Question

Can I prove or disprove this? Given two positive real numbers a and b, if a < b then a < b^2. I found an example that uses 0.1 and 0.2 but those are rational numbers. Or can someone help me?

Answer 1

it's ok. rationals are real.

Answer 2

a = 1/8, b = 1/4.
a < b
1/8 < 1/4
(1/4)^2 = 1/16
1/8 > 1/16.
Therefore, a > b^2.
If two positive whole numbers were used, a < b^2.