Division on Numbers is Not Associative

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

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

Proof
By definition of division:

So we see that:
 * $a \div \paren {b \div c} = \paren {a \div b} \div c \iff c = 1$

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