Changes

</pre>

</pre>

The picture illustrates the analysis of the inclusive disjunction ((''dx'')(''dy'')) into the exclusive disjunction: .''dx''(''dy'') + ''dy''(''dx'') + ''dx dy'', a proposition that may be interpreted to say "change x or change y or both".  And this can be recognized as just what you need to do if you happen to find yourself in the center cell and desire a detailed description of ways to depart it.

The picture illustrates the analysis of the inclusive disjunction <math>(\!|(\!| \operatorname{d}x |\!)(\!| \operatorname{d}y |\!)|\!)</math> into the following exclusive disjunction:

 

: <p><math>\operatorname{d}x\ (\!| \operatorname{d}y |\!) + \operatorname{d}y\ (\!| \operatorname{d}x |\!) + \operatorname{d}x\ \operatorname{d}y.</math></p>

 

The latter proposition may be interpreted as saying "change <math>x\!</math> or change <math>y\!</math> or both".  And this can be recognized as just what you need to do if you happen to find yourself in the center cell and desire a detailed description of ways to depart it.

We have just computed what will variously be called the ''difference map'', the ''difference proposition'', or the ''local proposition'' ''Df''_''p'' for the proposition ''f''(''x'',&nbsp;''y'') = ''xy'' at the point ''p'' where ''x'' = 1 and ''y'' = 1.

We have just computed what will variously be called the ''difference map'', the ''difference proposition'', or the ''local proposition'' ''Df''_''p'' for the proposition ''f''(''x'',&nbsp;''y'') = ''xy'' at the point ''p'' where ''x'' = 1 and ''y'' = 1.