What is $\mathbb{R}^\mathbb{R}$

Question

I do not know what it is.

$\mathbb{R}$ is the set of real numbers.

How come $\mathbb{R}\times\mathbb{R}\times \ldots $?

Thanks.

Answer 1

It's the set of all functions $\mathbb R\rightarrow\mathbb R$. In general $X^Y$ is the set of all functions $Y\rightarrow X$.