Technically speaking, because it's not a set, we should say it involves the collection of all sets that don't contain themselves. But then, who's asking...
The paradox is about the set of all sets that do not contain themselves, or a theorem that such a set does not exist.
In the context of the paradox you need to call it a set, otherwise it would not be a paradox
I'm asking. What prevents that collection from being a set?
The paradox is about the set of all sets that do not contain themselves, or a theorem that such a set does not exist.
In the context of the paradox you need to call it a set, otherwise it would not be a paradox