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Topic: 1=,999[bar]-to infinity thus mathematics ends in meaninglessness
Replies: 44   Last Post: Dec 16, 2010 8:25 AM

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 David R Tribble Posts: 3,426 Registered: 7/21/05
Re: 1=,999[bar]-to infinity so mathematics does not end in meaninglessness-
Posted: Dec 3, 2010 6:11 PM

Johan E. Mebius (JEMebius) wrote:
>> To obtain 0.999[bar] as the outcome of a long division: [...]
>

David R Tribble wrote:
>> Yeah, I did this in the never-ending discussion of 0.999...
>> on Wikipedia some months ago.
>> http://en.wikipedia.org/wiki/Talk:0.999.../Archive_14#Another_long_division
>>
>> Divide 1 into 1, but underestimate the first digit of the
>> quotient as 0 instead of 1, and then continue dividing
>> past the decimal point:
>>
>> 0.999...
>> ----------
>> 1 ) 1.000...
>> 0.
>> ---
>> 1.0
>> .9
>> ----
>> 10
>> 9
>> ---
>> 10
>> ...

>

Johan E. Mebius (JEMebius) wrote:
> I was not aware of the Talk item in Wikipedia at
> http://en.wikipedia.org/wiki/Talk:0.999.../Archive_14#Another_long_division
> - my thanks for this link!

Yeah, the discussions about 0.999... on Wikipedia are almost
as incredibly long as they have been here on sci.math.
And usually just as inane.

> Yeah, I did this in the never-ending discussion of 0.999... in this newsgroup
> some =years= ago. I guess you made an independent rediscovery of
> this "0.9 + 0.1" trick.

Yeah, I kind of stumbled upon it by accident, starting with
a "what if we did this?" kind of approach. It's also loosely
based on decimal division computer algorithms (see Knuth,
vol. 1), wherein the initial estimate of the next dividend digit
is underestimated and then corrected.

You gave a more detailed mathematical explanation of why
it works, though.

> Furthermore, I guess I was the first person to publish this.

Probably. Although it would not surprise me if it was found in
some old (pre-1940s, for example) textbook somewhere.