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# Constant function

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Constant functions are those functions which assign to each point in their domain of definition the same "constant" value of the codomain,

${\displaystyle f:A\to B;~~\exists c\in B~~\forall x\in A:f(x)=c.}$

If B is a ring, then the set of all constant functions from A to B (for any arbitrary non-empty A) is a subring of the ring of functions from A to B, isomorphic to B.

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Two important constant functions in the OEIS are A000004 (where ${\displaystyle f(n)=0}$ for all ${\displaystyle n}$) and A000012 (${\displaystyle f(n)=1}$).