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There are nonequivalent geometries, nonequivalent groups finite and infinite, nonequivalent logics ( fregean and nofregean http://www.formalontology.it/suszkor.htm), even nonequivalent logicians;-) ...

There are collections too big to be a set, e.g. the collection of all sets (in ZFC), and there are collections that cannot be sets for "pure" logical reasons, e.g. the collection of sets that do not ...