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Why can a proper subset be a subset of itself?
Because every set is a subset of itself. A proper subset cannot, however, be a proper subset of itself.
How many subsets in an empty set?
The empty set has only one subset: itself. It has no proper subsets.
B is the subset of A what happened if elements are deleted from B?
Since B is a subset of A, all elements of B are in A.If the elements of B are deleted, then B is an empty set, and also it is a subset of A, moreover B is a proper subset of A.
Does the set of all sets other than the empty set include the empty set?
The collection of all sets minus the empty set is not a set (it is too big to be a set) but instead a proper class. See Russell's paradox for why it would be problematic to consider this a set. According to axioms of standard ZFC set theory, not every intuitive "collection" of sets is a set; we must proceed carefully when reasoning about what is a set according to ZFC.
What do you call sets within another set?
If all elements of set A are also elements of set B, then set A is a subset of set B.
