There are finite sets, countably infinite sets and uncountably infinite sets.
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A null set.
Yes.
It's called an infinite set.
I believe you are talking about subsets. The empty set (set with no elements) is a subset of any set, including of the empty set. ("If an object is an element of set A, then it is also an element of set B." Since no element is an element of set A, the statement is vacuously true.)
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