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Math Help - Boolean atom

  1. #1
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    Boolean atom

    Hello,

    could someone,please, define what an atom in boolean algebra is and give some examples of identifying this "species" ?
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  2. #2
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    An "atom" in a Boolean Algebra is an element x, so that the only y satisfying y\le x are x itself and 0. For example, in the Boolean algebra of sets, in which \le is "subset" and 0 is the empty set, the atoms are the "singleton" sets, having only one member, so that the only subsets are itself and the empty set.
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    An "atom" in a Boolean Algebra is an element x, so that the only y satisfying y\le x are x itself and 0. For example, in the Boolean algebra of sets, in which \le is "subset" and 0 is the empty set, the atoms are the "singleton" sets, having only one member, so that the only subsets are itself and the empty set.
    Let B be a set of integers (divisors of number x) and the "meet" table would contain lowest multiples of pairs of those divisors, hence each entry is a singleton and thus an atom or else I am not getting it yet ? However there is also a question of expressing non-atomic elements in y way. Which tempts me to think that some of them must be non atoms...
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