Integral Domain with Characteristic Zero

Theorem
In an integral domain with characteristic zero, every non-zero element has infinite order.

Proof
Let $$\left({D, +, \circ}\right)$$ be an integral domain, whose zero is $$0_D$$ and whose unity is $$1_D$$, such that Let $$\operatorname{Char} \left({D}\right) = 0$$.

Let $$x \in D, x \ne 0_D$$.

Then:

$$ $$

$$ $$ $$

... that is, $$x$$ has infinite order in $$\left({D, +}\right)$$.