To complete the preceding answers picture (the obvious remaining part). If ${S\subset\mathbb R}$ is well ordered, then it is countable: indeed it has countable cofinality. Thus well-ordered subsets of R are exactly countable ordinals.
To complete Robin Chapman's answer the preceding answers (the obvious remaining part): if . If ${S\subset\mathbb R}$ is well ordered, then it is countable: indeed it has countable cofinality. Thus well-ordered subsets of R are exactly countable ordinals.
To complete Robin Chapman's answer (the obvious remaining part): if ${S\subset\mathbb R}$ is well ordered, then it is countable: indeed it has countable cofinality. Thus well-ordered subsets of R are exactly countable ordinals.