Constant function

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Let [ilmath]A[/ilmath] and [ilmath]B[/ilmath] be sets and [ilmath]f:A\rightarrow B[/ilmath] be any function between them. We call [ilmath]f[/ilmath] a "constant function" if:

  • [ilmath]\exists b\in B\forall a\in A[f(a)=b][/ilmath]
    • In words: every [ilmath]a\in A[/ilmath] is sent to the same [ilmath]b\in B[/ilmath] by [ilmath]f[/ilmath].

We may write [ilmath]f[/ilmath] as:

  • [ilmath]f:A\rightarrow B[/ilmath] given by [ilmath]f:a\mapsto b[/ilmath]


  • Constant map and constant mapping are obviously also used.
  • Trivial map might be used to describe a constant map (and I am sure I have seen it) but this is rare and ill-advised.



Grade: D
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