Joseph is right. The riddle he gave just demonstrates, correctly spoken proofs, that dividing an equation by zero or multiplying by infinity (whatever this is...) makes no sense at all.

Ininity is no number, so the 'equation' INF=INF makes no sense either. Make the following experiment:
Let y1 = 2 x a. y2 = 1 x a. If you now try to make 'a' growing and growing so that finally 'a' becomes an infinite number, one might think, that

y1 = INF and y2 = INF, and finally y1 = y2 is valid.

But that's wrong. From

y1 / y2 = 2 x a / (1 x a) = 2

we see, that y1 will always be twice the value of y2. So, we should write

y1 = INF1 and y2 = INF2

So, we see that INF is no concrete number and must not be used in an equation.

Dividing by zero or multiplying by infinity makes an equation to loose its regular solutions. So, these manipulations are strictly forbidden.

Kai