How many elements are there in the set {0,1,2,3,4,5}
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How many elements does the set {1, 2, 2, {3, 4}, 5} have?
In standard set theory, due to the Axiom of Extensionality, it has 4 elements. But in multiset theory, it has 5 (that is, its cardinal is 5). A multised may have repeated elements. So, the right answer is: it depends. Are you talking of sets according to which theory? Remember that the notion of set is not absolute, but depends on the theory. A set containing itself as an element may be a set in Zermelo’s original 1908 theory, but it is not a set in ZF, due to the axiom of regularity (ZF being consistent).
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