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A comment on The field of “useful reals” between rational and real numbers (2019).

Re:The field of “useful reals” between rational and real num... by arberavdullahu on Tuesday March 24, 2020 @05:50PM (#22679432)
The author claims that this set is countable but not sure if that is true. My argument is based on Cantor's theorem [1], which states that the power set has cardinality strictly greater than the set.

In order for the set of symbols to be finite field it must grow therefore since rational is infinitely countable from Cantor it must hold that "useful reals" is uncountable.

[1] https://en.wikipedia.org/wiki/Cantor%27s_theorem

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Re:The field of “useful reals” between rational and real num... by selectionbias on Tuesday March 24, 2020 @05:53PM (#22679465)
If you have a finite set of symbols, then the set of finite sequences of those symbols is countable. The key here is 'finite sequences', if you were to allow for infinite sequences then the set if uncountable.
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