Ques-2-Metric-Space-Question-Let-d-be-a-metric-on-a-non-empty-set-X-Show-that-the-function-U-is-defined-by-U-x-y-d-x-y-1-d-x-y-where-x-and-y-are-arbitrary-element-X-is-also-a-metri

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Question Number 191787 by Mastermind last updated on 30/Apr/23

$$\mathrm{Ques}.2\left(\mathrm{Metric}\mathrm{Space}\mathrm{Question}\right)$$$$\mathrm{Let}\mathrm{d}\mathrm{be}\mathrm{a}\mathrm{metric}\mathrm{on}\mathrm{a}\mathrm{non}-\mathrm{empty}$$$$\mathrm{set}\mathrm{X}.\mathrm{Show}\mathrm{that}\mathrm{the}\mathrm{function}\mathrm{U}\mathrm{is}$$$$\mathrm{defined}\mathrm{by}\mathrm{U}(\mathrm{x},\mathrm{y})=\frac{\mathrm{d}(\mathrm{x},\mathrm{y})}{1+\mathrm{d}(\mathrm{x},\mathrm{y})},\mathrm{where}$$$$\mathrm{x}\mathrm{and}\mathrm{y}\mathrm{are}\mathrm{arbitrary}\mathrm{element}\mathrm{X}\mathrm{is}\mathrm{also}$$$$\mathrm{a}\mathrm{metric}\mathrm{on}\mathrm{X}.$$

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