1. (a) Prove: If y > 0, then there exists n ∈ N such that n – 1 ≤ y (b) Prove that the n in part (a) is unique. 2. (a) Prove: If x and y are real numbers with x (b) Repeat part (a) for irrational...

1. (a) Prove: If y > 0, then there exists n ∈ N such that n – 1 ≤ y <>

(b) Prove that the n in part (a) is unique.

2. (a) Prove: If x and y are real numbers with x <>

(b) Repeat part (a) for irrational numbers.

3. Let y be a positive real number. Prove that for every n ∈ N there exists a unique positive real number x such that xⁿ
= y.