Difference between revisions of "Zeno's paradox"
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| − | Zeno's paradox, formulated by the [[Polytheism|polytheist]] [[Zeno|Zeno the Greek]], is a [[Philosophy|philosophical]] [[ | + | '''Zeno's paradox''', formulated by the [[Polytheism|polytheist]] [[Zeno|Zeno the Greek]], is a [[Philosophy|philosophical]] [[paradox]] about the number {{1/2}}. 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 <math>\frac{1}{2} + \frac{1}{4} + ...</math> has a value (notice each successive term is half of its predecessor). [[ | + | Mathematically, Zeno's paradox asks if <math> \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ...</math> has a value (notice each successive term is half of its predecessor). Using an [[infinite series]], [[mathematician]]s can express this value symbolically as: |
| − | <math>\sum_{i=1}^\infty \frac{1}{ | + | :<math>\sum_{i=1}^\infty \frac{1}{2^i}</math>, |
| − | + | which numerically attains the value: | |
| − | + | :<math>1</math> | |
| − | <math>1 | ||
[[Category:Philosophy]] | [[Category:Philosophy]] | ||
[[Category:Mathematics]] | [[Category:Mathematics]] | ||
Latest revision as of 23:31, August 11, 2008
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 <math> \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ...</math> has a value (notice each successive term is half of its predecessor). Using an infinite series, mathematicians can express this value symbolically as:
- <math>\sum_{i=1}^\infty \frac{1}{2^i}</math>,
which numerically attains the value:
- <math>1</math>