On Thu, 31 May 2007 19:07:20 -0700, firstname.lastname@example.org 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.