1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proof question from How to Prove It

  1. Jan 3, 2010 #1
    proof question from "How to Prove It"

    3.2.8 Suppose a & b are nonzero real numbers. Prove that if a < 1/a < b < 1/b then a < -1

    I understand intuitively why this is true, but I can't figure out how to prove it. According to the hints at the back of the book it says to prove a < 0, then use to prove a < -1.

    When I go through the inequalities I come up with this:

    a < 1/b
    ab < 1

    1/a < b
    1 < ab

    I know that when you multiply both sides of inequality you have to switch the signs. But if both a and b are negative the signs both switch so I don't really understand how this can be true.
     
  2. jcsd
  3. Jan 3, 2010 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: proof question from "How to Prove It"

    Just take it one step at a time. If a<1/a then either a is in (0,1) or (-infinity,-1). You can show that, right? Same for b. Now if b is also in (0,1) and a<b can 1/a be less than 1/b?
     
  4. Jan 4, 2010 #3
    Re: proof question from "How to Prove It"

    Thanks, I understand it now.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Proof question from How to Prove It
  1. How to prove this. (Replies: 4)

  2. How to prove? (Replies: 1)

  3. How to prove? (Replies: 3)

Loading...