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- noun set theory One of the axioms in
axiomatic set theory , equivalent to the statement that an arbitrarydirect product of non-empty sets is non-empty.
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oroboros commented on the word axiom of choice
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
sionnach commented on the word axiom of choice
Equivalent to Zorn's lemma.
December 3, 2007