Prove native the field axioms that the additive identity, 0, has actually no multiplicative inverse.

Proof. The evidence is by contradiction. Intend otherwise, the there is some
*
such the
*
(this is the an interpretation of multiplicative inverse). Then, by part (b) of this exercise, we understand that
*
for any kind of
*
. Hence,

*
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since equality is transitive. However, this contradicts ar Axiom 4 the

*
and
*
should be unique elements
*




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