Question

prove that every sphere is a convex set.​

Answer 1

Answer:

A set is called a convex set when it satisfy the condition sx + (1-s)yeM and s lies between 0 and 1.

All set of sphere values satisfies this condition and therefore sphere is called a convex set. Check the sphere values and you will get a convex set.

Step-by-step explanation:

Answer 2

Answer: Consider the norm of sx+(1−s)y. Let x, y belongs to B'x and s belongs to [0, 1], then by triangle inequality the equation forms is

||sx+(1−s)y||≤||sx||+||(1−s)y||=s||x||+(1−s)||y||≤s+(1−s)=1.

Therefore, sx+(1−s)y belongs to B'x is said to be convex. The convex of any type of sphere is proved by the triangle inequality law. The value of s must lies between 0 and 1.