Let $x$ be a real number. Prove that if $x^2\lt x$, then $x\lt1$ Let $x$ be a real number. Prove that if $x^2\lt x$, then $x\lt1$
I do not know how to proceed. I assume its proof is by contrapositive?

Proof by contrapositive is the easiest: let $x \ge 1$, then $x^2 = x \cdot x >= x$. Q.E.D.
