The short answer is that if you take the partial sums of the first n terms, you get the sequence 1, 1, 2, 3, 4, … which settles down to have its nth element being n−1 and thus is a representative sequence for the number ω−1. I think you’ll be able to follow the maths in the paper quite well, especially if trying a few examples of things you’d like to sum or integrate for yourself on paper.
(There is some tricky stuff to do with ultrafilters, but that mainly comes up as a way of settling the matter for which of two sequences represents the higher number when they keep trading the lead infinitely many times.)
The short answer is that if you take the partial sums of the first n terms, you get the sequence 1, 1, 2, 3, 4, … which settles down to have its nth element being n−1 and thus is a representative sequence for the number ω−1. I think you’ll be able to follow the maths in the paper quite well, especially if trying a few examples of things you’d like to sum or integrate for yourself on paper.
(There is some tricky stuff to do with ultrafilters, but that mainly comes up as a way of settling the matter for which of two sequences represents the higher number when they keep trading the lead infinitely many times.)