The author of my book stated

The Continuum Hypothesis:There exists no setsuch that

where

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 ?