Can someone explain the Zeno's paradox of "Achilles and the Tortoise" using the idea of infinitesimals?
MIT 18.01 Single Variable Calculus (OCW)
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The basic idea of Zeno's paradox was this:
Zeno thought up of a situation. In this situation, a soldier was fleeing from an arrow. The basic idea of the paradox here was that the soldier would be running at a speed that was slower than that of the arrow, ten times slower. Basically, in the time that the soldier would flee, the arrow would close 1/10 of a distance away, then 1/100 of a distance and so on and so forth. The paradox here is that the distance between the arrow and the soldier never converges to zero, but if we sum up all of the distances measured, the results show that as time goes to infinity, the arrow will definitely meet up with the soldier.
Im guessing dominus is referring to infinite series; http://en.wikipedia.org/wiki/Series_(mathematics)
Zeno made a mistake. He thought that sum of infinite would be infinite.
But, after the invention of calculus, by Leibniz (not a**h*le Newton), Leibniz was able to prove that sum of infinite can be finite.
Hence, Achilles can actually surpass the tortoise that had a certain lead over it.
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lol why are you hating on Newton??
coz he was an egoistic nerd, coz he was selfish, coz he destroyed Leibniz's life by using his position at Royal Society to credit the discovery of calculus to his name.. I can go on ..
I think more posts like these should be in the philosophy section lol.
@dominusscholae you really think that mathematics doesn't require philosophy?? Pure theoretical mathematics requires as much philosophy as mathematics...
How would you solve Hilbert's problems without philosophy? And doesn't a math major need to know about reasoning and critical thinking.... ???