In Kolmogorov and Fomin's Introduction to Real Analysis, there are a pair of problems which seem to be asking the reader to prove the Continuum Hypothesis. These are in Section 3, problems 12 and 13, which I shall reproduce below.
Problem 12: Prove that the set $M$ of all ordinals corresponding to a countable set is itself uncountable.
Problem 13: Let $\aleph_1$ be the power (cardinality) of the set $M$ in the preceding problem. Prove that there is no power (cardinality) $m$ such that $\aleph_0 < m < \aleph_1$.
To me, this seems to offer two equally absurd interpretations: the first, where you assume $\mathbb{c} <\aleph_1$, and then you have to "prove" that the power of the continuum doesn't exist, the second is assuming $\mathbb{c}=\aleph_1$, and then you have to prove something that was shown to be undecidable in ZFC!
Does anyone have any insight on the nature of what this problem is asking? I've been wracking my brain trying to figure it out with some of my classmates (this problem was not assigned as homework), and none of us can crack it.