### Countable vs. uncountable infinity?

I am surprised you didn't mention continuous, uncountable infinity vs. infinite arrays/lists.
For example, temperature, while we know that due to quantum mechanics, it is in fact digital, Aristotle would probably have thought that it was analog, smooth.
These are measured as real numbers.
You can count to 10, 57, or 4.
You can even count to -9, 0, etc, by counting like this:
0,1,-1,2,-2,3,-3...
You can even count to -562/197 if you are clever.
1/1, -1/1, 1/2, -1/2 2/1, -2/1, 3/1, -3/1, 2/2, -2/2, 1/3, -1/3. This will eventually reach -562/197. It will be the 315676th item in the list.
But, try and count the irrational or real numbers.
some hypothetical way of counting:
a.bcde...
f.ghij
k.lmno
p.qrst
u.vwxy

but.... I can think of a number that isn't on that list, it has the first digit of the first number, plus 1, as its first digit, second of second, +1, as its second, etc. Basically, I can do this no matter what crazy scheme you count with.
I guess +1 means +1 mod 10 in this case, since we don't want a 10 as a digit.