Changes

→‎Note 7: markup
Line 5,754: Line 5,754:  
|
 
|
 
<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),
Line 5,768: Line 5,768:  
|}
 
|}
   −
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>
+
|
|-
+
<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}),
 +
\\[6pt]
 +
\operatorname{E}_{ij}
 +
& : &
 +
f
 +
& \mapsto &
 +
\operatorname{E}_{ij}f,
 +
\\[6pt]
 +
\operatorname{E}_{ij}f
 +
& = &
 +
\operatorname{E}f|_{\operatorname{d}x = i, \operatorname{d}y = j}
 +
& = &
 +
f(x + i, y + j).
 +
\end{array}</math>
 
|}
 
|}
  
12,080

edits