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 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.