Quote Originally Posted by User Name: View Post
There is a problem I see with the lim and sup proofs. Although correct, the result requires the assumption that 1 = .999... For example, if you try proof by contradiction, assuming .999... < 1, then sup(.9, .99, .999, ...) = .999... < 1. I use sup in this case for the ease of notation, and since, in this context, they have the same underlying concept.
Just when I thought we agreed :P. My proof used limits and I never assumed that "1 = .999...". It only uses the definition of "0.999..." and the limit of "10^-x" as x goes to infinity. If you really think that, can you point out where in my proof I assumed any such thing (just out of curiousity).