On May 31, 9:30 pm, quasi <q...@null.set> wrote: > On Thu, 31 May 2007 19:07:20 -0700, 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. > > You claimed to have proved .999 is not equal to 1, so you've proved a > false statement. Without looking further, that already means that > means your proof is invalid. > > But I did look a little further. A quick scan of your proof shows you > are using your own alternative definitions for standard concepts. > Sorry, that's also cause for immediate rejection of your proof. You > are not allowed to do that -- read the rules. > > I'm not saying that you are not allowed to attack the standards. You > can do that. Moreover, if you can show the standard concepts are > logically inconsistent, then those standards would have to be > abandoned. But to show such an inconsistency, you can't redefine the > concepts you are trying to attack. You have to use the existing > definitions, as they are already defined, and somehow prove a > contradiction. That's not what you did. You used alternative > definitions for standard concepts, and you reused the exact same > names. That renders your proof invalid. > > quasi
I appreciate your stance. I would ask that you take my proof at face value and not read into in existing conventions I don't specifically invoke. If you cannot do this, if you first enforce that I must embody the entire field of mathematics before being able to state anything of truth as I must do it solely in their terms, well then.
I never attempt to contradict a truth such that the limit as the positions becomes infinite in 0.999... is 1. I ask you only to conceive an entity that has an infinite unbounded set of contributive values in the form 9/10^n. If you cannot conceive such an entity, my argument is not for you as I address only this entity.
I would further say that the entity I intend to be expressing is the same one most students understood 0.999... to be upon first presentation.