<email@example.com> wrote in message news:firstname.lastname@example.org... > >> A sum of an infinite set is defined as a certain limit. > Through convention alone. We have asserted this definition. > >> You have contradicted yourself. A sum of an infinite set is a limit. >> How else would you define a sum of an infinite set? > > Well I think it is clear that the geometic series that represents > 0.999... would sum to 0.999... yet the limit is 1. Defining the sum of > an infinite set is a convenience of notation so that we need not > append lim n-> infinity to the beginning of every infinite series. In > my own studies I append just such a thing. > > >> You need to think again about what an infinite sum means. >> > > Perhaps you may find it beneficial to ponder the relation an entity > has to its limit. >
An infinte sum. Is a limit. Yup. It's a limit of partial sums. Get used to it :).