# Constant Function is Continuous/Real Function

## 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:

Constant Function is Uniformly Continuous: Real Function
Uniformly Continuous Function is Continuous: Real Function.

$\blacksquare$