Zeno's paradox tells us that before covering a distance d we should cover a fraction of the distance.The maximum smallest fraction to be covered is 0m (it is obtained by dividing d infinitely). If the speed of motion is say 1m/s in small scale doesn't it mean that we cover a point in 0 time.As 0+0+0...=1 when time approaches 1s distance too approaches 1m.Here before covering 0m the body covers the fraction of that distance!. When infinitely many 0m is covered the required distance is reached.Also using this idea before covering d, fraction of that distance is covered as d/x=0+0+0.. . (Note1-the fact that 0+0+0...=d where d is a positive real no. is obtained from the fact that a line is made from infinite no. of points of length 0m.The equation 1/0=infinity is also helpful.Note2-the speed 1m/s is also from 0s+0s+0s... . )

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TopNewestAn attempt to resolve this:

It is incorrect to state \(0+0+0...=d\)

It instead, should be written as:

\[\lim _{ n\rightarrow \infty }{ \sum _{ k=1 }^{ d }{ \frac { d }{ n } } } =d\] – Julian Poon · 2 years ago

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– Joseph Amal C X · 2 years ago

Maybe both are correct and represent the same.I had presented the logic behind 0+0+0...=d.-thanks sir.Log in to reply

– Julian Poon · 2 years ago

I actually younger than you :PLog in to reply

– Joseph Amal C X · 2 years ago

So you are 0+0+0... years old.I guess 14years old.Log in to reply

Any non zero quantity divided by zero is not defined. Any non zero quantity divided by a very small quantity would give you a very large quantity (tending to infinity). Similarly, if you divide any quantity by a very large quantity, you are going to get a very small quantity but not zero. I have explained this concept in details in one of my posts. – Kuldeep Guha Mazumder · 1 year, 9 months ago

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Zeno’s Paradox may be rephrased as follows. Suppose I wish to cross the room. First, of course, I must cover half the distance. Then, I must cover half the remaining distance. Then, I must cover half the remaining distance. Then I must cover half the remaining distance…and so on forever. The consequence is that I can never get to the other side of the room. Now the resolution to Zeno’s Paradox is easy. Obviously, it will take me some fixed time to cross half the distance to the other side of the room, say 2 seconds. How long will it take to cross half the remaining distance? Half as long—only 1 second. Covering half of the remaining distance (an eighth of the total) will take only half a second. And so one. And once I have covered all the infinitely many sub-distances and added up all the time it took to traverse them? Only 4 seconds, and here I am, on the other side of the room after all. – Shobhit Singh · 2 years ago

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– Joseph Amal C X · 2 years ago

Yours is the progression version while i wrote on the regression version of the paradox-refer the brilliant wiki on Zeno's paradox.My explanation for the progression version is that- You want to cover a distance d which takes about x sec at constant speed d/x meter per second.When we want to cover half d (numerator) it should take half of x sec(denominator). This can be expressed as 1/2 multiplied to both numerator and denominator.The next step is 1/2 whole square multiplied to both numerator and denominator.Next will be 1/2 cube.This means that each next step will take smaller and smaller time.Also in this case 1\10000 of a second is there to sustain constant speed 1\10000 of distance should be covered.The no. of tasks don't matter what matters is the time taken for it.As long as time flows motion should be attained.Log in to reply

– Joseph Amal C X · 2 years ago

Briefly speaking- if distance is said to contain infinitely many distances then time should also contain infinitely many time.Using this the assumption in the brilliant wiki that there is infinite no. of task so no work is made irrelevant as we also have infinite no. of time.The remaining assumption on regression that there is no first step is nullified as the first step is 0m/s(shown in the note). The remaining assumption on progression that there is no last step is also invalid as the last step was shown to exist in the response to my friend Shobhit Singh.Log in to reply

– Joseph Amal C X · 2 years ago

Soon I would write a note on progression.Sorry for replying so late, was quiet busy with exams.Did you like it.Do you think the math community should know it.Log in to reply