# metric 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 sa

Question
Asked Apr 3, 2019
10 views

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

check_circle

## Expert Answer

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...

### Want to see the full answer?

See Solution

#### Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

### Advanced Math

© 2020 bartleby. All Rights Reserved.