On 1 Jun., 04:07, chaja...@mail.com wrote: > > Using the standard definition of the real numbers together with the > > standard definition of an infinite decimal as a limit, it's easy to > > prove that .999... _is_ equal to 1, hence it's automatic that your > > proof is flawed. > > Taken on those terms I would have to agree with you within the > confines that the limit is only allowed to yield real numbers. > > But that's fine, preclude out of hand that my proof can have no > validity without even reading it. > > I cannot accept that 0.999... is literal equal to 1 when we teach this > to students without the concept of limit. Everyday on message boards > across the world, some new student mentions that they learned > something that seems wrong, that 0.999... is exactly equal to one. No > one ever told them the limit as the places grow is 1. This is also > pretty obvious to everyone and the student would have had no > objections. > > My claim is not a claim in terms of limits. I have defined my number > as an infinite decimal and not mentioned limits. This reflects how I > and most student across the country were taught this issue. I later > mention limits in my analysis/proof only to say that limits do not > reflect the entity that yields them. My proof is standing up for that > part of our understanding that made every single one of us feel that > 0.999... equally one seemed off somehow.
This sounds like the difference between 0.999... and 1 is about the same as the difference between "The 43rd president of the United States" and "George W. Bush".