It can be defined at any time in any way. You could define it as always equaling 42.

No, you cannot. It is not only not useful, it breaks math - you can't arbitrarily define a division result without breaking all related operations, like multiplication and substraction.

What you **can** do, as maxwell demon correctly pointed out, is to extend algebra so division by zero makes sense. This means, of course, to redefine all basic operations, and since IEEE floats are built around basic linear algebra there **is** a natural reason why division by zero gives errors: it its either indeterminate or has no solution. When IEEE defined division by zero as infinity was not to provide a valid solution for it but to ease error handling afterwards.

You should consider toning down the patronizing. Your original statement is incorrect.