Prove that for all natural numbers n, there exists a natural number m^2 such that
n ≤ m^2 ≤ 2n
The Attempt at a Solution
I know how to prove this directly or by construction but my professor wants it solved by induction. When you're solving something by induction you have to show that for some statement p(n), p(n) → p(n+1). But in this problem how would I even start, if I start with the above inequality I can't seem to get it of the form n+1.