definition of graph of map
Topics
About: set
The table of contents of this article
- Starting Context
- Target Context
- Orientation
- Main Body
- 1: Structured Description
- 2: Natural Language Description
Starting Context
- The reader knows a definition of map.
Target Context
- The reader will have a definition of graph of map.
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.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
\( S_1\): \(\in \{\text{ the sets }\}\)
\( S_2\): \(\in \{\text{ the sets }\}\)
\( f\): \(: S_1 \to S_2\)
\( f'\): \(: S_1 \to S_1 \times S_2, p \mapsto (p, f (p))\)
\(*f' (S_1)\): \(\subseteq S_1 \times S_2\)
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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, \(f': S_1 \ to S_1 \times S_2, p \mapsto (p, f (p))\), \(f' (S_1) \subseteq S_1 \times S_2\)
