Thread: Multiplicative inverse 71.7

Show that 0 cannot have a multiplicative inverse in any of our number systems.

Originally Posted by tigergirl

Show that 0 cannot have a multiplicative inverse in any of our number systems.

We will need the fact that for all x.

This can be proved if needed.

Now supose that does have an inverse. Call it

Then by defintion of multiplicive inverse



But by our theorem above this is a contradiction. So the assumption that zero has an inverse must be false.