Re: Demonstrating that 0.999... = 1

From: David C. Ullrich (ullrich_at_math.okstate.edu)
Date: 09/17/04 

Date: Fri, 17 Sep 2004 07:07:20 -0500

On Fri, 17 Sep 2004 08:11:48 GMT, rmercham@incandec.com (Ray Mercham)
wrote:

>On Thu, 16 Sep 2004 16:26:37 -0500, David C. Ullrich <ullrich@math.okstate.edu>
>wrote:
>
>>On Thu, 16 Sep 2004 15:20:54 GMT, rmercham@incandec.com (Ray Mercham)
>>wrote:
>>
>>>On Thu, 16 Sep 2004 09:21:02 -0500, David C. Ullrich <ullrich@math.okstate.edu>
>>>wrote:
>>>
>>>>On Thu, 16 Sep 2004 12:26:33 GMT, artmason@yahoo.com (Art) wrote:
>>>>
>>>>>On Thu, 16 Sep 2004 13:49:39 +0200, "Denis Feldmann" <denis.feldmann@wanadoo.fr>
>>>>>wrote:
>>>>>
>>>>>>> I would have thought that transparantly obvious. The original poster
>>>>>>> avoided doing anything that would involve wondering what happened "at
>>>>>>> the end". That was, I assume, the whole point of his/her posting.
>>>>>>>
>>>>>>> Your example, on the other hand, immediately raises the question:
>>>>>>> "What happens to the leftmost one when you multiply by 10".
>>>>>>
>>>>>>
>>>>>>You seem specially obtuse, or trolling, or playing devil's advocate. WHERE
>>>>>>DO YOU SEE A LEFTMOST ONE DIGIT IN ...1111 ? (and why is this question
>>>>>>different to "what is the rightmost one digit of 0.1111....?")
>>>>>
>>>>>You seem specially obtuse, or trolling, or playing devil's advocate. :)
>>>>>
>>>>>The whole point of the OP's post was to explain to the sort of people who
>>>>>_would_ worry about a 'leftmost 1'.
>>>>
>>>>Fine. Now explain what Denis and I don't get: Why would these people
>>>>_not_ worry about the rightmost 9 in 0.999...?
>>>
>>>I assumed it was because the OP took great care to ensure that nothing special
>>>happened at some imagined rightmost digit.
>>>
>>>If someone _is_ worrying about the supposed 'end' of a string of digits, they
>>>will certainly worry about:
>>>
>>>1) A carry
>>>2) A borrow
>>>3) 'Moving' the digit
>>>
>>>What makes the original demo work is that it removes any problem with what might
>>>be 'happening'. Whether you believe there is or isn't a rightmost digit, you
>>>don't have to worry about it because it demonstrably doesn't react with its
>>>neighbor(s).
>>
>>And again (and again and again) how is what I said about ...111 any
>>different in regard to any of this?
>
>To quote another poster:
>
>You seem specially obtuse, or trolling
>
>But one last try - What you said about ...111 would likely elicit the question
>"what happens right at the left when you multiply by 10?"

if you say so. This is not an answer to the question I've been asking.
What is the _difference_? If what you just said is true, then _why_ is
it not true that the OP is likely to elicit the question of what
happens at the rightmost place when you multiply 0.111... by 9?

You keep saying the question is likely to come up in one case but
not in the other. But you haven't given any indication of _why_
it comes up in one case but not the other.

>The whole problem with people who do not understand that 0.999... = 1 is that
>they are concerned with what happens at the "ends" of infinite strings of
>digits. By multiplying by ten (which most people are taught involves sticking a
>zero on the left and moving the number one place to the left - because it's a
>part of multi-digit multiplication), you have introduced that element of doubt
>into your "proof".
>
>So they'd never buy it in a million years.
>
>So you've come up with an absurdity that even a non mathematician will not
>believe.
>
>Well done - good work ;)

************************

David C. Ullrich