Changes

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.

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} + \frac{1}{8} + ...</math> 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 <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}{2^i}</math>,  

:<math>\sum_{i=1}^\infty \frac{1}{2^i}</math>,  

(see [[Series (mathematics)]]) which has the value

which numerically attains the value:

:<math>1</math>

:<math>1</math>

[[Category:Philosophy]]

[[Category:Philosophy]]

[[Category:Mathematics]]

[[Category:Mathematics]]