Infinitely Counting Real Numbers

Question

I would like to show an idea on how to make real numbers infinitely countable. It is quite simple, too simple for me to believe it has been overlooked. So my question is, what have I overlooked?

So the "countable" list would start like this {0.1, 0.2, 1.1, 2.1, 1.2, 0.3, 0.4, 1.3, 2.2, 3.1 ...}, the way Cantor diagonally counted the list of rational numbers and potentially covering every real number there is.

And for the numbers after the decimal point, you go down a column and count normally after the decimal point but reverse the number.

Answer 1

This construction only covers the real numbers that have a finite decimal representation. These numbers are all rational - but you don't even cover all rational numbers, since they may have a periodic decimal representation [e.g. $\frac{1}{3} = 0.\overline{3}$].

Answer 2

All the numbers in your list have finite decimal expansions, so they are rational. In particular, $\sqrt 2$ is not on your list.