In article <firstname.lastname@example.org>, WM <email@example.com> wrote:mail.com> wrote:
> > > > which is oo = Limit[n-->oo] 10^k > > and it not represented by any numeral. > > That is of little interest! You want to excuse one mistake by another > one.
It is of interest to every one who, unlike WM, can think straight about things. > > The sequence > 1 > 11 > 111 > ... > with its limit > oo = Limit[n-->oo] SUM[k=0 to n] 10^k > = 1*10^0 + 1*10^1 + 1*10^2 + 1*10^3 + ... > = ...111 > is represented by digits. So is my original sequence.
Your original "sequence" eventually replaces each non-zero digit to the left of the radix point with a zero digit, which then remains in that digit position thereafter, so WM's sequence ends up with all zeros to the left of the radix point.
If WM disputes this, let him identify any digit position for which this does not happen as I have described!
> The number of > digits is oo when calculated by analysis, but 0 when calculated by set > theory.
The number of non-zero digits to the left of a radix point in a limit requiring "infinitely many digits" cannot be calculated by analysis, as the result in analysis is not a number, and thus as a number cannot exist at all.
> This is one contradiction. And in mathematics one > contradiction is sufficient to run a proof by contradiction.
WM makes the most interesting spelling errors!
Or maybe that is just the way he misunderstands proofs. --