Answer to Question #98552 in Algebra for Mohammed Moro

Question

Suppose a is an irrational number. Prove that 1/a is also an irrational number.

Answer 1

Let's suppose 1/a is rational, then 1/a = m/n, where m is integer, and n is natural.

Then a is equal to n/m, so it is rational too - that's contradiction. Assumption '1/a is rational' was wrong.

Conclusion: 1/a is irrational.