
Re: It is a very bad idea and nothing less than stupid to define 1/3 = 0.333...
Posted:
Oct 5, 2017 9:22 AM


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_

