Changes

User:Jon Awbrey/SCRATCHPAD (view source)

Revision as of 21:34, 29 January 2009

1,142 bytes removed , 21:34, 29 January 2009

→‎Variant 1

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

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

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| width="84%" 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>f(x) ~=~ g(x)</math>

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

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|- style="height:24px"

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

|- style="height:56px"

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| <math>\text{E1b.}\!</math>

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

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

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|- style="height:24px"

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

|- style="height:56px"

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| <math>\text{E1c.}\!</math>

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

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

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|- style="height:24px"

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

|- style="height:56px"

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| <math>\text{E1d.}\!</math>

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

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| style="border-left:1px solid black; text-align:center" | <math>\text{E1d : S1b}\!</math>

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|}

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~~ ~~

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~~{| align="center" cellpadding="2" cellspacing="0" style="border-left:1px solid black; border-top:1px solid black; border-right:1px solid black; border-bottom:1px solid black" width="90%"~~

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

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~~| width="2%" |  ~~

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~~| width="18%" |  ~~

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~~| width="60%" |  ~~

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

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

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~~| style="border-top:1px solid black" |  ~~

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

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

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

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

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~~|  ~~

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

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

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

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

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~~|  ~~

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

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

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

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~~|- style="height:36px"~~

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~~| style="border-top:1px solid black" |  ~~

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~~| style="border-top:1px solid black" | <math>\text{R3a.}\!</math>~~

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

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

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~~|- style="height:24px"~~

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~~|   ||   ||  ~~

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

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~~|- style="height:36px"~~

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~~|  ~~

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~~| <math>\text{R3b.}\!</math>~~

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

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

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~~<math>\text{R3b : R1b}\!</math>~~

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~~<math>\text{R3b : R2a}\!</math>~~

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~~|- style="height:24px"~~

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~~|   ||   ||  ~~

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

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~~|- style="height:36px"~~

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~~|  ~~

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~~| <math>\text{R3c.}\!</math>~~

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

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

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Jon Awbrey

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edits