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Why worry about the axiom of choice? - MathOverflow - http://mathoverflow.net/questions/22927/why-worry-about-the-a...

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If I am working on a problem which is not directly related to logic or set theory, can important mathematical insight be gained by understanding its dependence on the axiom of choice? If I am working on a problem and I find a two page proof which uses the fact that every commutative ring has a maximal ideal but I can envision a ten page proof which circumvents the axiom of choice, is there any sense in which my two page proof is "worse" or less useful? · Скажи это моей лошади