Ring is not Empty

Theorem
A ring can not be empty.

Proof
In a ring $\left({R, +, \circ}\right)$, $\left({R, +}\right)$ forms a group.

From Group is not Empty, the group $\left({R, +}\right)$ contains at least the identity, so can not be empty.

So every ring $\left({R, +, \circ}\right)$ contains at least the identity for ring addition.