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**dori1123** Let $\displaystyle S_\omega $ be the minimal uncountable well-ordered set.

(a) Show that $\displaystyle S_\omega$ has no largest element.

(b) Show that for every $\displaystyle \alpha \in S_\omega$, the subset $\displaystyle \{x | \alpha < x\}$ is uncountable.

(c) Let $\displaystyle X_0$ be the subset of $\displaystyle S_\omega$ consisting of all elements $\displaystyle x$ such that $\displaystyle x$ has no immediate predecessor. Show that $\displaystyle X_0 $ is uncountable.

I know how to do (a) and (b) but don''t know (c), can anyone help?