Subtraction on Numbers is Not Associative

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

That is, in general:
 * $a - \paren {b - c} \ne \paren {a - b} - c$

Proof
By definition of subtraction:

So we see that:
 * $a - \paren {b - c} = \paren {a - b} - c \iff c = 0$

and so in general:
 * $a - \paren {b - c} \ne \paren {a - b} - c$