Zeno's First Paradox (Do Motion Is Illusion????)
This is one of the famous paradox involving infinity as well as infinitesimal. Zeno was a geek philosopher and created a set of Philosophical Problems
I love this paradox as it helps to understand concept of "infinity" and "infinitesimal" clearly.
Zeno's first paradox purports to show that the motion is impossible because if u want to walk from one point to another then you must first cross half the distance between the points and then half of the remaining distance and so on .........
FOR EXAMPLE ---
If the two points are one km apart you will first reach 1/2 km from start, then 3/4km and then 7/8km and so on. After you have taken some steps of the journey you will cross a distance equal to {1-(1/2 )^N} . Where N is power of 1/2. No matter how big N is , you will never reach your destination, & there will always be some "infinitesimal" distance left
Therefore 'Zeno' started that motion is never possible but since we can see motion then it should be nothing more than illusion.
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But today we all are aware of the fact that motion is reality. In Zeno's equation "{1-(1/2)^N}" if N becomes "infinity" then "1/2 ^ N" will be equal to "0' ! Hence.. We reached our destination! (As by fitting 1/2 ^ N=0 in Zeno's equation we get "1" . hence we covered 1km which was the distance between our destination and our initial position !
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I hope you liked this Paradox !
"UNIVERSE - THE UNSOLVED RIDDLE " [facebook.com/cosmo.addicts]
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