How to prove $\mathbb{R}$x$\mathbb{N}$ is not enumerable

Question

How to prove $\mathbb{R}$x$\mathbb{N}$ is not enumerable? I dont know how to prove these, i know $\mathbb{R}$ is not enumarable so $\mathbb{R}$x$\mathbb{N}$ can be enumareble. Please i need help.

Answer 1

If you know $\Bbb R$ is not enumerable, you can inject it into $\Bbb {R \times N}$ by $x \to (x,1)$ to show $\Bbb {R \times N}$ is not enumerable.