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.

