Consider the $\mathbb{Q}$-vector-space $$\{ f : \mathbb{R} \longrightarrow \mathbb{R} \mid f \text{ is continuous and } \mathrm{Image}(f) \subseteq \mathbb{Q} \}$$ What is its dimension?
Consider the $\mathbb{Q}$-vector-space
$$\{ f : \mathbb{R} \longrightarrow \mathbb{R} \mid f \text{ is continuous and } \mathrm{Image}(f) \subseteq \mathbb{Q} \}$$
What is its dimension?