Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Replies: 42   Last Post: Oct 9, 2017 11:53 AM

 Messages: [ Previous | Next ]
 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 8, 2017 8:20 AM

Am Sonntag, 8. Oktober 2017 13:23:05 UTC+2 schrieb FromTheRafters:
> It happens that netzweltler formulated :
> > Am Samstag, 7. Oktober 2017 14:18:44 UTC+2 schrieb FromTheRafters:
> >> netzweltler wrote :
> >>> Am Samstag, 7. Oktober 2017 01:42:15 UTC+2 schrieb Jim Burns:
> >>>> On 10/6/2017 6:03 AM, netzweltler wrote:
> >>>>> Am Freitag, 6. Oktober 2017 02:54:40 UTC+2
> >>>>> schrieb Jim Burns:

> >>>>>> On 10/5/2017 3:12 PM, netzweltler wrote:
> >>>>>>> Am Donnerstag, 5. Oktober 2017 17:59:25 UTC+2
> >>>>>>> schrieb Jim Burns:

> >>>>>>>> On 10/5/2017 10:00 AM, netzweltler wrote:
> >>>>>>>>> Am Donnerstag, 5. Oktober 2017 15:22:35 UTC+2
> >>>>>>>>> schrieb Jim Burns:

> >>>>
> >>>>>>>> [...]
> >>>>>>>>>> _We don't do what you're describing_
> >>>>>>>>>
> >>>>>>>>> Nevertheless,

> >>>>>>>>
> >>>>>>>> "Nevertheless"?
> >>>>>>>> Do you agree that what you're describing
> >>>>>>>> is not what we're doing?

> >>>>>>
> >>>>>> *NETZWELTLER*
> >>>>>> DO YOU AGREE THAT WHAT YOU'RE DOING
> >>>>>> IS NOT WHAT WE'RE DOING?

> >>>>>
> >>>>> Let's say I agree. Doesn't mean that it is obvious to me
> >>>>> what *you* are doing.

> >>>>
> >>>> Great. Let's say you agree. Will you stop saying that
> >>>> "0.999... means infinitely many commands"?

> >>>
> >>> No. Because it is not obvious to me why the equation
> >>> 0.999... = 0.9 + 0.09 + 0.009 + ...
> >>> should be wrong.

> >>
> >> It's not wrong. The first one is a representation of the number one.
> >> The second is a representation of the number one. Two things equal to
> >> the same thing are equal to each other.
> >>
> >> [...]

> >
> > I'd have to look it up: Did you say that 0.999... IS the result of infinitely
> > many addition operations or IS NOT the result of infinitely many addition
> > operations?

>
> If you had an oracle with enough time which could do the arithmetic and
> hand you an answer, then yes. Without such an oracle, then I'd have to
> say no. That's why I said "after" doing infinitely many steps you would
> have that number exactly. John Conway used language similar to 'after
> infinitely many of these steps, there is an explosion of sets...' to
> describe a similar notion in describing his construction of the
> surreals, so I'm not exactly breaking any new ground here.
>
> I'm saying that that representation (or rather the infinite sum version
> which you previously laid out) is a result of taking the infitite
> string of nines (or rather terms) and repeatedly truncating them to a
> usable (printable) length so as to be defined as a textual
> representation of that number. Since the number of truncations are not
> finite the ellipsis is used to indicate this fact. This doesn't mean
> that the number itself is reliant upon the ability to do infinite
> arithmetic to have anyones permission to exist.
>
> As someone else has already pointed out, e and ? are numbers and can be
> used in mathematics perfectly, especially in polar notation. Sometimes
> they effectively cancel each other out such as in Euler's Identity. A
> 'problem' exists when attempting to express either of these existing
> numbers in decimal expansion representation (to write them down) and it
> looks as if it can't be done exactly if you look at the representation
> as if it were arithmetic defining a number rather than a representation
> built from that number and defined as representing that number.
>
> Euler solved the Basel Problem *exactly*, despite the fact that ?
> appears in the numerator and ? can't be 'reached' by doing the
> arithmetic inherent in any of its representations in less than infinite
> time.

I don't see the "infinite time" problem. What is the time a single addition operation takes? 0? More? Even if you don't allow 0 time for a single addition operation, try this:

t = 0: Add 0 + 0.9
t = 0.9: Add 0.9 + 0.09
t = 0.99: Add 0.99 + 0.009
...

Every operation take some time greater than 0. Nonetheless, we have done infinitely many additions by t = 1. No "infinite time" involved. No oracle needed.

Date Subject Author
10/2/17 Guest
10/2/17 netzweltler
10/2/17 Jim Burns
10/3/17 netzweltler
10/3/17 FromTheRafters
10/3/17 Jim Burns
10/3/17 FromTheRafters
10/3/17 Jim Burns
10/3/17 FromTheRafters
10/3/17 netzweltler
10/3/17 bursejan@gmail.com
10/4/17 netzweltler
10/3/17 FromTheRafters
10/3/17 Jim Burns
10/3/17 FromTheRafters
10/3/17 netzweltler
10/3/17 Jim Burns
10/4/17 netzweltler
10/4/17 Jim Burns
10/4/17 netzweltler
10/5/17 Jim Burns
10/5/17 netzweltler
10/5/17 Jim Burns
10/5/17 netzweltler
10/5/17 Jim Burns
10/5/17 netzweltler
10/5/17 Jim Burns
10/5/17 FromTheRafters
10/6/17 netzweltler
10/6/17 Jim Burns
10/7/17 FromTheRafters
10/8/17 FromTheRafters
10/8/17 netzweltler
10/8/17 Jim Burns
10/8/17 netzweltler
10/8/17 Jim Burns
10/9/17 netzweltler
10/9/17 Jim Burns
10/9/17 netzweltler
10/9/17 Jim Burns
10/7/17 Jim Burns