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hairyfigment comments on Stupid Questions Open Thread Round 2 - Less Wrong
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Does a well-ordering on the constructable version of R provably do this? I fear I can't tell if you've addressed my question yet.
Constructible version of R (if it is inside R and not the whole R) is just like Q: dense, small part of the whole, and usually zero-measure. So, this construction will yield something of measure zero if you define measure on the whole R.