[byteknight]

Now we can add me to the list of confused.

> ... when it has succeeded in giving us an infinite digit sequence for the output real number.

How can it actually ever succeed then? Infinity never ends.

[legacynl]

I don't think the examples are meant as actual real world things, but rather abstractions to help reason about the problem.

The most important thing about the halting problem, is that Turing gave an example of a computational problem that is unsolvable, thereby proofing that from all possible computational problems, some of them are be unsolvable.