Subtraction on Numbers is Not Associative

Theorem
The operation of subtraction on the numbers is not associative.

That is, in general:
 * $$a - \left({b - c}\right) \ne \left({a - b}\right) - c$$

Proof
By definition of subtraction:

$$ $$

$$ $$

So we see that:
 * $$a - \left({b - c}\right) = \left({a - b}\right) - c \iff c = 0$$

and so in general:
 * $$a - \left({b - c}\right) \ne \left({a - b}\right) - c$$