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Can anyone help me, how to prove in general, that that every ultrametric space is a metric space?

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    Begin by writing down the two definitions. Check the properties required one by one. Write in your question what happened and where you got stuck. – GEdgar Mar 08 '20 at 12:35
  • @GEdgar I had a problem to show that the triangle inequality, but now I got it, thanks –  Mar 08 '20 at 12:44

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$\max \{a, b\} \leq a+b$ for any $a,b \geq 0$.