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**novice** If $\displaystyle A$ is any well-ordered set of real numbers, then every subset of $\displaystyle A$ has a least element. If $\displaystyle B$ is a nonempty subset of $\displaystyle A$, then $\displaystyle B$ has a least element.

Question: Since $\displaystyle A$ is well ordered and $\displaystyle B $ has a least element, and since having a least element is not a sufficient condition for a nonempty set to be well-ordered, does it mean that $\displaystyle B$ is not necessarily well-ordered?