On Jan 10, 9:08 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > 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? > > Regards, WM
Your binary tree have UNCOUNTABLY many paths each defined as a sequence of labels of its NODES, even though it has countably many nodes. That's what you are not getting. Anyhow.