Re:Mathematicians Measure Infinities, Find They’re Equal
by lisper on Thursday September 14, 2017 @10:47AM
(#15248542)
> my point is simply that there are two variants of this task
There are infinite variants of this task. But only one of them is mathematically interesting with respect to the claim that the reals cannot be put into one-to-one correspondence with the naturals.
> including waiting until after the supposed counter-example has been generated
Obviously, if I give you a real you can then generate a list that includes that real. That isn't very interesting.
Yes; to be clear, my point is simply that there are two variants of this task:
- Given an integer i and our list (or the infinite procedure that generates it), then the task is easy since we can diagonalise.
- Given an integer i and no knowledge of our list, the task becomes impossible, since the supposed "real not in your list" is actually independent of the list (by definition); hence we're free to choose any list we like, including waiting until after the supposed counter-example has been generated, and sticking that at the head of our list.