On Jun 22, 1:14 pm, Virgil <Vir...@home.esc> wrote: > In article > <e6cef47a-8776-48b7-b21a-627a6366d...@g19g2000yqc.googlegroups.com>, > > > > > > Newberry <newberr...@gmail.com> wrote: > > On Jun 21, 9:38 pm, Virgil <Vir...@home.esc> wrote: > > > In article > > > <2896ff83-7d48-4bcb-80fa-ea38b8e1b...@40g2000pry.googlegroups.com>, > > > > Newberry <newberr...@gmail.com> wrote: > > > > On Jun 21, 6:11 am, Sylvia Else <syl...@not.here.invalid> wrote: > > > > > On 21/06/2010 1:39 PM, Newberry wrote: > > > > > > > Not sure why you think you had to tell us how the anti-diagonal is > > > > > > defined. You claimed you could CONSTRUCT it. Please go ahead and do > > > > > > so. > > > > > > I'm sure he will - right after you provide the list of reals. > > > > > > Sylvia. > > > > > Dear Sylvia, I did not claim that I could construct a list of reals, > > > > but Virgil claimed he could construct an anti-diagonal. > > > > To what list? > > > > An antidiagonal to a list of decimal representations of reals is simple. > > > > Ignore any integer digits (to the left of the decimal point) in the > > > listed numbers and have 0 to the left of the decimal point in the > > > anti-diagonal. If the nth decimal digit of the nth listed number is 5, > > > then make the nth decimal digit of the antidiagonal 7, otherwise make it > > > 3. > > > > This rule prevents it from being equal to any real in the listing. > > > > The above is only one of many effective rules for constructing an > > > antidiagonal different from each listed number. > > > How is this effective if the diagonal has infinite amount of > > information? > > The list of naturals has an "infinite amount of information" in many > senses, but a finite rule of construction contains it all.
I do not know how to quantify the amount of information the list of naturals carries. If it is not 0 then it is a few bits at most.
You talk nonsense and you know it. The list of naturals is compressible the diagonal is generally incompressible.
> > > > > > > > If, as in Cantor's original argument, one has a list of binary > > > sequences, one takes the nth value of the antidiagonal to be the > > > opposite value from the nth value of the nth listed sequence.- Hide quoted text - > > - Show quoted text -- Hide quoted text - > > - Show quoted text -