Proof: Bounded Sets Can Be Contained In Open or Closed Balls Centered Anywhere in a Metric Space

In this video we prove that a bounded set S in a metric space E is contained in an open or closed ball with center "p" FOR ANY "p" in E.

Proof of: "a" less than "b" and "c" less than or equal to "d" implies (a+c) is strictly less than (b+d):