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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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   Powerset construction

   In the theory of computation and Automata theory, 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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   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, including the empty set and S itself.
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   HBase

   HBase is an open source, non-relational, distributed database modeled after Google's BigTable and is written in Java. ... HBase began as a project by the company Powerset out of a need to process massive amounts of data for the purposes of natural language search.
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   Bruce Horn

   Bruce Lawrence Horn, a programmer with Apple Computer, was the creator of the Macintosh Finder and the Macintosh Resource Manager. ... Powerset was acquired by Microsoft in the fall of 2008 and is part of Live Search.
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   Infinite set

   In set theory, an infinite set is a set that is not a finite 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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   Complete lattice

   In mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet). ... Free complete lattices in this sense can be constructed very easily: the complete lattice generated by some set S is just the powerset 2S, i.e. the set of all subsets of S, ordered by subset inclusion.
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   Finite set

   In mathematics, a finite set is a set that has a finite number of elements. ... That is, the powerset of the powerset of S is Dedekind-finite (see below).
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   Hasse diagram

   In order theory, a branch of mathematics, a Hasse diagram (pronounced /ˈhæsə/, German: /ˈhasə/) is type of mathematical diagram used to represent a finite partially ordered set, in the form of a drawing of its transitive reduction. ... By making the y-coordinate of each set in the powerset be proportional to the cardinality of the set, the leftmost diagram shows that the powerset is a graded poset.
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    Ultrafilter

    In the mathematical field of set theory, an ultrafilter on a set X is a collection of subsets of X that is a filter, that cannot be enlarged (as a filter). ... An important special case of the concept occurs if the considered poset is a Boolean algebra, as in the case of an ultrafilter on a set (defined as a filter of the corresponding powerset).

Explore the following pages on Powerset:

• Powerset (company),
• Powerset construction,
• Power set,
• HBase,
• Bruce Horn,
• Infinite set,
• Complete lattice,
• Finite set,
• Hasse diagram,
• Ultrafilter

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