- #1
GridironCPJ
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Homework Statement
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)
Homework Equations
The three conditions above.
The Attempt at a Solution
I've gone in circles, getting nowhere.