- #1
cordyceps
- 50
- 0
Homework Statement
Given any real x > 0, prove that there is an irrational number between 0 and x.
Homework Equations
I'm not sure if the concepts of supremums or upper bounds can used.
The Attempt at a Solution
Take an irrational number say Pi. We can always choose a number n such that n*Pi is between 0 and x. Thus for every real x > 0, there is at least one irrational number between 0 and x.
Is this correct? If so, what other methods are there?