Division by $0$
Everyone knows that $(x/y)\times y = x$
So why does $(x/0)\times 0 \ne x$?
According to Wolfram Alpha, it is 'indeterminate'. What does this mean?
Also, are there any other exceptions to that rule?
$x/y$ means "the unique number such that $y \cdot (x/y) = x$." If $x$ is any number, does there exist a unique number $a$ such that $0 \cdot a = x\;$?