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User:Jon Awbrey/SCRATCHPAD (view source)
Revision as of 17:30, 26 January 2009
, 17:30, 26 January 2009→Equation Sequences
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==Equation Sequences : Old Versions==
{| align="center" cellpadding="4" style="text-align:left" width="90%"
|
|-
| <math>[| \downharpoonleft s \downharpoonright |]</math>
| <math>=\!</math>
| <math>[| F |]\!</math>
|-
|
| <math>=\!</math>
| <math>F^{-1} (\underline{1})</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ s ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ F(x, y) = \underline{1} ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ F(x, y) ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ \underline{(}~x~,~y~\underline{)} = \underline{1} ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ \underline{(}~x~,~y~\underline{)} ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ x ~\operatorname{exclusive~or}~ y ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ \operatorname{just~one~true~of}~ x, y ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ x ~\operatorname{not~equal~to}~ y ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ x \nLeftrightarrow y ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ x \neq y ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ x + y ~\}.</math>
|-
|
|}
{| align="center" cellpadding="4" style="text-align:left" width="90%"
|
|-
| <math>[| F^\$ (p, q) |]</math>
| <math>=\!</math>
| <math>[| \underline{(}~p~,~q~\underline{)}^\$ |]</math>
|-
|
| <math>=\!</math>
| <math>(F^\$ (p, q))^{-1} (\underline{1})</math>
|-
|
| <math>=\!</math>
| <math>\{~ x \in X ~:~ F^\$ (p, q)(x) ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ x \in X ~:~ \underline{(}~p~,~q~\underline{)}^\$ (x) ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ x \in X ~:~ \underline{(}~p(x)~,~q(x)~\underline{)} ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ x \in X ~:~ p(x) + q(x) ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ x \in X ~:~ p(x) \neq q(x) ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ x \in X ~:~ \upharpoonleft P \upharpoonright (x) ~\neq~ \upharpoonleft Q \upharpoonright (x) ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ x \in X ~:~ x \in P ~\nLeftrightarrow~ x \in Q ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ x \in X ~:~ x \in P\!-\!Q ~\operatorname{or}~ x \in Q\!-\!P ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ x \in X ~:~ x \in P\!-\!Q ~\cup~ Q\!-\!P ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ x \in X ~:~ x \in P + Q ~\}</math>
|-
|
| <math>=\!</math>
| <math>P + Q ~\subseteq~ X</math>
|-
|
| <math>=\!</math>
| <math>[|p|] + [|q|] ~\subseteq~ X</math>
|-
|
|}
==Equation Sequences : New Versions==
{| align="center" cellpadding="4" style="text-align:left" width="90%"
|
|-
| <math>[| \downharpoonleft s \downharpoonright |]</math>
| <math>=\!</math>
| <math>[| F |]\!</math>
|-
|
| <math>=\!</math>
| <math>F^{-1} (\underline{1})</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ s ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ F(x, y) = \underline{1} ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ F(x, y) ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ \underline{(}~x~,~y~\underline{)} = \underline{1} ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ \underline{(}~x~,~y~\underline{)} ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ x ~\operatorname{exclusive~or}~ y ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ \operatorname{just~one~true~of}~ x, y ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ x ~\operatorname{not~equal~to}~ y ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ x \nLeftrightarrow y ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ x \neq y ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ (x, y) \in \underline\mathbb{B}^2 ~:~ x + y ~\}.</math>
|-
|
|}
{| align="center" cellpadding="4" style="text-align:left" width="90%"
|
|-
| <math>[| F^\$ (p, q) |]</math>
| <math>=\!</math>
| <math>[| \underline{(}~p~,~q~\underline{)}^\$ |]</math>
|-
|
| <math>=\!</math>
| <math>(F^\$ (p, q))^{-1} (\underline{1})</math>
|-
|
| <math>=\!</math>
| <math>\{~ x \in X ~:~ F^\$ (p, q)(x) ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ x \in X ~:~ \underline{(}~p~,~q~\underline{)}^\$ (x) ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ x \in X ~:~ \underline{(}~p(x)~,~q(x)~\underline{)} ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ x \in X ~:~ p(x) + q(x) ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ x \in X ~:~ p(x) \neq q(x) ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ x \in X ~:~ \upharpoonleft P \upharpoonright (x) ~\neq~ \upharpoonleft Q \upharpoonright (x) ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ x \in X ~:~ x \in P ~\nLeftrightarrow~ x \in Q ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ x \in X ~:~ x \in P\!-\!Q ~\operatorname{or}~ x \in Q\!-\!P ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ x \in X ~:~ x \in P\!-\!Q ~\cup~ Q\!-\!P ~\}</math>
|-
|
| <math>=\!</math>
| <math>\{~ x \in X ~:~ x \in P + Q ~\}</math>
|-
|
| <math>=\!</math>
| <math>P + Q ~\subseteq~ X</math>
|-
|
| <math>=\!</math>
| <math>[|p|] + [|q|] ~\subseteq~ X</math>
|-
|
|}
==Box Displays==
==Box Displays==