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Let $(X,d)$ be a metric space and let $Y$ be a nonempty subset of $X$. Show that $d$ defines a metric space on $Y$.

I'm not sure how to go about this, I was thinking of just checking the properties hold in $Y$, but not sure if that's the correct approach.

Any help is appreciated, thanks.

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    @$A$lti Happy to help. I added my comment as an answer to make it easier for others to spot.2012-10-17

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This is indeed the correct approach. Just verify that the required properties of $d$ also hold in $Y$. As you have noticed, it is trivial to do so.