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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 1, 2017 10:53 AM

Am Sonntag, 1. Oktober 2017 15:20:16 UTC+2 schrieb FromTheRafters:
> After serious thinking netzweltler wrote :
> > Am Sonntag, 1. Oktober 2017 13:56:01 UTC+2 schrieb FromTheRafters:
> >>
> >> It seems counterintuitive when a number is viewed (or represented) as
> >> an infinite unending 'process' of achieving better and better
> >> approximations, and that we can never actually reach the destination
> >> number. In my view, this sequence and/or infinite sum is a
> >> representation of the destination number "as if" we could have gotten
> >> there by that process.

> > If the process doesn't get us there then we don't get there. Where do you get
> > your "as if" from?

>
> If you had sufficient time, then you would get there.

Show how time is involved in our process.

>
> >> IOW "*After* infinitely many 'better'
> >> approximations" we reach the destination number *exactly* even if we
> >> cannot 'pinpoint' that number on the number line.

> > Please define "*After* infinitely many 'better' approximations". All we've
> > got is infinitely many approximations - each approximation telling us that we
> > get closer to 1 but don't reach 1. There is no *after* specified in this
> > process.

>
> There is also no "time" mentioned, so why is there an assumption of a
> process which takes time to complete? It is already completed (pi
> exists as a number despite our inability to pinpoint it on the number
> line by using an infinite alternating sum or any of the other infinite
> processes) we just can't pinpoint it because we exist in a time
> constrained universe with processes which take time to complete.

If you insist on introducing time to our process, try this:

t = 0: write 0.9
t = 0.9: append another 9
t = 0.99: append another 9
...

By time t = 1 we have completed infinitely many steps and we know all we need to know about our process:
Since time is continuous we reach time t = 1 and after.
By t = 1 we have completed writing 0.999...
Since the steps of addition are discrete, we can tell that we don't reach point 1 - neither during the process nor *after* the process by t = 1.

If your claim is, that we reach point 1, you need to show which step on this _complete_ list of infinitely many steps accomplishes that.

> >
> >> A 'limit' is not an
> >> approximation, it is the destination number (if there is one in that
> >> field) implied by the sequence or series in question.

>
> You could define a sequence or series by progressing from zero, to zero
> plus one, to zero plus one plus one half, to zero plus one plus one
> half plus one quarter, etcetera. This looks like it goes on forever
> getting closer and closer to some number without actually ever getting
> there.
>
> You could also define the same sequence or series by starting from two
> and pulling something from one toward you by half the remaining
> distance each time. In this second case, you already know the
> destination even though the other representation of the same sequence
> looks like it never gets there. Using the concept of infinity as
> in,"infinitly many steps" you relieve yourself of the neccessity of
> calculating the infinite sum approximations since you already know the
> destination number (known as a limit). Despite the fact that the
> process itself is neverending, these two 'things' are both
> representations of the same number - namely two.

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