One possible set, out of infinitely many, is positive irrational numbers.
Possible subsets of a set are all the combinations of its elements, including the empty set and the set itself. If a set has ( n ) elements, it has ( 2^n ) subsets. For example, a set with three elements, such as {A, B, C}, has eight subsets: {}, {A}, {B}, {C}, {A, B}, {A, C}, {B, C}, and {A, B, C}.
5 subsets of 4 and of 1, 10 subsets of 3 and of 2 adds up to 30.
There are infinitely many composite numbers. There are, therefore, infinitely many subsets of ten such numbers. There are, therefore, infinitely many possible sums.
That means, figure out how many different subsets a set has. In general, if a set has n elements, it has 2n different subsets.
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An element doesn't have subsets. Sets can have subsets.
One possible set, out of infinitely many, is positive irrational numbers.
8 subsets
In a subset each element of the original may or may not appear - a choice of 2 for each element; thus for 3 elements there are 2 × 2 × 2 = 2³ = 8 possible subsets.
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Only a set can have subsets, a number cannot have subsets.
5 subsets of 4 and of 1, 10 subsets of 3 and of 2 adds up to 30.
A set with 27 members has 2^27 = 134217728 subsets - including itself and the null set.
It is impossible. If a set has n elements, the cardinality of its power set [the number of its subsets] is 2n which must be even.
There are infinitely many composite numbers. There are, therefore, infinitely many subsets of ten such numbers. There are, therefore, infinitely many possible sums.