<email@example.com> wrote in message news:firstname.lastname@example.org... > > >> 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. >
So you assert that R does not form a metric space?
By the way, you are not using the word decimal appropriately.