On May 31, 1:02 am, chaja...@mail.com wrote: > On May 31, 12:33 am, William Hughes <wpihug...@hotmail.com> wrote: > > > let a = 0.999... be a real number. We do not need > > to give a full definition at this point > > a<=1 > > and > > a>(1-(1/10^n) for any natural number n > > You have defined 0.999... to be a real number without jusitification. > I can make no such assumption. Each position within 0.999... can be > expressed as a real number, but the totality, the very infinite nature > of it, seems to render it a never ending relation more than a specific > explicit location on the real number line.
Oh, I'm SO glad you said this. I think the same thing! In fact, it generalizes to other digits besides 9 as well! The case with 0 is particularly interesting. Clearly 0.000... is also a "never ending relation more than a specific location on the real number line." I mean, *obviously* it's different from 0. Look at all those additional digits on the end!
PS. Sadly, because this is sci.math, I have to be explicit that I am speaking ironically.