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Axiom of Choice, quotes June 1, 2008

Posted by Alexandre Borovik in Uncategorized.
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  • The Axiom of Choice is obviously true, the Well-ordering theorem obviously false, and who can tell about Zorn’s lemma ?” ::— Jerry Bona -(This is a joke: although the axiom of choice, the well-ordering principle, and Zorn’s lemma are all mathematically equivalent, most mathematicians find the axiom of choice to be intuitive, the well-ordering principle to be counterintuitive, and Zorn’s lemma to be too complex for any intuition.)
  • “The Axiom of Choice is necessary to select a set from an infinite number of socks, but not an infinite number of shoes.” ::— Bertrand Russell -(The observation here is that one can define a function to select from an infinite number of pairs of shoes by stating for example, to choose the left shoe. Without the axiom of choice, one cannot assert that such a function exists for pairs of socks, because left and right socks are (presumably) identical to each other.)
  • “The axiom gets its name not because mathematicians prefer it to other axioms.” ::— A. K. Dewdney -( This quote comes from the famous April Fool’s Day article in the computer recreations column of the Scientific American , April 1989.)

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