To get the following proof I followed another similar example, but I'm not sure if it's correct. Does this proof properly show existence and uniqueness?(adsbygoogle = window.adsbygoogle || []).push({});

Show that if x is a nonzero rational number, then there is a unique rational number y such that xy = 2

Solution:

Existence: The nonzero rational number y = 2/x is a solution of xy = 2 because x(2/x) = 2 = x(2/x) - 2 = x - x = 0.

Uniqueness: Suppose s is a nonzero rational number such that xs = 2. Then, xy =2 = xy - 2 = 0 and xs = 2 = xs - 2 = 0. Then:

xy - 2 = xs - 2

xy = xs

y = s

This would be a complete proof wouldn't it?

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# Uniqueness proof

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