Zeno claimed to be a great philosopher and mathemagician, but everyone knows that's not true. He was formally known as Zeno of Elea, but he was the only Zeno living from 490 to 430 B.C., so everyone just called him Zeno. Except his niece, Helen of Troy. She just called him "Elle".
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| - Zeno's Paradox
- Zeno's paradox
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| - Zeno claimed to be a great philosopher and mathemagician, but everyone knows that's not true. He was formally known as Zeno of Elea, but he was the only Zeno living from 490 to 430 B.C., so everyone just called him Zeno. Except his niece, Helen of Troy. She just called him "Elle".
- Ancient mathematicians did not have a theory of limits. A Greek philosopher named Zeno of Elea (5th century B.C) devised the following paradox. Achilles and the tortoise had a race. Achilles could run 10 times as fast as the tortoise, but the tortoise had a hundred yard start. Achilles runs the hundred yards, but the tortoise is now 10 yards ahead. Achilles runs the 10 yards, but the tortoise is now 1 yard ahead. Achilles runs the 1 yard, but the tortoise is now 1/10 yard ahead, and so on. How can Achilles overtake the tortoise? At this point, Achilles overtakes the tortoise.
- Zeno's paradox, formulated by the polytheist Zeno the Greek, is a philosophical paradox about the number ½ . It states that a person can never traverse from one point to another point because he would first go half the distance, then half of what remains, then half of what remains next, and then half of that half. This process keeps continuing indefinitely by halving subsequent distances repeatedly. This argument seems to suggest no one can make this trip in finite time, but this is obviously not true. , which numerically attains the value:
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| abstract
| - Ancient mathematicians did not have a theory of limits. A Greek philosopher named Zeno of Elea (5th century B.C) devised the following paradox. Achilles and the tortoise had a race. Achilles could run 10 times as fast as the tortoise, but the tortoise had a hundred yard start. Achilles runs the hundred yards, but the tortoise is now 10 yards ahead. Achilles runs the 10 yards, but the tortoise is now 1 yard ahead. Achilles runs the 1 yard, but the tortoise is now 1/10 yard ahead, and so on. How can Achilles overtake the tortoise? Because the ancient Greeks did understand limits, in their logic the problem could not be solved. However, we know that the sum of the series At this point, Achilles overtakes the tortoise.
- Zeno's paradox, formulated by the polytheist Zeno the Greek, is a philosophical paradox about the number ½ . It states that a person can never traverse from one point to another point because he would first go half the distance, then half of what remains, then half of what remains next, and then half of that half. This process keeps continuing indefinitely by halving subsequent distances repeatedly. This argument seems to suggest no one can make this trip in finite time, but this is obviously not true. Mathematically, Zeno's paradox asks if has a value (notice each successive term is half of its predecessor). Using an infinite series, mathematicians can express this value symbolically as: , which numerically attains the value:
- Zeno claimed to be a great philosopher and mathemagician, but everyone knows that's not true. He was formally known as Zeno of Elea, but he was the only Zeno living from 490 to 430 B.C., so everyone just called him Zeno. Except his niece, Helen of Troy. She just called him "Elle".
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