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}.
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}.