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

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.
.