achiles goes double fast than the turtle that has an advantage
when achiles reaches the previous position of the turtle it advanced 1/2 and when achiles reaches that second position turtle has it advanced 1/4, and so for
so the turtle will have an advantage during the 1st second of 0.5 in the next half second 0.25
in the next quarter second 0.125 advantage
so the time will half forever and distance will half forever as well
so in a way according limit concept time cant pass cause it has to half forever first and achilles cant overtake the trutle since it always have half distance advantage
but yet time goes on and achiles overtakes
so is it disproved this paradox or it really shows a contradiction between the aparent world and the mathematical one?
1+1/2+1/4+1/8+...=2 and does not equal infinity. Almost basic math.
He'll catch the turtle after 2 seconds and at 2 meters (asuming that turtle moves with 1m/s and starts with 1m advantage from Zeno who moves with 2m/s).
No one in sane mind ever turns when he has any other option.
Originally posted by raaaid: well i dont think zeno was stupid, he probably knew that
Sure he did. With this "paradox" he didn't want to prove anything, all he wanted was to tell apart the people who know basic math of infinite sums from those who don't.
Originally posted by raaaid: achiles goes double fast than the turtle that has an advantage
when achiles reaches the previous position of the turtle it advanced 1/2 and when achiles reaches that second position turtle has it advanced 1/4, and so for
so the turtle will have an advantage during the 1st second of 0.5 in the next half second 0.25
in the next quarter second 0.125 advantage
so the time will half forever and distance will half forever as well
so in a way according limit concept time cant pass cause it has to half forever first and achilles cant overtake the trutle since it always have half distance advantage
but yet time goes on and achiles overtakes
so is it disproved this paradox or it really shows a contradiction between the aparent world and the mathematical one?
Actually when Zeno came up with this no-one had a satisfactory mathematical concept of infinity. He really was arguing that dividing the world up into little bits must be wrong, because it leads to nonsensical results. Modern maths claims to have solved this, as per Tiny Tim's reply, but I have my doubts. What, for instance, does it mean to infinitely divide a quark?
Forums 
