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


Kirby Cook wrote:

> The flaw in the oft-cited second "proof", or demostration, which
tries
> to show that there is no number between 1.999... and 2, may be found
in
> the law of the reciprocal, by analogy and inference. Say, for
instance,
> that there is no number between the infinite sum (difference)
1-.999...
> and zero.Taking it step by step, 1-.9 has a reciprocal of 1/(1-.9) or

> 10; 1-.99 has a recirpocal of 100, and so on. So, if you assert that


> there is no number between 1-.999... and zero, then you are also
> asserting that there is no number between 1000... and a point often
> termed the point at infinity. And how many of you will buy that?

If I am reading your argument correctly, this is an odd claim.

Can you give an example of a number between 1-.999.... and
zero ? That would be more convincing.

It seems like your argument is (where 'N' is that number
you want to pick)

0 < N < (1 - .99) ==> 0 < N < 1 /(1 - .99)

and by extension 0 < N < Infinity

...or more like

0 < N < (1 - .99) ==> 1/0 < 1/N < 1/(1-.99)

(+/-) Infinity < N < (+/-) Infinity

since |1/X| > |1/Y| indicates |X|<|Y|

The use reciprocals here seems dubious to me.. since you
are asking if something lies between a small number in zero.

Also, there is 1/(1-.999....) ....

If you don't already accept the truth of the conclusion
(and you think 1-.999.... is really equal to zero),
then (1-.999...) is also a dubious thing to take a reciprocal
of, since it is equal to zero.


-Mysid

.

Relevant Pages

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