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User:Jon Awbrey/SCRATCHPAD (view source)

Revision as of 21:40, 30 January 2009

1,287 bytes removed ,  21:40, 30 January 2009
→‎Definition 2
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===Definition 2===
 
===Definition 2===
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<pre>
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<br>
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Definition 2
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If X, Y c U,
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then the following are equivalent:
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D2a. X = Y.
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D2b. u C X  <=>  u C Y, for all u C U.
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</pre>
      
{| align="center" cellpadding="0" 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%"
 
{| align="center" cellpadding="0" 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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{| align="center" cellpadding="0" cellspacing="0" width="100%"
 
{| 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{Definition 2}\!</math>
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| width="80%" | &nbsp;
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| width="2%"  | &nbsp;
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| width="20%" | <math>\text{Definition 2}\!</math>
 
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|}
 
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| <math>\operatorname{D2b.}</math>
 
| <math>\operatorname{D2b.}</math>
 
| <math>x \in P ~\Leftrightarrow~ x \in Q</math>
 
| <math>x \in P ~\Leftrightarrow~ x \in Q</math>
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| align="cennter" | <math>(\forall x \in X)</math>
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| align="center" | <math>\forall x \in X</math>
 
|}
 
|}
 
|}
 
|}
    
<br>
 
<br>
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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%"  | &nbsp;
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| width="18%" | &nbsp;
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| width="60%" | &nbsp;
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| align="center" width="20%" | <math>\text{Definition 1}\!</math>
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|- style="height:40px"
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| style="border-top:1px solid black" | &nbsp;
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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-top:1px solid black" | &nbsp;
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|- style="height:40px"
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| &nbsp;
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| <math>\text{then}\!</math>
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| <math>\upharpoonleft Q \upharpoonright ~:~ X \to \underline\mathbb{B}</math>
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| &nbsp;
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|- style="height:40px"
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| &nbsp;
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| <math>\text{such that:}\!</math>
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| &nbsp;
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| &nbsp;
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|- style="height:40px"
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| style="border-top:1px solid black" | &nbsp;
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| style="border-top:1px solid black" | <math>\text{D1a.}\!</math>
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| style="border-top:1px solid black" | <math>\upharpoonleft Q \upharpoonright (x) ~\Leftrightarrow~ x \in Q</math>
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| align="center" style="border-top:1px solid black" | <math>\forall x \in X</math>
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|}
      
===Definition 3===
 
===Definition 3===
Jon Awbrey
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