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What is the dual of { } ?I have a question for the logicians and category/set theorists among LtU readers. Background: I'm currently dealing with a simple matching algorithm for strings. One can create a search pattern either by building a set of admissible characters {a, b, c, ... } from the empty set {} or a search pattern from matching basically any character ( like using a . operator in regexps ) and withdraws a set of characters that shall not be matched: ANY  {a, b, c, ... } For disambiguation purposes I'm interested in making all those sets disjoint. It shall not be really significant in the discussion that characters are matched. This is just an implementation detail. The question is about the status of ANY? As it seems the full ZF set theory would be far too much specification. It entirely suffices that each of those sets S can be finally constructed or finally deconstructed as for ANY  S. In one case one starts with a "set of no entities" and in the other case with a "set of all entities". The latter clearly violates the principle that the set is constructed after the elements. I know ANY isn't entirely insane because I have a working implementation with the usual relations like union, difference, subset and intersection. What I'd like to know is about a more in depth treatment of ANY in the literature. I expect more interest from computing scientists given the above motivation than from classical mathematics. By Kay Schluehr at 20090204 18:23  LtU Forum  previous forum topic  next forum topic  other blogs  6720 reads

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