ \forall_{i=1}^n \ e_i = a_i \ \mbox{or} \ e_i = 0.</math>

The ''positive propositions'', {pos : '''B'''''n'' → '''B'''} = ('''B'''''n'' '''¥>''' '''B'''), may be expressed as products of the following form:

: <math>\textstyle \prod_{i=1}^n e_i = e_1 \cdot \ldots \cdot e_n \ \mbox{where} \ \forall_{i=1}^n \ e_i = a_i \ \mbox{or} \ e_i = 1.</math>

The ''singular propositions'', {''x'' : '''B'''''n'' → '''B'''} = ('''B'''''n'' '''××>''' '''B'''), may be expressed as products of the following form:

: <math>\textstyle \prod_{i=1}^n e_i = e_1 \cdot \ldots \cdot e_n \ \mbox{where} \ \forall_{i=1}^n \ e_i = a_i \ \mbox{or} \ e_i = (a_i) = \lnot a_i.</math>

I = {1, …, ''n''}.

''J'' &sube; I

J &sube; I

A''J''

AJ

l''J'' : '''B'''''k'' → '''B'''

<math>\ell_J : \mathbb{B}^k \to \mathbb{B}</math>

θ : ('''K'''''n'' → '''K''') → '''K'''

<math>\theta</math> : ('''K'''''n'' → '''K''') → '''K'''

<math>\theta\!</math> : ('''K'''''n'' → '''K''') → '''K'''

<math>\vartheta</math> : ('''K'''''n'' → '''K''') → '''K'''

<math>\vartheta\!</math> : ('''K'''''n'' → '''K''') → '''K'''

<math>\chi\!</math> : ''X'' → <math>\bigcup_x \ \chi_x\!</math>

<math>\chi\!</math> : '''K'''''n'' → (('''K'''''n'' → '''K''') → '''K''')

<math>\chi\!</math> : ('''K'''''n'' → '''K''') → ('''K'''''n'' → '''K''')

<math>\cong</math>

<math>\lceil x \rceil</math>

{| cellpadding=6
| ''x''''i''(''x'')
| χ(''x'' ∈ ''L''''i'')
| <math>\lceil x \in L_i \rceil</math>
| ''L''''i''(''x'')
|-
| ''x''''i''(''x'')
| <math>\chi (x \in L_i)</math>
| <math>\lceil x \in L_i \rceil</math>
| ''L''''i''(''x'')
|}

{| cellpadding=4
| ‹0, 0, 0›
| ‹0, 0, 0›
|-
| ‹0, 0, 1›
| ‹0, 0, 1›
|-
| ‹0, 1, 0›
| ‹0, 1, 0›
|-
| ‹0, 1, 1›
| ‹0, 1, 1›
|-
| ‹1, 0, 0›
| ‹1, 0, 0›
|-
| ‹1, 0, 1›
| ‹1, 0, 1›
|-
| ‹1, 1, 0›
| ‹1, 1, 0›
|-
| ‹1, 1, 1›
| ‹1, 1, 1›
|}

Jon Awbrey

12,080

edits

Changes

User:Jon Awbrey/SYMBOL (view source)

Revision as of 22:28, 19 May 2007

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