Prove that if a is any well-ordered set of real numbers and b is a nonempty subset of $a$, then $b$ is also well-ordered.

If a is non empty ordered set, it has a least element. Let be a non empty subset, we can show that b is well ordered in the same relation. If C is non trivial subset of b, then it is also non trivial subset of a. But a is well ordered, since c has least element. Thus b is well ordered.