Question

Prove that if a is an irrational number then 1/a is also irrational

Answer 1

Answer:

1/a is also the irrational number

Answer 2

“If a is irrational then 1/a is irrational” is equivalent to “If 1/a is rational then a is rational.” We can prove the second statement. If 1/a is rational, there are integers p and q (q not 0) such that 1/a = p/q. (Note that since 1/a is not 0, p cnnot be 0 either.)