>>12267736Ok I see what you mean. You can't put it next to the last digit because there is no last digit (no end) but you can still put it so it's at the end of the digits. In any case, it makes sense to put the digit at the end (meaning in the resulting string the new digit is at the end).
For example, (0,1) in the reals has no end but you can put 1 so it is at the end. You can say that you put 1 at the end.
Similarly you can embed countable ordinals in Q while respecting the order.
The naturals could be
1-1/n, then you can put an ordinal at the end by adding 1. Nobody would deny that 1 is the last digit, and it's not just next to the numbers but the end of the numbers. It's quite continuous.
