For every real number $x$, if $x - \lvert x \rvert + \frac{1}{x} - \lvert \frac{1}{x} \rvert = 1$ then $x$ is irrational
If $x$ equals $\sqrt{2}$ I get an inequality... So is this claim false?
2026-04-01 16:45:37.1775061937
If $x - \lvert x \rvert + \frac{1}{x} - \lvert \frac{1}{x} \rvert = 1$ then $x$ is irrational
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No. The claim is that if the claim is true then x is irrational.
The claim is not if x is irrational then the claim is true.
This is the sames as claiming "If x is a fish, it lives in water" but a whale lives in water but isn't a fish, so it isn't true.