924: Graph of Map

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definition of graph of map

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Topics

About: set

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The table of contents of this article

• Starting Context
• Target Context
• Orientation
• Main Body
• 1: Structured Description
• 2: Natural Language Description

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Starting Context

• The reader knows a definition of map.

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Target Context

• The reader will have a definition of graph of map.

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Orientation

There is a list of definitions discussed so far in this site.

There is a list of propositions discussed so far in this site.

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Main Body

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1: Structured Description

Here is the rules of Structured Description.

Entities:
$S_1$: $\in \{\text{ the sets }\}$
$S_2$: $\in \{\text{ the sets }\}$
$f$: $:S_1\to S_2$
$f^{\prime }$: $:S_1\to S_1\times S_2,p\mapsto (p,f(p))$
$\ast f^{\prime }(S_1)$: $\subseteq S_1\times S_2$
//

Conditions:
//

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2: Natural Language Description

For any sets, $S_1,S_2$, any map, $f:S_{1}to{S}_2$, and the map, $f^{\prime }:S_{1}to{S}_1\times S_2,p\mapsto (p,f(p))$, $f^{\prime }(S_1)\subseteq S_1\times S_2$

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References

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