The Math Forum

Search All of the Math Forum:

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

Math Forum » Discussions » sci.math.* » sci.math

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

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

Replies: 4   Last Post: Oct 4, 2017 4:05 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

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 4, 2017 4:05 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Am Mittwoch, 4. Oktober 2017 13:43:34 UTC+2 schrieb FromTheRafters:
> netzweltler was thinking very hard :
> > Am Mittwoch, 4. Oktober 2017 11:44:35 UTC+2 schrieb Zelos Malum:
> >>> In fact it means exactly infinitely many commands.
> >>> But of course if you define a series to be equal to its limit, then that's
> >>> like defining an apple equal to an orange. That is your problem, not ours.

> >>
> >> It doesn't because it is not operations upon operations, it is just a
> >> representation of one element in real numbers.

> >
> > It does. And 0.875 is representing 3 operations, e.g.
> > 0.8 + 0.07 + 0.005 or
> > 0.5 + 0.25 + 0.125.
> >
> > It can be an element AND represent some number of operations.

> I agree. The thing is that a finite number of steps (or commands) can,
> at best, give a good enough approximation of some numbers.

The 3-step operations above give the number exactly. You can get this number after any finite number of operations. Whereas you can't get the number 0.874999... after a finite number of operations.

> By adding
> 'ad infinitum' to the 'end' of these, and assuming it can be completed
> in that (NaN) number of steps, you can arrive at the exact answer. This
> is a case where it is not about the trip, but about the (eventual)
> destination being defined exactly.
> As you already know, an arrow traveling from zero toward a target at
> two which can be described as going halfway there then halfway the
> remaining distance, then halfway again, may seem like an unending
> process with only better and better approximations being attainable.
> But, if I can get that same step by step process by stating that the
> process is actually pulling the arrow half the distance (from zero to
> two for example) then I don't need the unending process anymore as I
> already have the destination and the fact that the process is the same
> confirms that two is the answer I want.
> Insisting on the process while standing two units in front of the
> archer will not save you from getting the point. :)

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.