In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 30 Apr., 18:56, Dan <dan.ms.ch...@gmail.com> wrote: > > > You did not write down any digits. Therefore your example fails > > > > > A real number can be listed by a terminating decimal, by a periodic > > > > > decimal, or by a formula supplying each of its decimals. > > > > I gave you a formula for each of the decimals of the anti-diagonal , > > provided you would have given the formula for the list. > > Yes, but the list can be given by a formula only. I did not exclude > that. I said: A real number can be listed by a terminating decimal, by > a periodic > decimal, or by a formula supplying each of its decimals. > It is not possible to list irrationals *by writing their decimals*
But, and this is all that Cantor needs, it is possible to list the nth digit of the nth number, so long as there is any way to list the numbers.
> > Do you really want to go in the physics? > > I am in physics.
Then you are not in mathematics.
> The realm we can ever use is finite.
Only for physicists, not for mathematicians.
"As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."