On 3 Mai, 18:51, Dan <dan.ms.ch...@gmail.com> wrote:
> Each real number in your list is followed implicitly by an infinite > amount of zeroes , just as the antidiagonal is followed explicitly by > an infinite amount of ones .
> 0.11100000..... differs from > 0.11111111..... = 1/9 at the fourth digit .
Why do you think that you can construct what the constructer of the list could not? > > Real numbers (like pi , or e , or 1/9 ) have their decimal > representation formally complete in actual infinity . > Natural numbers decimal representation ranges only in potential > infinity .
No, that is a contradiction. First the set of natural numbers has cardinality aleph_0. Therefore it is actually infinite.
> If you don't like it, stick to natural numbers.
Second the naturals are used to index the digits of the decimals. For that sake they are required to be actually infinite.
> That you can't write the full decimal representation of 1/9 doesn't > change its existence .
It is not a matter of writing, but of constructing. It is simply ipossible to surpass all natural indices. And they are already in the list.