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help| In mathematics, given a set S, the power set (or powerset) of S, written , P(S), ℘(S) or 2, is the set of all subsets of S. In axiomatic set theory (as developed e.g. in the ZFC axioms), the existence of the power set of any set is postulated by the axiom of power set. Any subset F of is called a family of sets over S. If S is the set {x, y, z}, then the complete list of subsets of S is as... Read enhanced Wikipedia article |
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Powerset (company)
Powerset is a company based in San Francisco, California that is developing a natural language search engine for the Internet. Powerset is working on building a natural language search engine that can find targeted answers to user questions (as opposed to keyword based search). -
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Power set
In mathematics, given a set S, the power set (or powerset) of S, written , P(S), ℘(S) or 2S, is the set of all subsets of S. -
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Powerset construction
In the theory of computation, the powerset construction or subset construction is a standard method for converting a nondeterministic finite automaton (NFA) into a deterministic finite automaton (DFA) which recognizes the same formal language. -
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Natural language search engine
Powerset -On May 11, 2008, the company unveiled a tool for searching a fixed subset of Wikipedia using conversational phrases rather than keywords. -
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Complete lattice
In summary, one can say that every complete lattice is isomorphic to the image of a closure operator on a powerset lattice. -
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Infinite set
In ZF, a set is infinite if and only if the powerset of its powerset is a Dedekind-infinite set, having a proper subset equinumerous to itself. -
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Nondeterministic finite state machine
This can be performed using the powerset construction, which may lead to an exponential rise in the number of necessary states. -
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Set theory
Kripke-Platek set theory, which omits the axioms of infinity, powerset, and choice, and weakens the axiom schemata of separation and replacement. -
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Code (set theory)
Using a pairing function on ω (such as (n,k) goes to (n2+2·n·k+k2+n+3·k)/2), we can map the powerset of ω×ω into the powerset of ω. -
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Boolean prime ideal theorem
It is worth noting that for the special case where the Boolean algebra under consideration is a powerset with the subset ordering, the "maximal filter theorem" is called the ultrafilter lemma.
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