```Date: Jan 12, 2013 11:23 AM
Author: ross.finlayson@gmail.com
Subject: Re: FAILURE OF THE DISTINGUISHABILITY ARGUMENT. THE TRIUMPH OF<br> CANTOR: THE REALS ARE UNCOUNTABLE!

On Jan 11, 6:40 pm, Virgil <vir...@ligriv.com> wrote:> In article> <117f2274-de68-4a54-b90d-f3e423c3d...@c16g2000yqi.googlegroups.com>,>>  WM <mueck...@rz.fh-augsburg.de> wrote:> > On 11 Jan., 10:39, Virgil <vir...@ligriv.com> wrote:> > > In article> > > <3810bc42-c275-4897-94ba-8280508e9...@10g2000yqk.googlegroups.com>,>>> > Correct. But Cantor's list requires decimals or equivalent> > representations.>> Actually, Cantors original list for anti-diagonalization was of> sequences of letters from {m,w}, not digits, and were not interpreted as> numbers.>>...>> Aus dem Paradies, das Cantor uns geschaffen, soll uns niemand vertreiben> können.>> No one shall expel us from the Paradise that Cantor has created.>> David Hilbert> --"That's not "Cantor's original argument", for what he may have firststated it.http://en.wikipedia.org/wiki/Cantor's_theorem#HistoryFor subsets M of N, the ordinal indices of S range from zero in alphathrough omega, let f_alpha(M) be onto {0} and f_omega(M) be onto {1},then, G_alpha(M) = 1 - f_alpha(M) -> {1} = f_omega(M). Here fsatisfies the hypothesis of being a function from N at least into Sand doesn't see the contradiction.  Here there are obviously infiniteordinals between alpha and omega, between which there are functionsfrom N onto {0,1}.  Basically this S has only one of the two values onthe ends, and two in the middle, with symmetry and reflection, and theordinal omega would look like 2^omega.  Basically for each member of Sfrom zero, there is a corresponding bit-wise complement, in the sameorder, in reverse, from omega, such that G_alpha = f_omega-alpha.Thusly, G is not: not in S. Then, that would get back into Cantorhimself justifying counting backward from "limit ordinals", or thatomega is simply the next limit ordinal.For Russell's, let phi-x be or include that "not-phi-x is false",i.e., truth.If all the propositions in the language have truth values, and thetheorem is about their self-referential content, then admit their self-referential statement, here that in the language one, or the other, ofthe statement, and its negation, is a statement in the language. "Adam and Eve might have still been there hadn't they ate from the treeof knowledge.  Hilbert's Programme:  completeness.Regards,Ross Finlayson
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