On 10 Jan., 18:47, Zuhair <zaljo...@gmail.com> wrote: > On Jan 10, 1:06 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > > So accordingly we > can discriminate a number of reals up to the number of all Omega_sized > tuples of finite initial segments of reals,
As omega is not a finite number, you have no finite distingusihability.
> and this would be Aleph_0 > ^ Aleph_0 and we have NO intuitive justification to say that the > number of such tuples is countable.
2^aleph_0 would be sufficient.
That is an argument made by > INTUITIVE analogies using similes that are fairly natural. Anyhow I do > conceded that using such intuitive similes is not that easy to grasp, > many people would find it difficult to follow. However the result is > that there is NO intuitive grounds to say that the number of all reals > are countable.
But there is a striking ground that is more fundamental than any wrong or correct logical conclusion, namely that you cannot find out any real number of the unit interval the path-representation of which is missing in my Binary Tree constructed from countable many paths. At least by nodes, you cannot distinguish further reals, can you?