Re: Proof 0.999... is not equal to one.

On 31 May 2007 05:04:58 -0700, chajadan@xxxxxxxx wrote:

This has been a very educational evening for me. I would still like to
point out that no one has refuted my proof itself or pointed to
specific error or logical over-stepping it may contain.

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.

You're not entitled to change the standard definitions. You are
allowed to define a new number system of your own, but then call it
something else so as not to conflict with the existing standards.

However, by not accepting limits as numbers, you lose a lot of
mathematics. The beauty of limits is that, in most ways, they're just
as good as numbers. They can be added, subtracted, multiplied and
divided (with the usual restriction about dividing by 0). Moreover
they adhere to all standard laws of numbers (associative laws,
commutative laws, distributive laws, etc), and they interact
transparently with the rational numbers. The gain in terms of
completeness of the number system far outweighs any initial aversion.

quasi
.

Relevant Pages

  • Re: abundance of irrationals!)
    ... and he used the standard definition using limits. ... His first proof did not use binaries at all. ... his proof using decimal expansions of ...
    (sci.math)
  • Antisymmetry: Winter and Stueckelberg
    ... > The standard definition will not work well, I think, because I think you ... > can not come up with a proper definition of limits to cover the case. ... limit the standard one and excluding epsilon=0. ... physical quantities like time and frequency require an antisymmetrical ...
    (sci.physics)