Proof on inequality $|x-1|$

Question

I had an inequality problem when dealing with proof

$0\lt|x-1|\lt a$, then $|x-1||x-1|\lt a^{2}$ ?

does this sound right?

That looks right, though it would look better with MathJax – J. W. Tanner Sep 01 '20 at 02:39 — J. W. Tanner, Sep 01 '20 at 02:39

score 2 · Accepted Answer · answered Sep 01 '20 at 02:43

2

Yes, if $0\le x<y$, then we have $$x^2<y^2$$

The function $f(x):\mathbb{R}^+ \to \mathbb{R}, f(x)=x^2$ is an increasing function on the nonnegative domain.

answered Sep 01 '20 at 02:43

Siong Thye Goh

1 Answers1