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: Unique infimum proof

  1. Mar 15, 2012 #1
    1. The problem statement, all variables and given/known data
    Let A be a subset of ℝ, now prove if inf(A) exists, then inf(A) is unique

    3. The attempt at a solution
    I am using an epsilon proof but i dont think i am going about it the right way, can someone nudge me in the right direction
  2. jcsd
  3. Mar 15, 2012 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    How you do it depends very much on what *definition* you are using for "inf". Different (but equivalent) definitions would need different types of proofs.

  4. Mar 15, 2012 #3
    Usually, for something like this, it is best to start of saying "Let x and y be inf(S)" and then show that x and y are, in fact, the same. Now, showing that |x - y| < epsilon might be a good strategy, but there are probably more efficient methods. But, as RGV said, it depends on how inf is defined for you. If you have defined it as a greatest lower bound, the method I mentioned works very well.
  5. Mar 15, 2012 #4
    yes i think im going to revise it as x and y are infimums for A then x<y and y<x so x=y
  6. Mar 15, 2012 #5
    That's a contradiction the way you wrote it. Did you mean [itex]x \leq y, \ \text{and} \ y \leq x,\ \text{so} \ x=y[/itex]?
  7. Mar 15, 2012 #6
    yes that is what i meant and i did write it that way x≥y y≥x
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook