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Stuart_Armstrong comments on The Crackpot Offer - Less Wrong
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Minor quibble: since binary 0.1111... is 1, you need a number like 0.1010101... to get an actual counterexample.
He's looking for a correspondence between the natural numbers and their subsets because the subsets have a correspondence with the interval of reals [0,1], right? So .1111... = 1 is a counterexample, since it corresponds to the set of all whole numbers. Being equal to 1 doesn't make it representable by a finite subset.
You're both wrong, as pointed out later down in the comments. Eliezer wasn't referring to
0.1111...; he was referring to the infinite string...1111.0. That doesn't represent any finite whole number, but it does represent an infinite set of whole numbers.And yes, being equal to 1 does make it representable by a finite subset. Notably,
{0}.