Re: Demonstrating that 0.999... = 1

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

Date: Fri, 17 Sep 2004 07:14:47 -0500

On Thu, 16 Sep 2004 18:59:36 -0400, "Michael Lockhart"
<ml1000@bellsouth.net> wrote:

>"David C. Ullrich" <ullrich@math.okstate.edu> wrote in message
>news:e92kk0ttgjcompkkcpnntrgo669v7icug9@4ax.com...
>> On Thu, 16 Sep 2004 15:37:48 GMT, prl@cyclops.com (PRL) wrote:
>> (*) 0.999... is the number x with this property: you can make
>> the finite decimal .999...9 as close to x as you want, just
>> by taking enough digits.
>>
>> You might want to note that first that _is_ the definition,
>> whether you like it or not, and second that whether you
>> like it or not you _should_ like it, because once you've
>> convinced someone that that _is_ the definition it seems
>> quite likely that you will also have succeeded in your
>> quest to convince him that 0.999... = 1, in a manner which
>> is a lot simpler than your OP. Because he's going to _agree_
>> that you can make 0.999...9 as close to 1 as you want,
>> just by taking enough digits!
>
>I think that's a particularly good way of phrasing it. The next time
>someone asks me about 0.999... and 1, I'll mention that and see if that sets
>them straight right off.

I'm not claiming that it _will_ set them straight, of course.

But if not it's because they don't accept that (*) _is_ the
definition. In which case there's no point in arguing about
it further - whether or not they think that (*) is what
0.999... "really" means or "should" mean it _is_ what it
_does_ mean.

If you find someone who doesn't buy that (*) is the definition
continuing to argue would be precisely like arguing with
someone who insists that dogs don't have four legs, and
points to the automobile in his driveway as a counterexample.
He's not really disagreeing with you on the facts of the
matter, he's just confused about what the word "dog" means,
and hence he doesn't understand what "dogs have four legs"
means - the _fact_ that he's insisting is false, namely
that cars have four legs, _is_ false, but simply irrelevant.

>Michael
>

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

David C. Ullrich

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