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

Revision as of 03:12, 28 May 2008

7 bytes added , 03:12, 28 May 2008

→‎Differential Propositions: spacing

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| true

| <math>1\!</math>

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|}

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|}<br>

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<br>

The next four Tables expand the expressions of <math>\operatorname{E}f</math> and <math>\operatorname{D}f</math> in two different ways, for each of the sixteen functions. Notice that the functions are given in a different order, here being collected into a set of seven natural classes.

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| <math>f_{1}\!</math>

| <math>(\!|x|\!)(\!|y|\!)</math>

−

| <math>\operatorname{d}x \operatorname{d}y</math>

+

| <math>\operatorname{d}x\ \operatorname{d}y</math>

| <math>\operatorname{d}x (\!|\operatorname{d}y|\!)</math>

| <math>(\!|\operatorname{d}x|\!) \operatorname{d}y</math>

Line 3,228: Line 3,227:

| <math>(\!|x|\!) y</math>

| <math>\operatorname{d}x (\!|\operatorname{d}y|\!)</math>

−

| <math>\operatorname{d}x \operatorname{d}y</math>

+

| <math>\operatorname{d}x\ \operatorname{d}y</math>

| <math>(\!|\operatorname{d}x|\!)(\!|\operatorname{d}y|\!)</math>

| <math>(\!|\operatorname{d}x|\!) \operatorname{d}y</math>

Line 3,236: Line 3,235:

| <math>(\!|\operatorname{d}x|\!) \operatorname{d}y</math>

| <math>(\!|\operatorname{d}x|\!)(\!|\operatorname{d}y|\!)</math>

−

| <math>\operatorname{d}x \operatorname{d}y</math>

+

| <math>\operatorname{d}x\ \operatorname{d}y</math>

| <math>\operatorname{d}x (\!|\operatorname{d}y|\!)</math>

|-

Line 3,244: Line 3,243:

| <math>(\!|\operatorname{d}x|\!) \operatorname{d}y</math>

| <math>\operatorname{d}x (\!|\operatorname{d}y|\!)</math>

−

| <math>\operatorname{d}x \operatorname{d}y</math>

+

| <math>\operatorname{d}x\ \operatorname{d}y</math>

|-

| <math>f_{3}\!</math>

Line 3,293: Line 3,292:

| <math>(\!|(\!|\operatorname{d}x|\!) \operatorname{d}y|\!)</math>

| <math>(\!|\operatorname{d}x (\!|\operatorname{d}y|\!)|\!)</math>

−

| <math>(\!|\operatorname{d}x \operatorname{d}y|\!)</math>

+

| <math>(\!|\operatorname{d}x\ \operatorname{d}y|\!)</math>

|-

| <math>f_{11}\!</math>

Line 3,299: Line 3,298:

| <math>(\!|(\!|\operatorname{d}x|\!) \operatorname{d}y|\!)</math>

| <math>(\!|(\!|\operatorname{d}x|\!)(\!|\operatorname{d}y|\!)|\!)</math>

−

| <math>(\!|\operatorname{d}x \operatorname{d}y|\!)</math>

+

| <math>(\!|\operatorname{d}x\ \operatorname{d}y|\!)</math>

| <math>(\!|\operatorname{d}x (\!|\operatorname{d}y|\!)|\!)</math>

|-

Line 3,305: Line 3,304:

| <math>(\!|(\!|x|\!) y|\!)</math>

| <math>(\!|\operatorname{d}x (\!|\operatorname{d}y|\!)|\!)</math>

−

| <math>(\!|\operatorname{d}x \operatorname{d}y|\!)</math>

+

| <math>(\!|\operatorname{d}x\ \operatorname{d}y|\!)</math>

| <math>(\!|(\!|\operatorname{d}x|\!)(\!|\operatorname{d}y|\!)|\!)</math>

| <math>(\!|(\!|\operatorname{d}x|\!) \operatorname{d}y|\!)</math>

Line 3,311: Line 3,310:

| <math>f_{14}\!</math>

| <math>(\!|(\!|x|\!)(\!|y|\!)|\!)</math>

−

| <math>(\!|\operatorname{d}x \operatorname{d}y|\!)</math>

+

| <math>(\!|\operatorname{d}x\ \operatorname{d}y|\!)</math>

| <math>(\!|\operatorname{d}x (\!|\operatorname{d}y|\!)|\!)</math>

| <math>(\!|(\!|\operatorname{d}x|\!) \operatorname{d}y|\!)</math>

Jon Awbrey

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