On Jan 10, 1:06 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 10 Jan., 04:52, Zuhair <zaljo...@gmail.com> wrote: > > > The reason is that we can have even at finite basis more n sized > > tuples of m values than n x m. > > Of course,, when order plays a role, then you have 10^3 tuples of > lenght 3 when using 10 colors. Who told you else? But if you use > length aleph_0, then you leave the finite realm - whether you do it > with digits or with finite initial segments. > > Regards, WM
What finite realm, I'm speaking about Omega_sized tuples of finite initial segments of reals, so each tuple have countably infinite number of entries, and each entry range over countably infinite number of values (because the total number of finite initial segements of reals is countable) so we would have Aleph_0 ^ Aleph_0 of such tuples, and not as you thought Aleph_0 x Aleph_0.
What I'm saying is that the distinguishability argument cannot establish proving countability of the reals from the fact that we have countably many initial segements of them, because the distinguishing process of each real resembles intuitively speaking my example number 2 where a change in color of shirts can manage to distinguish more persons than the number of colors of shirts after which they are distinguished per each trial of wearing of shirts. So accordingly we can discriminate a number of reals up to the number of all Omega_sized tuples of finite initial segments of reals, and this would be Aleph_0 ^ Aleph_0 and we have NO intuitive justification to say that the number of such tuples is countable. 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.