Exercise 1.9ΒΆ

One example of an \(x \in \mathbb{R}\) for which \(x < x^2\) is not true is \(\frac{1}{2}\); squaring \(\frac{1}{2}\) gives you \(\frac{1}{4}\).

In fact, for any \(x\) satisfying \(0 \leq x \leq 1\), we will have that \(x \geq x^2\); this is perhaps best illustrated by plotting \(y = x\) and \(y = x^2\) on a graph:

../../../_images/x-vs-x2.png