[empath75]

> To see that this is false simply realize that you don't actually have to write a decimal point to specify the real numbers in this range. Without the decimal point these real numbers just become natural numbers.

There are no natural numbers with infinite digits, so this is not correct.

[mturmon]

Your answer is buried, which is too bad, because it is the one-sentence rebuttal to the construction above.

[Zaak]

> There are no natural numbers with infinite digits, so this is not correct.

Exactly. If you allow an infinite number of digits you wind up with the p-adic numbers, which are uncountable just like the reals.