“To choose one sock from each of infinitely many pairs of socks requires the Axiom of Choice, but for shoes the Axiom is not needed.”

— Bertrand Russell

As quoted in Williams' Weighing the Odds: A Course in Probability and Statistics (2001), p. 498
Attributed from posthumous publications

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Bertrand Russell562

logician, one of the first analytic philosophers and politi… 1872–1970

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“The attempt to avoid a direct affirmation about infinite parallel straight lines caused Euclid to phrase the parallel axiom in a rather complicated way. He realized that, so worded, this axiom lacked the self-sufficiency of the other nine axioms, and there is good reason to believe that he avoided using it until he had to. Many Greeks tried to find substitute axioms for the parallel axiom or to prove it on the basis of the other nine. …Simplicius”

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Context: The attempt to avoid a direct affirmation about infinite parallel straight lines caused Euclid to phrase the parallel axiom in a rather complicated way. He realized that, so worded, this axiom lacked the self-sufficiency of the other nine axioms, and there is good reason to believe that he avoided using it until he had to. Many Greeks tried to find substitute axioms for the parallel axiom or to prove it on the basis of the other nine.... Simplicius cites others who worked on the problem and says further that people "in ancient times" objected to the use of the parallel postulate.