On Monday, October 2, 2017 at 12:45:50 AM UTC-6, netzweltler wrote:
> Correct. Time is of no concern. So, let me modify the list: > > t = 0: write 0.9 > t = 0.9: append another 9 > t = 0.99: append another 9 > ... > > to > > 1. write 0.9 > 2. append another 9 > 3. append another 9 > ... > > Do you still agree that this is a _complete_ list of all the actions needed to write 0.999... (already present - in no time)? It is a list of additions as well. All the additions it takes to sum up to 0.999... > Again the question: > If your claim is, that we reach point 1, you need to show which step on this list of infinitely many steps accomplishes that.
The claim is not that 1 is reached during the doing of those actions, even at the "end" of doing them - but an endless list of an infinite number of actions *has* no end. That's why it's called "endless".
Instead, 1 is the limit of that endless list.
So 1 can stand outside the endless list, and yet still be the limit. Because the limit is not part of the actions themselves.