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


<chajadan@xxxxxxxx> wrote in message
news:1180612896.731992.273150@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

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.


Infinite sum? Does it converge? Sounds like a limit to me.


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.

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.


Mate, have a rethink, because this is contrary to what you just wrote.

--
Glen


.

Relevant Pages

  • Re: Proof 0.999... is not equal to one.
    ... I allow the consequence of the infinite contibutive values alone ... William Hughes ... I avoid all limit definitions. ... representative of the function at all which will never yield a zero ...
    (sci.math)
  • Re: Proof 0.999... is not equal to one.
    ... the sum of all elements of an infinite ... So you are not using the standard definition. ... representative of the function at all which will never yield a zero ...
    (sci.math)
  • Re: infinity
    ... any set of infinite extent must include ... Therefore, in some vague and indefinite way, as a ... >> number can ever yield anything other than a finite ...
    (sci.math)
  • Re: infinity
    ... any set of infinite extent must include ... > number can ever yield anything other than a finite ... it may well be that the twilight zone is ...
    (sci.math)
  • Re: infinity
    ... William Hughes wrote: ... > Tony Orlow wrote: ... >> One can speak of infinite sets UP TO any arbitrary value. ... It exists at every iteration of the proof, ...
    (sci.math)