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- n. set theory 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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sionnach's Words
contumely, fomite, holmgang, poltroon, eleemosynary, obsidian, nugatory, grindcore, felch, recrudescent, pyx, parenteral and 3271 more...
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Mathematical
Including Logic as well.
e, asymptote, phi, integral, derivative, fx(dx), tesseract, googol, googolplex, set, dodecahedron, zero and 48 more...
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sionnach Equivalent to Zorn's lemma. Dec 3, 2007
oroboros 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.)
Feb 23, 2007