Constant Function is Continuous/Real Function
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Theorem
Let $f_c: \R \to \R$ be the constant mapping:
- $\exists c \in \R: \forall a \in \R: \map {f_c} a = c$
Then $f_c$ is continuous on $\R$.
Proof
Follows directly from:
$\blacksquare$
Sources
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): continuous function (v)