Zeno's Paradox
Introduction and Rationale:
The Zeno Paradoxes are a set of Paradoxes that are set up by the Greek Mathematician Zeno of Elea. Zeno is a mathematician who was believed to have been born even before Socrates (who was born on 469 BC). His Birthplace is in Italy.
The word 'Paradox' is a statement that apparently opposes itself (in terms of meaning), but may be still true(by thinking in terms of Mathematics and it's methods). Thus it might be invalid most of times but however it helps in developing one's way of perceiving things and thus improves our critical thinking. Zeno of Elea offered arguments that led to conclusions contradicting what we all know from our physical experience.
For any distance the arguments were paradoxes for the ancient Greek philosophers. …show more content…
Then he would again be travelling now by half of that distance that he travelled. This process is thus infinite and it would take infinite time for the hero to reach the tortoise. Thus this means that this would be a infinite and converging geometric series. This is called the Dichotomy Paradox. This variation is used to prove that the summation of infinite of the distance at each instant (each second) will be equal to the initial distance between Achilles. The other variation is slightly different the tortoise is also moving.
General Case:
Dichotomy Paradox Problem1:
The Achilles will now be travelling half of the distance that he initially travelled. Then he would again be travelling now by half of that distance that he travelled. This process is thus infinite and it would take infinite time for the hero to reach the tortoise.
Let us say that the tortoise is 2m away from the Achilles. Let us say that he is running the same way that I had explained above in the General Method Category.
S= 1+1/2 +1/4 +1/8 +1/16.............
Sn= a/((1-r) ) (where a=1 and r=(1/2)/1)=1/2=0.5
Sn=1/((1-0.5))
Sn= 1/((0.5)
Introduction and Rationale:
The Zeno Paradoxes are a set of Paradoxes that are set up by the Greek Mathematician Zeno of Elea. Zeno is a mathematician who was believed to have been born even before Socrates (who was born on 469 BC). His Birthplace is in Italy.
The word 'Paradox' is a statement that apparently opposes itself (in terms of meaning), but may be still true(by thinking in terms of Mathematics and it's methods). Thus it might be invalid most of times but however it helps in developing one's way of perceiving things and thus improves our critical thinking. Zeno of Elea offered arguments that led to conclusions contradicting what we all know from our physical experience.
For any distance the arguments were paradoxes for the ancient Greek philosophers. …show more content…
Then he would again be travelling now by half of that distance that he travelled. This process is thus infinite and it would take infinite time for the hero to reach the tortoise. Thus this means that this would be a infinite and converging geometric series. This is called the Dichotomy Paradox. This variation is used to prove that the summation of infinite of the distance at each instant (each second) will be equal to the initial distance between Achilles. The other variation is slightly different the tortoise is also moving.
General Case:
Dichotomy Paradox Problem1:
The Achilles will now be travelling half of the distance that he initially travelled. Then he would again be travelling now by half of that distance that he travelled. This process is thus infinite and it would take infinite time for the hero to reach the tortoise.
Let us say that the tortoise is 2m away from the Achilles. Let us say that he is running the same way that I had explained above in the General Method Category.
S= 1+1/2 +1/4 +1/8 +1/16.............
Sn= a/((1-r) ) (where a=1 and r=(1/2)/1)=1/2=0.5
Sn=1/((1-0.5))
Sn= 1/((0.5)