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Triangle inequality

  1. Jul 9, 2008 #1
    Is it possible to write the triangle inequality in 2 ways:

    1. d(x,z) <= d(x,y) + d(y,z)
    2. d(x,y) <= d(x,z) + d(z,y) ?

    If so, are these the only 2 ways?
  2. jcsd
  3. Jul 9, 2008 #2


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    Staff Emeritus
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    Well, you could say [itex]d(a,b)\le d(a,c)+ d(c,b)[/itex] or [itex]d(x,u)\le d(x,v)+ d(v,u)[/itex] or pretty much any letters you wanted. But I wouldn't say those were "different" any more than I would say the two you give are "different".
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