Problem: Let $V = \mathbb{R} ^\mathbb{R} $ denotes the set of all functions from $\mathbb{R} $ to $\mathbb{R} $. We say a function $f : \mathbb{R} \to \mathbb{R} $ periodic if there exists a positive integer $p$ such that $f(x) = f(x+p)$ for all $x \in \mathbb{R} $. Is the set of all periodic functions from $\mathbb{R} $ to $\mathbb{R} $ a subspace of $V$?
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