[deleted] wrote
PerfectSociety OP wrote
This seems to avoid the fact that the Arrow Paradox involves looking at instants of time, i.e. when the interval of time is 0 rather than some incredibly small number like Planck time. At a particular instant in time, the Arrow does not traverse any distance. So the problem that the paradox brings forth is that if at each instant in time the distance traversed is 0, then how can it be that when you add the distances traversed from all the instants together you get some non-zero answer?
rot wrote
looking at instants of time, i.e. when the interval of time is 0
not a math guy but is this possable?
this_one wrote
Sort of - you can look at "the limit as you approach 0". I.e. use smaller and smaller and smaller values until you can see the pattern and figure out what the answer would be if it was 0 an infinitesimal.
rot wrote
Like a parabola that approaches 0 but is never = 0
this_one wrote (edited )
0 squared is 0, so not quite. It's more like figuring out an asymptote. If you have the function y=1/x, you can't directly solve it for x = 0, but if you graph it, it's pretty easy to see that, depending which side of the y-axis you start on, the answer 'should' be either infinity or negative infinity.
The example in Zeno's Paradox isn't actually asymptotic, but you can solve it in the same kind of way
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