I'm trying to verify that if (M,d) is a metric space, then (N,e) is a metric space where e(a,b) = d(a,b) / (1 + d(a,b)). Everything was easy to verify except the triangle inequality. All I need is to show that:(adsbygoogle = window.adsbygoogle || []).push({});

a <= b + c

implies

a / (1 + a) <= (b / (1 + b)) + (c / (1 + c)

Any help would be greatly appreciated, thank you!

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# Verifying the metric space e = d / (1 + d)

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