It seems to me we can assign to every irrational from 0 to 1 an infinite whole number in the following way:
$$ 0.a_1a_2a_3a_4... \rightarrow ...a_4a_3a_2a_1 $$
For example:
$$ 0.14159265... \rightarrow ...56295141 $$
As the decimal representation of irrational numbers has infinitely many digits it follows that every whole number defined this way is infinite.
Does it mean that for every infinite whole number there exists a corresponding irrational* number from 0 to 1 and vice versa?
Does this mean that the set of infinite whole numbers is uncountable? Or am I wrong and we are not actually allowed to distinguish infinite numbers?
* Except for a countable set of rational numbers, represented by a repeating decimal
Since it's been pointed to me that there is no such thing as 'infinite whole numbers', the given above expression can be seen as definition of them. But in that case, they may have no relationship to the usual set of whole numbers, is that right?
And these numbers seem to be precisely 10-adic integers, so the question is answered.