Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

P-adic metric Strong triangle inequality

  1. Feb 11, 2010 #1
    Hi Guy's
    I was wondering If anyone new of a good link about the P-adic metric Strong triangle inequality. I am trying to constuct a proof to show that the p-adic is a metric space.
    Must the proof use the Strong triangle inequality ie

    [tex] d(a,c)\leq [/tex]max[tex]{d(a,b),d(b,c)}[/tex]

    or can it use the normal inequality ?



    [tex] d(a,c)\leq d(a,b),d(b,c)[/tex]
    [tex] d(a,c)=\mida-c\mid=\mid(a-b)-(c-b)\mid[/tex]

    regards
     
    Last edited: Feb 11, 2010
  2. jcsd
  3. Feb 17, 2010 #2
    Of course the strong triangle inequality implies the (usual) triangle inequality. So if you prove either one of them, you are done.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook