Let SΩ be the minimal uncountable well-ordered set.
(a) Show that SΩ has no largest element.
(b) Show that for every α ∈ SΩ, the subset {x | α<x} is uncountable.
(c) Let X0 be the subset of SΩ consisting of all elements x such that x has no immediate predecessor. Show that X0 is uncountable.
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