- #1

r0bHadz

- 194

- 17

## Homework Statement

Prove or disprove that there is a rational number x and an

irrational number y such that x^y is irrational

## Homework Equations

## The Attempt at a Solution

Please guys do not give me an answer. My only question is: what type of proof would you use?

It seems like with irrational numbers, proof by contradiction seems to be the best option in every proof I have encountered so far. The thing is, this course has a requirement of just calculus 1 and 2, and using Stewarts book I do not think he taught us anything about series expansions of irrational numbers unless I'm mistaken. I don't see how you can possibly answer this without that knowledge.

Like I said guys I really want to answer this my question myself. I do not want an answer, I found one on google already but I didnt read it. just simply: what proof would you use? My bet is proof by contradiction.

I'm going to sleep now, and I'm just interested in everyones responses, I will be back on this question in the morning.

As for the question itself, I don't see why it shouldn't be irrational. Sure, any irrational number is between two rational numbers, but I was taught that a irrational number never terminates. How could it possibly be rational if it's being raised to a number that never ends?

Anyways thanks guys, peace.