```Date: Jan 10, 2013 12:47 PM
Author: Zaljohar@gmail.com
Subject: Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF<br> CANTOR: THE REALS ARE UNCOUNTABLE!

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, WMWhat finite realm, I'm speaking about Omega_sized tuples of finiteinitial segments of reals, so each tuple have countably infinitenumber of entries, and each entry range over countably infinite numberof values (because the total number of finite initial segements ofreals 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 cannotestablish proving countability of the reals from the fact that we havecountably many initial segements of them, because the distinguishingprocess of each real resembles intuitively speaking my example number2 where a change in color of shirts can manage to distinguish morepersons than the number of colors of shirts after which they aredistinguished per each trial of wearing of shirts. So accordingly wecan discriminate a number of reals up to the number of all Omega_sizedtuples of finite initial segments of reals, and this would be Aleph_0^ Aleph_0 and we have NO intuitive justification to say that thenumber of such tuples is countable. That is an argument made byINTUITIVE analogies using similes that are fairly natural. Anyhow I doconceded that using such intuitive similes is not that easy to grasp,many people would find it difficult to follow. However the result isthat there is NO intuitive grounds to say that the number of all realsare countable.Zuhair
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