2 squared is 4, which is more than 2. However, 0.2 squared is 0.04, which is less than 0.2. Can someone explain this apparent contradiction where a number between 0 and 1 squared becomes less than the original number but everything else (more than 1) becomes more?

Question

And I understand for example if I’m talking about meters, it’ll become square meters so the comparison is not apples to apples anymore. But in situations where there is no unit (for example, a math equation where you need to find x, whatever X is), why is this not contradictory?

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Answer 1

well, we can try to describe how is that there is no cobtradiction:

we ask when does a number squared is less than itself:
x²<x
x² – x < 0
x(x-1)<0
and restricting only over positive values of x we see this
x-1 < 0 (dividing by x)
x < 1
so we see that when x is less than 1, x² is less than x