Is it true that $xy\geq x+y$ for all $x,y\in \mathbb R$? I just see the GM-AM inequality. But I would like to compare $xy$ with $x+y$ for any $(x, y)\in\mathbb{R}^2$.
It looks like $xy>x+y$ since the first one is multiplication and the second one is addition.
Can we prove this? For $(x, y)\in\mathbb{N}^2$, can we prove it now?

We have $xy \geq x+y \iff (x-1)(y-1) \geq 1$.
