netzweltler
Posts:
472
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 2:47 PM


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 that
0.999... = 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.

