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 >> ... >
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.