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Thread: Set theory - practical applications?

  1. #1 Set theory - practical applications? 
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    When I was in school this was called "new math." That will tell you how old I am. Anyway, I only learned some of the very basic stuff and never had a use for it since.

    Wikipedia has this under "Applications"

    Applications
    Set theory is seen as the foundation from which virtually all of mathematics can be derived. For example, structures in abstract algebra, such as groups, fields and rings, are sets closed under one or more operations.
    Well, maybe so, but set theory was not even invented until late 19th century, after most of the other math had already been discovered.

    Everybody learns this in school nowadays, so it must be pretty important. Educate me.


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    Forum Professor river_rat's Avatar
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    Set theory helps guide you away from the paradox's of naively following your nose in mathematics Harold, and there are a few major "errors" that seem to crop up continually if you are not careful.

    See Russell's paradox for an example

    The set theory formulism also helps in Computer science and logic, and tends to serve as a universal language for maths. However it is not the only universal language, but historically it is the one introduced first.


    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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    Quote Originally Posted by river_rat
    See Russell's paradox for an example
    Okay, I looked up Russell's paradox and it seems to be a problem with naive set theory that was resolved by higher-complexity set theories. But if I never used the naive set theory I wouldn't run into the paradox, and would be able to lead a normal, happy life, wouldn't I?
    I wonder if you could be a little more specific about how it is used in computer science and logic. Could I use it to solve those logic problems you find in some crossword puzzle books?
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  5. #4  
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    Set Theory is a consistent way of presenting other topics (which usually could be presented without using Set Theory). Example - Probability is nowadays often taught with reference to sets.
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