Re: Problems I have with 1.999...=2

Kirby Cook <kwmcook@xxxxxxxxxxx> wrote:
: Richard Tobin wrote:

:> In article <lZ9ge.12093$U01.10469@trnddc07>,
:> Kirby Cook <kwmcook@xxxxxxxxxxx> wrote:
:>
:>
:>>The assertion that the sum is infinite means, to me, that there is no
:>>point where it will equal 1 and be, therefore, finished, and finite.
:>
:>
:> No.
:>
:> The term "infinite sum" is shorthand for "the limit of the infinite
:> sequence of partial sums". The infinite sequence is indeed never
:> finished, but the infinite sum is not the infinite sequence, it is the
:> limit of it, which in this case is 1.
:>
:> As far as I am aware, 1 has been finished and finite for some time now.
:>
:> -- Richard

: Let me try it another way. My assertion might be stated (I hope) as
: follows. Given the set whose elements are nine tenths, nine tenths plus
: nine hundredths, nine tenths plus nine hundredths plus nine thousandths,
: etc., the least upper bound of the set is one, and one is not a member
: of the set.

That is true. 1 is not a member of the set { .9, .99, .999, ... }.
But if .999.... is a set, then it is not a number,
and the question does 1=.999.... does not make much sense.
If you interpret .999.... as a number, which is what most people
do, then you really do not have a lot of choices about what number
it is.

Stephen
.

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