Changes

User:Jon Awbrey/SCRATCHPAD (view source)

Revision as of 19:02, 31 January 2009

142 bytes removed , 19:02, 31 January 2009

→‎Rule 5

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{| align="center" cellpadding="0" cellspacing="0" width="100%"

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|- style="height:40px; text-align:~~right~~"

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|- style="height:40px; text-align:center"

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| width="98%" | <math>\~~text~~{~~Evaluation~~ Rule 1}\!</math>

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| width="80%" |  

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~~| width="2%" |  ~~

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| width="20%" style="border-left:1px solid black" | <math>\operatorname{Rule~3}</math>

|}

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| width="2%" style="border-top:1px solid black" |  

| width="14%" style="border-top:1px solid black" | <math>\text{If}\!</math>

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| width="84%" style="border-top:1px solid black" | <math>~~f, g~~ ~:~ X ~~\to \underline\mathbb{B}~~</math>

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| width="64%" style="border-top:1px solid black" | <math>Q ~\subseteq~ X</math>

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| width="20%" style="border-top:1px solid black; border-left:1px solid black" |  

|- style="height:40px"

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| <math>\text{and}\!</math>

| <math>x ~\in~ X</math>

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| style="border-left:1px solid black" |  

|- style="height:40px"

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| <math>\text{then}\!</math>

| <math>\text{the following are equivalent:}\!</math>

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| style="border-left:1px solid black" |  

|}

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|- style="height:40px"

| width="2%" style="border-top:1px solid black" |  

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| width="14%" style="border-top:1px solid black" | <math>\operatorname{~~E1a~~.}</math>

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| width="14%" style="border-top:1px solid black" | <math>\operatorname{R3a.}</math>

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| width="64%" style="border-top:1px solid black" | <math>f(x) ~=~ ~~g(x)~~</math>

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| width="64%" style="border-top:1px solid black" | <math>x ~\in~ Q</math>

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| width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" | <math>\operatorname{~~E1a~:~V1a}</math>~~

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| width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" | <math>\operatorname{R3a~:~R1a}</math>

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~~|- style="height:20px"~~

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~~|  ~~

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~~|  ~~

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~~|  ~~

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~~| style="border-left:1px solid black; text-align:center" | <math>::\!</math>~~

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~~|- style="height:40px"~~

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~~|  ~~

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~~| <math>\operatorname{E1b.}</math>~~

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~~| <math>f(x) ~\Leftrightarrow~ g(x)</math>~~

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~~| style="border-left:1px solid black; text-align:center" | <math>\operatorname{E1b~~~:~~~V1b~~}</math>

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|- style="height:60px"

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| <math>\operatorname{~~E1c~~.}</math>

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| <math>\operatorname{R3b.}</math>

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| <math>\~~underline{((}~ f~~(x) ~~~,~ g(x) ~\underline{))}~~</math>

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| <math>\upharpoonleft Q \upharpoonright (x)</math>

| style="border-left:1px solid black; text-align:center" |

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<math>\operatorname{~~E1c~~~:~~~V1c~~}</math>

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<math>\operatorname{R3b~:~R1b}</math>

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<math>\operatorname{~~E1c~~~:~~~$1a~~}</math>

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<math>\operatorname{R3b~:~R2a}</math>

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|- style="height:40px"

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| <math>\operatorname{~~E1d~~.}</math>

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| <math>\operatorname{R3c.}</math>

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| <math>\~~underline{~~((}~ ~~f ~,~ g~~ ~\underline{))}~~^\$ (x)~~</math>

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| <math>\upharpoonleft Q \upharpoonright (x) ~=~ \underline{1}</math>

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| style="border-left:1px solid black; text-align:center" | <math>\operatorname{~~E1d~~~:~~~$1b~~}</math>

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| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R3c~:~R2b}</math>

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Jon Awbrey

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