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

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- Oct 26th 2009, 08:45 AMtigergirlMultiplicative inverse 71.7
Show that 0 cannot have a multiplicative inverse in any of our number systems.

- Oct 26th 2009, 09:34 AMTheEmptySet
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.