Subtraction has no Identity Element

Theorem
The operation of subtraction on numbers of any kind has no identity.

Proof
there exists an identity $e$ in one of the standard number systems $\GF$.

That is:
 * $\forall x \in \GF: x = e$

But from Identity is Unique, if $e$ is an identity then there can be only one such.

From Proof by Contradiction it follows that $\GF$ has no such $e$.