I've been thinking about the reals a lot...beyond the rationals are all the real numbers like pi that have finite definitions, (even if those definitions, like pi's, require infinite computation.)
But there is also this vast set of reals that are simply undefineable, non-repeating sequences. These numbers are unmentionable and unknowable. Does it really even make sense to say that this subset of the reals exists in the same way that definable numbers do?
