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<pre>

The Figure shows the points of the extended universe <math>\operatorname{E}U = X \times Y \times \operatorname{d}X \times \operatorname{d}Y</math> that satisfy the difference proposition <math>\operatorname{D}f,</math> namely, these:

the interpretations in EU = X x Y x dX x dY

that satisfy the difference proposition Df,

namely, these:

1.   x  y  dx  dy

2.   x  y  dx (dy)

3.   x  y (dx) dy

4.   x (y)(dx) dy

1. &  x & y & dx & dy

5. (x) y  dx (dy)

6. (x)(y) dx  dy

2. &  x & y & dx & (dy)

3. &  x & y & (dx) &  dy

4. &  x & (y) & (dx) &  dy

5. & (x) &  y & dx & (dy)

6. & (x) & (y) &  dx & dy

By inspection, it is fairly easy to understand Df

An inspection of these six points should make it easy to understand <math>\operatorname{D}f</math> as telling you what you have to do from each point of <math>U\!</math> in order to change the value borne by the proposition <math>f(x, y).\!</math>

as telling you what you have to do from each point

of U in order to change the value borne by f(x, y).

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====Note 4====

====Note 4====