Math 410 Homework 1

MATH 410, HW 1

1. Let r denote a rational real number and let x denote an irrational real number.
Prove that r − x and r/x are both irrational numbers .

2. Prove that there is no rational number r for which r² = 12.

3. Prove that between any two different rational numbers there exist infinitely
many irrational numbers .

4. Find the limit

5. Assume that l. Does that imply that either l or
? Justify your answer.