firstname.lastname@example.org wrote: > > > > What is the distance between 0.99999... and one? > > > > Ciao > > > > Karl > > The distance is a non-real number I call a dubious number. It is of > indeterminate scale. It would take an infinity of them to equal one, > as mentioned at the end of my analysis. No real number increment would > be able to keep from surpassing one from zero in a finite number of > increments. > > While the distance it not a real number, the system of real numbers > cannot allow 0.999... to be one as shown in my proof. In the Classic > Proof, 10x - x requires an element of subtraction that decimal cannot > hope to express in its own terms. > > Bounds on the distance are not expressable in decimal notation. > Decimal notation, as described, is unable to express a large class of > real numbers. We know an infinity of numbers exist just after zero, > but decimal can only ever hope to express some reasonbly small > numbers. In between any smallest number decimal can express and zero > lie an infinity of inexpressable real numbers. These real numbers > would require only a finite mutliple to reach one.
I'm almost certain that you would be interested in "Is 0.999... = 1?", Fred Richman, _Mathematics Magazine_ 72 (1999), 404-408. Based on what you said above, I think that your ideas are quite similar to Richman's. His article is also available on the web at