That easiliy false. You can prove this by observing that all integers are, in particular, rational numbers. So, for instance, you can think of 4 as [tex] \frac{4}{1} [/tex], so [tex] 4 \in \mathbb{Z}\subset\mathbb{Q} [/tex]
And obviously, you have [tex] 4^2=16>4 [/tex]
It is true that the square of every rational number between 0 and 1 is smaller than the number itself.
But since not all rational numbers are between 0 and 1, the general claim is false.
