In article <email@example.com>, Newberry <firstname.lastname@example.org> 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. > > > 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.