![]() ![]() ![]() One of the many representations (and formulations) of Zeno of Elea's paradox relating to the. Under this line of thinking, it may still be impossible for Atalanta to reach her destination. If each jump took the same amount of time, for example, regardless of the distance traveled, it would take an infinite amount of time to cover whatever tiny fraction-of-the-journey remains. How could time come into play to ruin this mathematically elegant and compelling "solution" to Zeno's paradox?īecause there's no guarantee that each of the infinite number of jumps you need to take - even to cover a finite distance - occurs in a finite amount of time. ![]() It doesn't tell you anything about how long it takes you to reach your destination, and that's the tricky part of the paradox. This mathematical line of reasoning is only good enough to show that the total distance you must travel converges to a finite value. convergent series: one entire "thing" can be obtained by summing up one half plus one fourth plus one eighth, etc. By continuously halving a quantity, you can show that the sum of each successive half leads to a. ![]()
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