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Advanced MathQ&A Librarymetric space is a set M together with a distance function ρ(x,y) that represents thedistance" between elements a and y of the set M. The distance function must satisfy) plz,y)20 and plr,y) 0 if and only if y:(ii) p(x,y) o(y,z);(iii) p(z, y) a(x, z) +a(z, y) for all x, y, z in M.Let (M.p) be a metric space. A mapping T from M into M is called a contraction iffor some constant a with 0 saQuestion

Asked Apr 3, 2019

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pls explain to me step by step. pls dont skip any steps. thanks

Step 1

**Proof:**

The metric defined on *R *is *d (x, y) =* |*x – y|*.

In order to prove the real line is a metric space with given metric, check the three conditions as follows.

To check for the non-negativity of the metric.

Step 2

Check the symmetry property.

Step 3

Check the triangle inequ...

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