> E.g. we still do not know how many reals there are.
Umm... yeah we do, the cardinality of the continuum is the same as the cardinality of the power set of natural numbers. We've known this for 140 years.
Reading between the lines, I think the author is really talking about the "non-computable numbers" (i.e. those real numbers who can't be calculated to an arbitrary precision by any Turing machine), but if that's what the author is referring to, he should just say "non-computable numbers", not "real numbers", which is a much broader class.
Umm... yeah we do, the cardinality of the continuum is the same as the cardinality of the power set of natural numbers. We've known this for 140 years.
Reading between the lines, I think the author is really talking about the "non-computable numbers" (i.e. those real numbers who can't be calculated to an arbitrary precision by any Turing machine), but if that's what the author is referring to, he should just say "non-computable numbers", not "real numbers", which is a much broader class.