Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Difference of two irrational numbers

  1. Mar 29, 2007 #1
    Im wondering if its possible given x,y irrational, that x-y is rational (other than the case x=y). The reason Im asking this is that Im reading a book on measure theory and they try to construct a non measurable set and they start with an equivalence relation on [0,1} x~y if x-y is rational. Then they construct a set using the axiom of choice which contains exactly 1 element from each equivalence class. I know that the set of all rational numbers in [0,1) is an equivalence class, also each irrational number forms an equivalence class because for each irrational number x, x-x=0 (rational). Is there any other possibilities?
  2. jcsd
  3. Mar 29, 2007 #2
    Let x be any irrational, and let y=x+r. (with r any rational number). Then y and x are irrational, and y-x is rational.
  4. Mar 29, 2007 #3
    that was simple :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook