How this calculator works
Every distinct element has two choices: included or omitted. Enumerating those choices generates the power set. The empty subset and the original set are always present. Duplicate entries are collapsed according to numeric equality. Output grows exponentially, so the tool caps the input at 10 entries and lists at most 1024 subsets.
Formula
For a finite set S with n distinct elements, |P(S)| = 2^n.
Worked example
For S = {1, 2}, the subsets are {}, {1}, {2} and {1, 2}, giving 2^2 = 4. The empty set has only the empty subset, so its power set has 2^0 = 1 member.
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Frequently asked questions
Do repeated numbers create extra subsets?
No. Sets do not record duplicate elements, so repeated numeric values are removed.
Can elements be words?
The current engine accepts numeric lists only. Use distinct numbers to label non-numeric objects.
Is the empty set part of every power set?
Yes. Choosing no elements is always a valid subset.