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