Sniffnoy comments on The Pascal's Wager Fallacy Fallacy - Less Wrong
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Of course, whether a number is definable or not depends on the surrounding theory. Stick to first-order theory of the reals and only algebraic numbers will be definable! Definable in ZF? Or what?
EDIT Apr 30: Oops! Obviously definability depends only on the ambient language, not the actual ambient theory... no difference here between ZF and ZFC...