How to prove $\mathbb{R}^n < \mathbb{N}^\mathbb{R}$

Question

I know that the cardinality of $\mathbb{R}^n$ is equal to $\mathbb{R}$. I also know that the cardinality of $\mathbb{N}^n$ is equal to $\mathbb{N}$, but how do I prove that the cardinality of $\mathbb{R}^\mathbb{N}$ is smaller than the cardinality of $\mathbb{N}^\mathbb{R}$.

Answer 1

$$|\mathbb{N}^\mathbb{R}|\ge |2^\mathbb{R}|>|\mathbb{R}|=|\mathbb{R}^n|(=|\mathbb{R}^\mathbb{N}|).$$