# 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 r^{2}
= 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.

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