Set Question - is this possible?

Question

Is it possible to have a set $Y$, such that:

$Y \subset \mathbb{R}^n$

$\forall y \in Y, \forall\alpha > 1, \alpha y \in Y$

$Y$ is non-empty and bounded.

Is such a set an impossibility?

Thanks.

Answer 1

How about $Y=\{(0,\dots,0)\}$?