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User:Jon Awbrey/SCRATCHPAD (view source)

Revision as of 17:48, 26 January 2009

461 bytes removed ,  17:48, 26 January 2009
→‎Equation Sequences : New Versions
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{| align="center" cellpadding="4" style="text-align:left" width="90%"
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{| align="center" cellpadding="8" width="90%"
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|  
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|
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|-
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<math>\begin{array}{lll}
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| <math>[| F^\$ (p, q) |]</math>
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[| F^\$ (p, q) |]
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| <math>=\!</math>
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& = & [| \underline{(}~p~,~q~\underline{)}^\$ |]
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| <math>[| \underline{(}~p~,~q~\underline{)}^\$ |]</math>
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\\[6pt]
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|-
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& = & (F^\$ (p, q))^{-1} (\underline{1})
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| &nbsp;
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\\[6pt]
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| <math>=\!</math>
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& = & \{~ x \in X ~:~ F^\$ (p, q)(x) ~\}
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| <math>(F^\$ (p, q))^{-1} (\underline{1})</math>
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\\[6pt]
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|-
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& = & \{~ x \in X ~:~ \underline{(}~p~,~q~\underline{)}^\$ (x) ~\}
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| &nbsp;
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\\[6pt]
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| <math>=\!</math>
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& = & \{~ x \in X ~:~ \underline{(}~p(x)~,~q(x)~\underline{)} ~\}
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| <math>\{~ x \in X ~:~ F^\$ (p, q)(x) ~\}</math>
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\\[6pt]
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|-
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& = & \{~ x \in X ~:~ p(x) + q(x) ~\}
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| &nbsp;
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\\[6pt]
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| <math>=\!</math>
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& = & \{~ x \in X ~:~ p(x) \neq q(x) ~\}
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| <math>\{~ x \in X ~:~ \underline{(}~p~,~q~\underline{)}^\$ (x) ~\}</math>
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\\[6pt]
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|-
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& = & \{~ x \in X ~:~ \upharpoonleft P \upharpoonright (x) ~\neq~ \upharpoonleft Q \upharpoonright (x) ~\}
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| &nbsp;
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\\[6pt]
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| <math>=\!</math>
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& = & \{~ x \in X ~:~ x \in P ~\nLeftrightarrow~ x \in Q ~\}
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| <math>\{~ x \in X ~:~ \underline{(}~p(x)~,~q(x)~\underline{)} ~\}</math>
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\\[6pt]
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|-
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& = & \{~ x \in X ~:~ x \in P\!-\!Q ~\operatorname{or}~ x \in Q\!-\!P ~\}
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| &nbsp;
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\\[6pt]
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| <math>=\!</math>
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& = & \{~ x \in X ~:~ x \in P\!-\!Q ~\cup~ Q\!-\!P ~\}
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| <math>\{~ x \in X ~:~ p(x) + q(x) ~\}</math>
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\\[6pt]
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|-
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& = & \{~ x \in X ~:~ x \in P + Q ~\}
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| &nbsp;
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\\[6pt]
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| <math>=\!</math>
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& = & P + Q ~\subseteq~ X
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| <math>\{~ x \in X ~:~ p(x) \neq q(x) ~\}</math>
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\\[6pt]
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|-
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& = & [|p|] + [|q|] ~\subseteq~ X
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| &nbsp;
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\end{array}</math>
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| <math>=\!</math>
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| <math>\{~ x \in X ~:~ \upharpoonleft P \upharpoonright (x) ~\neq~ \upharpoonleft Q \upharpoonright (x) ~\}</math>
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|-
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| &nbsp;
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| <math>=\!</math>
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| <math>\{~ x \in X ~:~ x \in P ~\nLeftrightarrow~ x \in Q ~\}</math>
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|-
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| &nbsp;
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| <math>=\!</math>
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| <math>\{~ x \in X ~:~ x \in P\!-\!Q ~\operatorname{or}~ x \in Q\!-\!P ~\}</math>
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|-
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| &nbsp;
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| <math>=\!</math>
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| <math>\{~ x \in X ~:~ x \in P\!-\!Q ~\cup~ Q\!-\!P ~\}</math>
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|-
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| &nbsp;
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| <math>=\!</math>
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| <math>\{~ x \in X ~:~ x \in P + Q ~\}</math>
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|-
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| &nbsp;
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| <math>=\!</math>
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| <math>P + Q ~\subseteq~ X</math>
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|-
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| &nbsp;
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| <math>=\!</math>
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| <math>[|p|] + [|q|] ~\subseteq~ X</math>
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|-
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| &nbsp;
   
|}
 
|}
  
Jon Awbrey
12,089

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