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## Homework Statement

"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"

## Homework Equations

## The Attempt at a Solution

If B [tex]\subseteq[/tex] A, then B[tex]\subseteq[/tex]{x1, x2, x3...xn}.

Since B[tex]\subseteq[/tex]A, the smallest possible subset B can be is {x1} which has a least element, ie x1.

Therefore B is well-ordered.