[A puzzle which requires knowing what countable/uncountable mean]
Let $\mathbb{N}$ be the set of naturals: $\{1,2,\dots\}$.
Suppose $F$ is a subset of the power-set of $\mathbb{N}$ (i.e. $F$ is a set of subsets of $\mathbb{N}$), such that for any two distinct sets $A, B \in F$, either $A \subset B$ or $B \subset A$.
Basically $F$ is a chain of sets, each containing the previous one.
Is there an $F$ which is uncountable?
[Solution]
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