Prove this inequality involving metrics

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  • Thread starter TMO
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TMO
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Main Question or Discussion Point

For any metric ##(X, \rho)## and points therein, prove that ##|\rho(x, z) - \rho(y, u)| \leq \rho(x, y) + \rho(z, u)##.

I know that this will involve iterated applications of the triangle inequality...but I still need another hint on how to proceed.
 

Answers and Replies

  • #2
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Did you draw a sketch? Consider distances to z-x+y, for example.
 

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