netzweltler was thinking very hard : > Am Mittwoch, 4. Oktober 2017 11:44:35 UTC+2 schrieb Zelos Malum: >>> In fact it means exactly infinitely many commands. >>> But of course if you define a series to be equal to its limit, then that's >>> like defining an apple equal to an orange. That is your problem, not ours. >> >> It doesn't because it is not operations upon operations, it is just a >> representation of one element in real numbers. > > It does. And 0.875 is representing 3 operations, e.g. > 0.8 + 0.07 + 0.005 or > 0.5 + 0.25 + 0.125. > > It can be an element AND represent some number of operations.
I agree. The thing is that a finite number of steps (or commands) can, at best, give a good enough approximation of some numbers. By adding 'ad infinitum' to the 'end' of these, and assuming it can be completed in that (NaN) number of steps, you can arrive at the exact answer. This is a case where it is not about the trip, but about the (eventual) destination being defined exactly.
As you already know, an arrow traveling from zero toward a target at two which can be described as going halfway there then halfway the remaining distance, then halfway again, may seem like an unending process with only better and better approximations being attainable. But, if I can get that same step by step process by stating that the process is actually pulling the arrow half the distance (from zero to two for example) then I don't need the unending process anymore as I already have the destination and the fact that the process is the same confirms that two is the answer I want.
Insisting on the process while standing two units in front of the archer will not save you from getting the point. :)