Originally posted by FabianFnas
No, it cannot be done. Division by zero is not possible in any number system.
If you define an division operator where you can divide by zero, math as we know it breaks down completely.
(This is interesting! If I am wrong on this one I would gladly be proven in that. Math would be a lot funnier then! Do you have a definition somewhere where division by zero is possible, perhaps a link of some sort?)
It would have to be defined within a particular number system, which wouldn't be the number systems we use (R, Q etc), so any results wouldn't apply to these systems. So maths as we know it would still be fine.
Whether the new system would have any practical applications is debatable, but as long as division in this new system behaved in the same way as division in the systems we're used to when
not dividing by zero it might.
I don't have a link, but I thought I remembered a link to a paper doing something like this on these pages some time ago.
It's just a matter of definition, so you can't say it's impossible. (In a particularly trivial way I could swap the definitions of division and subtraction - division by zero is fine then!). You
can say it's possible in a particular framework.