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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