Difference between revisions of "Zeno's paradox"
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m (still needs a bit of work, but the math should be correct now) |
(No, it's definitely 2^i, and two terms isn't enough to extrapolate the rest of the series.) |
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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 {{1/2}} + {{1/4}} + ... has a value (notice each successive term is half of its predecessor). [[Mathematician|Mathematicians]] can express this value as: | + | Mathematically, Zeno's paradox asks if {{1/2}} + {{1/4}} + {{1/8}} + ... has a value (notice each successive term is half of its predecessor). [[Mathematician|Mathematicians]] can express this value as: |
| − | :<math>\sum_{i=1}^\infty \frac{1}{ | + | :<math>\sum_{i=1}^\infty \frac{1}{2^i}</math>, |
or more commonly, | or more commonly, | ||
Revision as of 04:32, January 12, 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 ½ + ¼ + Template:1/8 + ... has a value (notice each successive term is half of its predecessor). Mathematicians can express this value as:
- ,
or more commonly,
