<email@example.com> wrote in message news:firstname.lastname@example.org... > On May 31, 1:48 am, Richard Henry <pomer...@hotmail.com> wrote: >> On May 31, 12:19 am, chaja...@mail.com wrote: >> >> > > O.k., a=0.9999... is a real number. b=1 is a real number. >> >> > > What value has b-a? >> >> > > Karl- >> >> > I do not know that 0.999... is a real number. >> >> Then you are inventing a new mathematics and you can define 0.999... >> to be anything you like. > > My only claim in my proof is that real numbers cannot allow 0.999... > to be anything except less than one.
You must ask yourself if R is complete.
R is, among other equivalent definitions, the limit of all cauchy sequences of rationals. In layman's terms, we fill in all the gaps in Q (the rationals).
Now to me, and this is just a guess, you have trouble with limits of infinite sequences (and series). I'm not calling you stupid. This is just an observation. Since, if you accept this, then 0.999.... is certainly a real number:
...or something equivalent. If that is the case, you might want to seriously consider why, and if that opinion is in question.
> All of my other understandings > and thoughts are purely my own ideas and explorations that I'd > actually rather not delve into as they detract from the idea at hand > and only lend the ability to perceive as you have. > [...]