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

On 31 May 2007 05:01:36 -0700, chajadan@xxxxxxxx wrote:

You do however have to give some sort of definition for 0.999...
Whatever you define it to be it will either be equal to 1
or it will not be a real number.


My definition of 0.999... is the sum of all elements of an infinite
set defined by 0.9*(1/10)^n for all n in the set of wholes numbers
including 0 and is included in my proof. I do not attribute to this
entity any other characteristics, need not for it to be real or non-
real. I allow the consequence of the infinite contibutive values alone
to dictate all else.

A sum of an infinite set is defined as a certain limit.

No. If you use the standard limit definition, 10x-x = 9.
You are only correct if you use some other definition for
0.999... in which case the "subtraction" is not in the
real numbers. You need to define a new set of "numbers".
When you do so you will not get a field.

- William Hughes

I avoid all limit definitions. To me limits are their own area of
study that tell you potentially more about what bounds an entity that
about the entity itself.

You have contradicted yourself. A sum of an infinite set is a limit.
How else would you define a sum of an infinite set?

The limit of 1/x as x approaches infinity is 0, but this is not
representative of the function at all which will never yield a zero
value. I do not reject ideas that discuss and define 0.999... as a
limit - I only reject ideas that attempt use a limit to ~equate~ to
the entity described by that limit when this is not justified. I leave
this disclaimer only to take into account a constant limit, such as
the limit of 3 as x approaches infinity - where the limit is exactly
equal to the number that yields it.

You need to think again about what an infinite sum means.



--
Dave Seaman
Oral Arguments in Mumia Abu-Jamal Case heard May 17
U.S. Court of Appeals, Third Circuit
<http://www.abu-jamal-news.com/>
.

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