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User:Jon Awbrey/SCRATCHPAD (view source)
Revision as of 21:20, 30 January 2009
, 21:20, 30 January 2009→Definition 2
D2b. u C X <=> u C Y, for all u C U.
D2b. u C X <=> u C Y, for all u C U.
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:40px; text-align:right"
| width="98%" | <math>\text{Definition 2}\!</math>
| width="2%" |
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:40px"
| width="2%" style="border-top:1px solid black" |
| width="14%" style="border-top:1px solid black" | <math>\text{If}\!</math>
| width="84%" style="border-top:1px solid black" | <math>P, Q ~\subseteq~ X</math>
|- style="height:40px"
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| <math>\text{then}\!</math>
| <math>\text{the following are equivalent:}\!</math>
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|-
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{| align="center" cellpadding="0" cellspacing="0" width="100%"
|- style="height:40px"
| width="2%" style="border-top:1px solid black" |
| width="14%" style="border-top:1px solid black" | <math>\operatorname{D2a.}</math>
| width="64%" style="border-top:1px solid black" | <math>P ~=~ Q</math>
| width="20%" style="border-top:1px solid black" |
|- style="height:40px"
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| <math>\operatorname{D2b.}</math>
| <math>x \in P ~\Leftrightarrow~ x \in Q</math>
| align="cennter" | <math>(\forall x \in X)</math>
|}
|}
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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%"
|- style="height:40px"
| width="2%" |
| width="18%" |
| width="60%" |
| align="center" width="20%" | <math>\text{Definition 1}\!</math>
|- style="height:40px"
| style="border-top:1px solid black" |
| style="border-top:1px solid black" | <math>\text{If}\!</math>
| style="border-top:1px solid black" | <math>Q \subseteq X</math>
| style="border-top:1px solid black" |
|- style="height:40px"
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| <math>\text{then}\!</math>
| <math>\upharpoonleft Q \upharpoonright ~:~ X \to \underline\mathbb{B}</math>
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|- style="height:40px"
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| <math>\text{such that:}\!</math>
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|- style="height:40px"
| style="border-top:1px solid black" |
| style="border-top:1px solid black" | <math>\text{D1a.}\!</math>
| style="border-top:1px solid black" | <math>\upharpoonleft Q \upharpoonright (x) ~\Leftrightarrow~ x \in Q</math>
| align="center" style="border-top:1px solid black" | <math>\forall x \in X</math>
|}
===Definition 3===
===Definition 3===