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!

Symmetric Property in Metric Spaces Implied by Other Conditions of a Metric Space

  1. May 28, 2012 #1
    1. The problem statement, all variables and given/known data

    Show that the following three conditions of a metric space imply that d(x, y)=d(y, x):

    (1) d(x, y)>=0 for all x, y in R
    (2) d(x, y)=0 iff x=y
    (3) d(x, y)=<d(x, z)+d(z, y) for all x, y, z in R

    (Essentially, we can deduce a reduced-form definition of a metric space, one without explicitly stating the reflexivity condition because the other 3 conditions imply it)

    2. Relevant equations

    The three conditions above.

    3. The attempt at a solution

    I've gone in circles, getting nowhere.
     
  2. jcsd
  3. May 28, 2012 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    I would start looking for a counterexample of what you're trying to prove.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Symmetric Property in Metric Spaces Implied by Other Conditions of a Metric Space
  1. Metric Spaces (Replies: 10)

  2. Metric Spaces (Replies: 8)

  3. Metric Spaces (Replies: 6)

Loading...