axiom of choice love

axiom of choice

Definitions

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. One of the axioms in axiomatic set theory, equivalent to the statement that an arbitrary direct product of non-empty sets is non-empty.

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  • Equivalent to Zorn's lemma.

    December 3, 2007

  • Aside from the fact that this is the name of a rock group, the axiom of choice essentially says that you can make a choice an infinite number of times, as long as there is no rule governing such choice.

    "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) indistinguishable from each other.)

    February 23, 2007