Question

In a metric space (M.P )for all X,Y, ZEM the triangle inequality is
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Answer 1

Answer:

Given : a metric space ( M.p ) for all X, Y, Z ∈ M

To Find : the triangle inequality

Solution:

the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.

z ≤ x + y

|| x + y ||  ≤ || x ||  + || y ||

Equality sign only incase of Triangle with zero Area

reverse triangle inequality

|| x - y || ≥  | ||x|| - || y || |