Mathematics · True or False?
The answer is False.
It fails for every number between 0 and 1: 0.5² = 0.25 and 0.1² = 0.01 both shrink, while 0 and 1 themselves stay exactly the same, since 0² = 0 and 1² = 1. Every other real number does grow — including negative ones like (-3)² = 9, because the two minus signs cancel — and even (-0.5)² = 0.25 counts as "bigger", since any positive number is greater than any negative one.