Changes

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<math>\begin{array}{lcl}

<math>\begin{array}{lcl}

\operatorname{E} : (U \to \mathbb{B})

\operatorname{E} ~:~ (U \to \mathbb{B})

& \to &

& \to &

(\operatorname{E}U \to \mathbb{B}),

(\operatorname{E}U \to \mathbb{B}),

\\[6pt]

\\[6pt]

\operatorname{E} : f(x, y)

\operatorname{E} ~:~ f(x, y)

& \mapsto &

& \mapsto &

\operatorname{E}f(x, y, \operatorname{d}x, \operatorname{d}y),

\operatorname{E}f(x, y, \operatorname{d}x, \operatorname{d}y),

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Therefore, if we evaluate <math>\operatorname{E}f</math> at particular values of <math>\operatorname{d}x</math> and <math>\operatorname{d}y,</math> for example, <math>\operatorname{d}x = i</math> and <math>\operatorname{d}y = j,</math> where <math>i, j \in \mathbb{B},</math> we obtain:

Evaluating <math>\operatorname{E}f</math> at particular values of <math>\operatorname{d}x</math> and <math>\operatorname{d}y,</math> for example, <math>\operatorname{d}x = i</math> and <math>\operatorname{d}y = j,</math> where <math>i, j \in \mathbb{B},</math> leads to the following result:

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

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

| <math>\operatorname{E}_{ij} : (U \to \mathbb{B}) \to (U \to \mathbb{B}),</math>

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<math>\begin{array}{lclcl}

| <math>\operatorname{E}_{ij} : f \mapsto \operatorname{E}_{ij}f,</math>

\operatorname{E}_{ij}

& : &

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

(U \to \mathbb{B})

& \to &

(U \to \mathbb{B}),

\operatorname{E}_{ij}

& : &

f

& \mapsto &

\operatorname{E}_{ij}f,

\operatorname{E}_{ij}f

& = &

\operatorname{E}f|_{\operatorname{d}x = i, \operatorname{d}y = j}

& = &

f(x + i, y + j).

\end{array}</math>

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