Power Set Calculator

The power set of a set is the collection of every possible subset of that set. It includes the empty set, each one-element subset, every larger combination, and the original set itself. If a set has n distinct elements, its power set always has 2 raised to the power n members. This count follows from a simple choice: for each original element, a subset either includes it or leaves it out. Multiplying two choices across n independent elements gives 2 to the power n possible subsets. This calculator accepts comma-separated labels and constructs those combinations directly. For the set containing a and b, it returns the empty set, the subset containing only a, the subset containing only b, and the subset containing both. The order in which subsets appear does not change the power set because a mathematical set is unordered. Likewise, the order of elements within a subset has no mathematical significance, even though the calculator preserves input order to keep the output easy to read. Power sets appear throughout discrete mathematics, probability, logic, computer science, and data analysis. A collection of available features has a power set representing all feature selections. A group of candidate tasks has a power set representing every possible task bundle. In probability, the power set of a finite sample space can serve as its event space. Database queries, access-control combinations, test configurations, and optimization searches all use the same underlying idea. The number of results doubles whenever one new element is added. Three elements produce eight subsets, five produce thirty-two, and ten produce 1,024. That exponential growth is why this page limits generation to ten unique elements. The limit keeps the complete list readable and prevents a browser from creating an unexpectedly huge result. For a larger set, you can still calculate the count as 2 to the power n without listing every member. Repeated input labels are treated as one element because sets do not contain duplicates. Whitespace around commas is ignored, so entries such as red, green, blue work as expected. Use distinct labels if two objects need to remain distinguishable; for example, coin 1 and coin 2 should have different names. The generated notation uses square brackets instead of literal set braces so it remains clear in localized text while avoiding ambiguity with message placeholders. The empty-set symbol identifies the unique subset containing no elements.