Russell's Attic

(mathematics)An imaginary room containing countably manypairs of shoes (i.e. a pair for each natural number), andcountably many pairs of socks. How many shoes are there?Answer: countably many (map the left shoes to even numbers andthe right shoes to odd numbers, say). How many socks arethere? Also countably many, we want to say, but we can'tprove it without the Axiom of Choice, because in each pair,the socks are indistinguishable (there's no such thing as aleft sock). Although for any single pair it is easy to selectone, we cannot specify a general method for doing this.

单词	russell's attic
释义	Russell's Attic Russell's Attic (mathematics)An imaginary room containing countably manypairs of shoes (i.e. a pair for each natural number), andcountably many pairs of socks. How many shoes are there?Answer: countably many (map the left shoes to even numbers andthe right shoes to odd numbers, say). How many socks arethere? Also countably many, we want to say, but we can'tprove it without the Axiom of Choice, because in each pair,the socks are indistinguishable (there's no such thing as aleft sock). Although for any single pair it is easy to selectone, we cannot specify a general method for doing this.
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