> > If the collection is something else than all its elements, then you > may be right. Show this "else". In fact, an actually infinite set must > constitute such a thing that cannot be removed when every finite set > of elements is removed.
Now we have a definition of infinity.
The only set that can satisfy that definition is the empty set.
Actually what we have is an example of why set theory is formalized. There are no verbs that decide the existence of sets according to the acts of language users.