Intermediate value theorem

• Prove That Every Nonnegative Real Number Has an nth Root
  Use completeness and continuity to prove that for every a ≥ 0 and positive integer n, some nonnegative b satisfies bⁿ = a.
• Baby Rudin Chapter 4 Exercises 5 and 6: Solutions
  Solutions to Baby Rudin Chapter 4 Exercises 5 and 6: use the intermediate value theorem for constant sign and continuity to prove the zero set is closed.