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There are finite sets, countably infinite sets and uncountably infinite sets.

Q: What are kind of set?

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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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Yes.

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It's called an infinite set.

Set of integers.

A singular common noun

which kind of noun is set