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Math Help - Multiplicative inverse 71.7

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    Multiplicative inverse 71.7

    Show that 0 cannot have a multiplicative inverse in any of our number systems.
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    Quote Originally Posted by tigergirl View Post
    Show that 0 cannot have a multiplicative inverse in any of our number systems.
    We will need the fact that 0\cdot x=0 for all x.

    This can be proved if needed.

    Now supose that 0 does have an inverse. Call it e

    Then by defintion of multiplicive inverse

    e \cdot 0= 0 \cdot e=1

    But by our theorem above 0=e\cdot 0 =1 this is a contradiction. So the assumption that zero has an inverse must be false.
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