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

Kirby Cook <kwmcook@xxxxxxxxxxx> wrote:
: stephen@xxxxxxxxxx wrote:

:> Kirby Cook <kwmcook@xxxxxxxxxxx> wrote:
:> : Problems I have with 1.999...=2
:>
:> First problem, what do you mean by 1.999... ?
:>
: <snip>
: I think of it as a sum or progression.

: From the sci.math FAQ:

: "In modern mathematics, the string of symbols "0.9999..." is
: understood to be a shorthand for "the infinite sum 9/10 + 9/100
: + 9/1000 + ...." This in turn is shorthand for "the limit of the
: sequence of real numbers 9/10, 9/10 + 9/100, 9/10 + 9/100 + 9/1000,
: ..." Using the well-known epsilon-delta definition of limit, one
: can easily show that this limit is 1. The statement that
: 0.9999... = 1 is simply an abbreviation of this fact.

: 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.

Then you do not think 1.999... is a number and therefore
it is rather silly to expect a non-number to equal the
number 2, and 2-1.999... is meaningless.

Why did you stop reading your quote after the first sentence?
It tells you what "infinite sum" means, and it does not mean
what you say it means. The infinite sum is the limit.
The limit is "finished, and finite", and so is the infinite sum.

Stephen
.

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