ok i am stumped on a proof i am trying to construct of a metric:(adsbygoogle = window.adsbygoogle || []).push({});

d(x,y)=[tex]\frac{|x-y|}{1+|x-y|}[/tex]

so, out of the 3 requirements to be a metric, the first 2 are trivial and I am just working on proving the triangle inequality...

i need [tex]\frac{|x-y|}{1+|x-y|}[/tex] [tex]\leq[/tex] [tex]\frac{|x-z|}{1+|x-z|}[/tex] + [tex]\frac{|z-y|}{1+|z-y|}[/tex]

p^{2}(1+q+r+qr) [tex]\leq[/tex] q^{2}(1+p+r+pr)+r^{2}(1+p+q+pq)

can i now go to:

p(1+q+r+qr) [tex]\leq[/tex] q(1+p+r+pr)+r(1+p+q+pq) ???

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# Metric space proof

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