The author claims > And for some purposes, an ellipsis is not just a convenience, it's a necessity. For instance, "1, 2, 3, ..., n" represents all the integers

The author claims > And for some purposes, an ellipsis is not just a convenience, it's a necessity. For instance, "1, 2, 3, ..., n" represents all the integers from 1 to n, where n is some unspecified positive integer; there's no way to write that without an ellipsis. This claim is wrong. Let n be a positive integer. If one wants to denote the set of integers between 1 and n, then one can do so by just formally writing what one wants: {k in Integers | 1 <= k <= n}. If one wants the (ordered) list of integers between 1 and n, then one can write (k)_{k=1}^n.