Recent content by choccookies

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    Graduate Are Metric Space Infimums Equal for Non-Empty Subsets?

    could i do this: inf{dist(x,J): x member of Q} = inf{inf{d(x,y)|y member of J}:x member of Q} Since we know inf{d(x,y)|x member of Q, y member of J}= d(Q,J) Then the above is = inf{d,(Q,J)}, and then the same for the right hand side?
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    Graduate Are Metric Space Infimums Equal for Non-Empty Subsets?

    but how would i do this? using the three axioms of metrics?
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    Graduate Are Metric Space Infimums Equal for Non-Empty Subsets?

    HI I've got this question I don't know how to do; Let X be a metric space, and let Q,J be non-empty subsets of X. prove that inf{dist(x,J):x is a member of Q}= inf{dist(Q,y):y is a member of J}. I know that the dist(x,J):= inf{d(x,y)|y is a member of J}, I thought maybe if I tried to...