Changes

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{| align="center" cellpadding="6" width="90%"

| <math>\operatorname{E}f(x_1, \ldots, x_k, \operatorname{d}x_1, \ldots, \operatorname{d}x_k) ~=~ f(x_1 + \operatorname{d}x_1, \ldots, x_k + \operatorname{d}x_k).</math>

| <math>\operatorname{E}f(x_1, \ldots, x_k, \operatorname{d}x_1, \ldots, \operatorname{d}x_k) ~=~ f(x_1 + \operatorname{d}x_1, \ldots, x_k + \operatorname{d}x_k).</math>

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Given that this expression uses nothing more than the ''boolean ring'' operations of addition <math>(+)\!</math> and multiplication <math>(\cdot),</math> it is permissible to multiply things out in the usual manner to arrive at the following result:

Given that this expression uses nothing more than the "boolean ring"

operations of addition (+) and multiplication (·), it is permissible

to "multiply things out" in the usual manner to arrive at the result:

Ef(x, y, dx, dy)   =   x·y  + x·dy  + y·dx  + dx·dy.

| <math>\operatorname{E}f(x, y, \operatorname{d}x, \operatorname{d}y) ~=~ x~y ~+~ x~\operatorname{d}y ~+~ y~\operatorname{d}x ~+~ \operatorname{d}x~\operatorname{d}y.</math>

To understand what this means in logical terms, for instance, as expressed

To understand what this means in logical terms, for instance, as expressed

in a boolean expansion or a "disjunctive normal form" (DNF), it is perhaps

in a boolean expansion or a "disjunctive normal form" (DNF), it is perhaps