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A subset of a set S can be S itself. A proper subset cannot.
No, by definition. A proper subset is a subset that contains some BUT NOT ALL elements of the original set.
A set "A" is said to be a subset of of set "B", if every element in set "A" is also an element of set "B". If "A" is a subset of "B" and the sets are not equal, "A" is said to be a proper subset of "B". For example: the set of natural numbers is a subset of itself. The set of square numbers is a subset (and also a proper subset) of the set of natural numbers.
the difference between a subset and a proper subset
Since ASCII ⊊ unicode, I don't know if there are ASCII codes for subset and proper subset. There are Unicode characters for subset and proper subset though: Subset: ⊂, ⊂, ⊂ Subset (or equal): ⊆, ⊆, ⊆ Proper subset: ⊊, ⊊,