1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Triangle inequality proof in Spivak's calculus

  1. Jan 6, 2014 #1

    So hi, there's one little thing which I'm not understanding in the proof. After the inequality Spivak considers the two expressions to be equal. Why?!?

    I just don't see why we can't continue with the inequality and when we have factorized the identity to (|a|+|b|)^2 we can just replace (a+b)^2 with (|a+b|)^2 and take the square root of both sides to finally have :

    |a+b| <= |a|+|b|

    Thank you for explaining !
  2. jcsd
  3. Jan 6, 2014 #2
    No need to answer, it's understood !
  4. Jan 6, 2014 #3


    User Avatar
    Gold Member

    You could also start from ##-|a| \leq a \leq |a|##.
  5. Jan 6, 2014 #4
    Well, I have another question. When Spivak justifies the passage from the squares to |a+b| <= |a|+|b| he says the following : x^2<y^2 supposes that x<y for x,y in N. Now, the only thing bugging me is the following : Why didn't he do the following x^2<=y^2 supposes that x<=y for x,y in N ? Because what he says only justifies the inequality and not the equality ! Like a part is missing ! Am I right ? Thank you!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted