On 3 Jan., 14:52, gus gassmann <g...@nospam.com> wrote:
> Exactly. This is precisely what I wrote. IF you have TWO *DIFFERENT* > reals r1 and r2, then you can establish this fact in finite time. > However, if you are given two different descriptions of the *SAME* real, > you will have problems. How do you find out that NOT exist n... in > finite time?
Does that in any respect increase the number of real numbers? And if not, why do you mention it here? > > Moreover, being able to distinguish two reals at a time has nothing at > all to do with the question of how many there are, or how to distinguish > more than two. Your (2) uses a _different_ concept of distinguishability.-
Being able to distinguish a real from all other reals is crucial for Cantor's argument. "Suppose you have a list of all real numbers ..." How could you falsify this statement if not by creating a real number that differs observably and provably from all entries of this list?