In article <email@example.com>, <firstname.lastname@example.org> wrote: >I have written a proof that 0.999... cannot be equal to one in the >system of real numbers. > >While at the end of it all you may not fully agree with my proof, much >I as have never seen a proof asserting they were equal that I was able >to consider valid, I'm sure you will agree that the >ideas I present are not a simply rehashing of basic objections of >others before me.
Your "proof" is the usual mish-mash of inadequate definitions and hand-waving.
The equality is straightforward once you have precisely defined 0.999...
A reasonable definition is that 0.999... is the limit of the sequence
0.9 0.99 0.999 ...
The members of this sequence are 1 - 10^n, and the limit is 1. Therefore 0.999... = 1.
So, before proceeding any further, what is *YOUR* definition of 0.999...?
-- Richard -- "Consideration shall be given to the need for as many as 32 characters in some alphabets" - X3.4, 1963.