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Topic: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...

Replies: 31   Last Post: Oct 3, 2017 3:02 AM

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 netzweltler Posts: 473 From: Germany Registered: 8/6/10
Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...

Posted: Oct 2, 2017 1:58 PM

Am Montag, 2. Oktober 2017 17:59:21 UTC+2 schrieb Jim Burns:
> On 10/1/2017 3:22 AM, netzweltler wrote:
>

> > Do you agree that 0.999... means infinitely many commands
> > Add 0.9 + 0.09
> > Add 0.99 + 0.009
> > Add 0.999 + 0.0009
> > ...?

>
> 0.999... does not mean infinitely many commands.

But that's exactly what it means. Infinitely many commands. Infinitely many additions. Infinitely many steps trying to reach a point on the number line.

> There is a set of results of certain finite sums, a set of
> numbers. We can informally write that set as
> { 0.9, 0.99, 0.999, ... }
> That is an infinite set, but we can give it a finite description.
>
> (Our finite description won't use '...'. The meaning of
> '...' depends upon it being obvious. If we are discussing
> what '...' means, it must not be obvious, so we ought to
> avoid using '...')
>
> There is number which is the unique least upper bound of that set.
> The least upper bound is a finite description of that number.
>
> 0.999... means "the least upper bound of the set
> { 0.9, 0.99, 0.999, ... }".
> That number can be show to be 1, by reasoning in a finite manner
> from these finite descriptions of what we mean.
>
> If you give 0.999... some meaning other than what we mean,
> and then it turns out there are problems of some sort with

Date Subject Author
9/30/17 mitchrae3323@gmail.com
9/30/17 netzweltler
9/30/17 FromTheRafters
9/30/17 mitchrae3323@gmail.com
10/1/17 netzweltler
10/1/17 mitchrae3323@gmail.com
10/1/17 jsavard@ecn.ab.ca
10/1/17 mitchrae3323@gmail.com
10/2/17 netzweltler
10/2/17 Jim Burns
10/2/17 netzweltler
10/1/17 FromTheRafters
10/1/17 netzweltler
10/1/17 FromTheRafters
10/1/17 netzweltler
10/1/17 FromTheRafters
10/2/17 netzweltler
10/2/17 FromTheRafters
10/2/17 netzweltler
10/2/17 FromTheRafters
10/2/17 netzweltler
10/2/17 bursejan@gmail.com
10/2/17 Me
10/2/17 netzweltler
10/2/17 bursejan@gmail.com
10/2/17 bursejan@gmail.com
10/2/17 bursejan@gmail.com
10/3/17 netzweltler
10/2/17 FromTheRafters
10/2/17 jsavard@ecn.ab.ca
10/2/17 netzweltler