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Showing posts with the label Atlantic Ocean

ZFC Set Theory

I happened onto a logic blog recently and, before my eyes burnt out with the beauty of the abstractions involved, I learned a new term. ZFC Set Theory. The first two letters, "ZF," abbreviate names, Zemelo and Frankel. Both big names in the history of logic -- I need say no more of them now. The C stands for "choice" as in the "axiom of choice." Now, that sounds important. What choice can there be in logic? Well, the axiom of choice involves mutually disjoint nonempty sets. Take for example two such sets: the set of all teacups and the set of all named bodies of water on the planet. The axiom of choice means that for any set of such sets, it is possible to create a transversal set, containing exactly one element from each. Simple enough in this case: I can simple designate one set as consistent of teacup A plus Lake Erie. Another set consists of teacup B plus the Atlantic Ocean. And so forth. Why is this important? Well, Bertrand Russell in 1904 ...