We define the empty set as the set that contains no elements, but is there more

We define the empty set as the set that contains no elements, but is there more

We define the empty set as the set that contains no elements, but is there more than one empty set? So is there "an" empty set as opposed to "the" empty set? May one be able to receive values, while another is truly empty, etc.? And how is it possible to define the empty set by the absence of members or by emptiness?

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