Re: Is continuum completely filled up?

cbrown@xxxxxxxxxxxxxxxxx writes

Numbers which cannot be realised in the real world have a different
status from those which can?

Sure. The existence of a subset of the reals whose members obey some
such descriptive statement follows from whatever sufficiently rigorous
definition of "realised in the real world" you want to apply. Then
numbers not in that set have a different "status" than the numbers
which are in that set.

Cheers - Chas

Well, maybe it wasn't a very meaningful thought. It just seemed to me to be wrong to classify e.g. pi along with some transcendental that is a genuinely random sequence of digits. I know that pi has a random sequence of digits too (and it is probably a safe bet that distinguished tomes have been written concerning the statistical characteristics of its decimal expansion) - but pi does not encapsulate an actually infinite amount of information, which is what you would require to specify an instance of the other...
Andy Smith