On 10/9/2017 11:14 AM, netzweltler wrote: > Am Montag, 9. Oktober 2017 12:45:19 UTC+2 schrieb Jim Burns:
>> Anyway, whatever it is you mean or don't mean is beside the >> point, which is that _the standard meaning_ of 0.999... >> does not mean infinitely many commands. >> >> This is actually a better reason to stop saying that, >> but it looked for a moment as though you intended your >> infinite sum 0.9 + 0.09 + 0.009 + ... to mean something. >> I just wanted to point out that, if it means something, >> it means 1. > > I can define 0.999... to mean "infinitely many additions" > without having to assign a value to it.
The point of infinite decimals -- an extension of finite decimals -- is for there to be values assigned to them.
If you're running your own show, there is no way to stop you from spouting whatever nonsense you choose to spout. In that sense, you can define 0.999... to mean anything you want. Define 0.999... to be a square circle. Sure, why not?
But, that is not what we mean by 0.999... We do not mean "square circle" and we do assign a value to 0.999...
Just because you invented some nonsense does not mean that your nonsense is relevant to what we mean by 0.999...
> In fact "infinitely many additions" means > "not assigning a value to it". > > I just wanted to point out that 0.999... means "something".
What 0.999... means is not what you mean by 0.999... And what 0.999... means is not infinitely many operations.