Changes

<math>\operatorname{d}x</math> when crossing the border between <math>x\!</math> and <math>\texttt{(} x \texttt{)}</math> and as <math>\operatorname{d}y</math> when crossing the border between <math>y\!</math> and <math>\texttt{(} y \texttt{)},</math> in either direction, in either case.

<math>\operatorname{d}x</math> when crossing the border between <math>x\!</math> and <math>\texttt{(} x \texttt{)}</math> and as <math>\operatorname{d}y</math> when crossing the border between <math>y\!</math> and <math>\texttt{(} y \texttt{)},</math> in either direction, in either case.

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We can form propositions from these differential variables in the same way

Propositions can be formed on differential variables, or any combination of ordinary logical varibles and differential logical variables, in the same ways that propositions can be formed on the ordinary logical variables alone.  For instance, the proposition <math>\texttt{(} \operatorname{d}x \texttt{(} \operatorname{d}y \texttt{))}</math> may be read to say that <math>\operatorname{d}x \Rightarrow \operatorname{d}y,</math> in other words, there is "no change in <math>x\!</math> without a change in <math>y\!</math>".

that we would any other logical variables, for instance, interpreting the

proposition (dx (dy)) to say "dx => dy", in other words, however you wish

the effect that there is "no change in x without a change in y".

Given the proposition f(x, y) in U = X x Y,

Given the proposition f(x, y) in U = X x Y,

the (first order) 'enlargement' of f is the

the (first order) 'enlargement' of f is the