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axioms empty set

Some axioms are quite interesting. For example, the axiom of the empty set - "an empty set exists". But I ask, how empty is it? How much nothing is contained within it? Can it contain 'one' amount, 'some' amount, 'all' amounts or 'no' amounts of nothing? If the empty set exists it surely implies that the set containing the answer to the previous question exists within a set. The only one that we know 'can' exist without needing further axioms is the only one that does not seem to make sense to a normal mind: the empty set contains no amount of nothing.

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