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Directory talk:Jon Awbrey/Papers/Differential Propositional Calculus (view source)

Revision as of 03:25, 19 June 2008

415 bytes added , 03:25, 19 June 2008

→‎Expanded on a Logical Basis: fill table

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<math>\begin{smallmatrix}

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(y) & \operatorname{d}x\ (\operatorname{d}y) & + &

+

(y) & \operatorname{d}x\ (\operatorname{d}y) & + &

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(x) & (\operatorname{d}x)\ \operatorname{d}y & + &

+

(x) & (\operatorname{d}x)\ \operatorname{d}y & + &

((x, y)) & \operatorname{d}x\ \operatorname{d}y \\

−

y & \operatorname{d}x\ (\operatorname{d}y) & + &

+

y & \operatorname{d}x\ (\operatorname{d}y) & + &

−

(x) & (\operatorname{d}x)\ \operatorname{d}y & + &

+

(x) & (\operatorname{d}x)\ \operatorname{d}y & + &

−

(x, y) & \operatorname{d}x\ \operatorname{d}y \\

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(x, y) & \operatorname{d}x\ \operatorname{d}y \\

−

(y) & \operatorname{d}x\ (\operatorname{d}y) & + &

+

(y) & \operatorname{d}x\ (\operatorname{d}y) & + &

−

x & (\operatorname{d}x)\ \operatorname{d}y & + &

+

x & (\operatorname{d}x)\ \operatorname{d}y & + &

−

(x, y) & \operatorname{d}x\ \operatorname{d}y \\

+

(x, y) & \operatorname{d}x\ \operatorname{d}y \\

−

y & \operatorname{d}x\ (\operatorname{d}y) & + &

+

y & \operatorname{d}x\ (\operatorname{d}y) & + &

−

x & (\operatorname{d}x)\ \operatorname{d}y & + &

+

x & (\operatorname{d}x)\ \operatorname{d}y & + &

((x, y)) & \operatorname{d}x\ \operatorname{d}y \\

\end{smallmatrix}</math>

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<math>\begin{smallmatrix}

−

+

\operatorname{d}x\ (\operatorname{d}y) & + &

+

(\operatorname{d}x)\ \operatorname{d}y \\

+

\operatorname{d}x\ (\operatorname{d}y) & + &

+

(\operatorname{d}x)\ \operatorname{d}y \\

\end{smallmatrix}</math>

|}

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<math>\begin{smallmatrix}

−

+

\partial x & + & \partial y \\

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\partial x & + & \partial y \\

\end{smallmatrix}</math>

|}

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{| align="center"

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|-

+

|

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~~| height="36px" |~~ <math>f_{5}\~~!</math>~~

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<math>\begin{smallmatrix}

−

|-

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f_{5} \\

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~~| height="36px" | <math>~~f_{10}\!</math>

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f_{10} \\

+

\end{smallmatrix}</math>

|}

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{| align="center"

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|-

+

|

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~~| height="36px" |~~ <math>(y)\~~!</math>~~

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<math>\begin{smallmatrix}

−

|-

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(y) \\

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~~| height="36px" | <math>y~~\!</math>

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y \\

+

\end{smallmatrix}</math>

|}

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<math>\begin{smallmatrix}

−

+

(\operatorname{d}x)\ \operatorname{d}y & + &

+

\operatorname{d}x\ \operatorname{d}y \\

+

(\operatorname{d}x)\ \operatorname{d}y & + &

+

\operatorname{d}x\ \operatorname{d}y \\

\end{smallmatrix}</math>

|}

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<math>\begin{smallmatrix}

−

+

\partial y \\

+

\partial y \\

\end{smallmatrix}</math>

|}

Jon Awbrey

12,080

edits