>>117516570.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.01, 0.11, 0.12 ...
This list gives you all the decimals between 0 and 1, but it doesn't give you all the reals
it's not that difficult to list the rationals, consider the list
0, 1/1, -1/1, 1/2, -1/2, 2/1, -2/1, 1/3, -1/3, 2/3, -2/3, 3/1, -3/1, 3/2, -3/2, ...
it may be more obvious that this lists all the rationals if instead you think of the list
0/1, 1/1, 1/2, 1/3, 2/3, 1/4, 3/4, ...
which gives us all rationals in the interval [0,1]. Taking the reciprocal of those (apart from 0) and interspersing them so they're every other element in the list gives us all the positive rationals and 0. Then we can again take the negation of every element on the list and intersperse that in the list as we did before to get all the rationals.
But we haven't done anything controversial here. Now notice that your own listing contains only finite decimals, which can of course be expressed as fractions. You have
0, 1/10, 2/10, 3/10, 4/10, 5/10, 6/10, 7/10, 8/10, 9/10, 1/100, 11/100, 12/10, ...
notice how your own list contains all the finite decimals in the interval [0,1], but it doesn't contain *any* infinite decimals, so for example 1/3 is not on your list. So not only does it not contain all the reals on the interval [0,1], it doesn't even contain all the rationals.
