The author of my book stated
The Continuum Hypothesis: There exists no set such that
He then went on raising a question: Is there as set such that ?
Following the question, he proved that , and at the end of the proof, he said the proof shows that there is no largest set. In particular, there is a set S with .
Remark: I have not a clue what he meant in blue texts.
Question: Is there or is there not that ?