Thread: Boolean atom

Hello,

could someone,please, define what an atom in boolean algebra is and give some examples of identifying this "species" ?

An "atom" in a Boolean Algebra is an element x, so that the only y satisfying are x itself and 0. For example, in the Boolean algebra of sets, in which 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.

Originally Posted by HallsofIvy

An "atom" in a Boolean Algebra is an element x, so that the only y satisfying are x itself and 0. For example, in the Boolean algebra of sets, in which 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...