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!

Elementary inequality

  1. Nov 5, 2008 #1
    I'm looking over a proof and I'm wondering from which principles does it follow that
    [tex] \mid a - b \mid < 1 \to \mid a \mid < \mid b \mid + 1 [/tex]

    I can see that [tex] |a - b | \le |a| + |-b| = |a| + |b| [/tex] and that [tex] |a| - |b| < |a| + |b| [/tex] but I just can't connect the dots.
  2. jcsd
  3. Nov 5, 2008 #2

    Ahh, got it [tex] |a| = |(a+b)-b| \le |a-b| + |b|[/tex] which means [tex] |a| - |b| \le |a-b| [/tex] the result immediately follows
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Elementary inequality
  1. An inequality (Replies: 3)

  2. An inequality (Replies: 4)