> ... outputting an irrational number as a measurement does not* imply that it's able to output any member of the complement of the rationals in the reals.* It

> ... outputting an irrational number as a measurement does not* imply that it's able to output any member of the complement of the rationals in the reals.* It's my fault, I'm sure, but you have missed the point entirely. The argument to which I responded, and which I extended absurdly, does imply that every real number is a valid output of a chance setup, and further assumes that each real number, including "any member of the complement of the rationals in the reals", is an equally likely outcome of that setup. That is anyway the conventionally understood definition of "pick a real number uniformly at random between 0 and 1". I would attempt to clarify the rest of what I wrote, but your condescension dissuades me.