The empty set has only one subset: itself. It has no proper subsets.
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It depends on the set x. If set x is of cardinality n (it has n elements) then it has 2n subsets.
A set with n elements has 2n subsets. The number of proper subsets is one less, since 2n includes the set itself.
In a set, as it is usually defined, elements can't be repeated. "Mathematics" has 8 distinct letters, so your set would have 8 letters. The number of possible subsets (this includes the empty set, and the set itself) is two to the power 8.
A finite set with N distinct elements has 2N subsets.
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