```Date: Oct 2, 2017 2:47 PM
Author: netzweltler
Subject: Re: It is a very bad idea and nothing less than stupid to define 1/3<br> = 0.333...

Am Montag, 2. Oktober 2017 20:35:56 UTC+2 schrieb Jim Burns:> On 10/2/2017 1:58 PM, netzweltler wrote:> > 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.> > That's not the standard meaning.So, you disagree that0.999... = 0.9 + 0.09 + 0.009 + ... ?> You give it some other meaning, and then you find a problem> with the meaning you gave it. Supposing I wanted to sort out> what that other meaning was, and how to make sense of it, my> attention to your meaning would not affect the standard meaning.> > I am not a math historian, but the impression I have> is that great care was taken in choosing the standard meaning> in order to avoid problems like the ones you are finding.> > You have the ability to create and then wallow in whatever> problems you choose. No one is able to take that power away> from you. But you can't "choose" by an act of your will to> make your created problem relevant to what everyone else> is doing. You are not the boss of us.> > > 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> >> your meaning, than that is your problem, not ours.
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