3. [5 points]

(a) Prove the following by contradiction:

"There does not exist a smallest positive rational number."

(b) Define a sequence cn (n ≥ 1) recursively by

C₁ = 0, C₂ = []+n² for n ≥ 2.

(i) Compute the values of C₂, C3 and c4.

(ii) Use strong mathematical induction to show that

Cn 4(n-1)² for all n ≥ 1.