I was watching a lecture on computable real numbers, And in the lecture they talked about how this set of numbers is countable. And I could see this because the numbers that a computer generates would be listable, I could write them down on a list. For example pi is a computable real number. But it seems like I should be able to construct any real number with like an infinite series or something. But then again we have cantors diagonal argument. It just seems a little strange to me. If I do a calculation it seems like i could come up with any real number. Like I couldn't know which real numbers i couldn't compute. And like if I was trying to compute something, it wouldn't be like, well you cant do this calculation because your trying to compute an uncomputable real.