In particular, > the real number is not given by an infinite sequence that is actually written down anywhere, but rather as an algorithm, or a black box, which

In particular, > the real number is not given by an infinite sequence that is actually written down anywhere, but rather as an algorithm, or a black box, which accepts a number n and outputs the n-th digit. At no point do I manipulate an infinite amount of information, yet I can look at any digit I want. Of course, I cannot look at all digits in a finite time, which is sort of the point of the post.