netzweltler
Posts:
461
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 5, 2017 10:00 AM


Am Donnerstag, 5. Oktober 2017 15:22:35 UTC+2 schrieb Jim Burns: > On 10/4/2017 3:58 PM, netzweltler wrote: > > > While it is true that there is no line on the list > > 0 > write 0.9 > > 1 > append another 9 > > 2 > append another 9 > > ... > > that produces other than a finite string, it is true that > > the complete list produces an infinite string. > > "We are dealing with infinitely many finite stepwise processes" > > is true for each line of the list. > > "we are dealing with an infinite stepwise process" is true > > for the complete list. We wouldn't get the resulting > > 0.999... otherwise. > > This is backwards. The finite initial segments > 0.9, 0.99, 0.999, ... > _do not_ result in the infinite decimal > 0.999... > > We have the infinite decimal _first_ , and then we trim it > to finite length, operate on the finite decimals in the > familiar way, and define the unique least upper bound of > all of the finite sums as the value of the infinite decimal. > > _We don't do what you're describing_
Nevertheless, the process 0 > write 0.9 1 > append another 9 (to the 0.9 already written) 2 > append another 9 (to the 0.99 already written) ... results in 0.999...
Whereas the process you specified earlier 0 > 0.9 1 > 0.99 2 > 0.999 ... is nothing else but an infinite list of terminating decimals.

