Zeno's paradoxes don't understand.

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SUMMARY

Zeno's paradoxes, particularly the arrow paradox, illustrate the concept of infinite divisibility in space. The discussion emphasizes that while we can conceptually divide a finite distance into infinitely many points, this does not imply that the universe itself is infinite. The Planck length is identified as the smallest measurable unit, reinforcing the idea that distances can be infinitely subdivided yet remain finite. The mathematical perspective asserts that a point has no size, leading to the conclusion that a line contains an infinite number of points.

PREREQUISITES
  • Understanding of Zeno's paradoxes, particularly the arrow paradox.
  • Familiarity with the concept of infinite divisibility in mathematics.
  • Knowledge of the Planck length as a fundamental unit of measurement.
  • Basic grasp of mathematical definitions of points and lines.
NEXT STEPS
  • Research the implications of Zeno's paradoxes in modern physics.
  • Explore the concept of infinite sets in mathematics, focusing on Cantor's theory.
  • Study the significance of the Planck length in quantum mechanics.
  • Investigate how mathematical models describe physical reality, particularly in geometry.
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Philosophers, mathematicians, physicists, and anyone interested in the foundations of space and time, as well as the implications of infinity in theoretical discussions.

jposs
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I'm pretty sure this is the arrow guy who couldn't figure out how to cross the stream because of the infinite points between here and there. I don't get it. I how there are many more points between here and there that we can count, or comprehend, the points at the end of the days have to be finite somewhere at least in my mind. Sure, many things we try to count are as good as infinite but it seems to our knowledge no matter how big the universe is it isn't infinite, so how can the points on some random short line be truly countless?
 
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Do correct me if I'm wrong but isn't it so that when a short distance would be devided into two, into infinity you would have an infinite amount of points between here and there, there by impossible to cross the distance/stream.
 
The Planck length step the limit as to how far you can divide it up
 
rc1102 said:
The Planck length step the limit as to how far you can divide it up

Forgive my disgusting lack of knowledge in so many places, mostly through misjudged choices, I recognize the name only. So far for lack of a better term the rest is all Greek to me.
 
jposs said:
Sure, many things we try to count are as good as infinite but it seems to our knowledge no matter how big the universe is it isn't infinite, so how can the points on some random short line be truly countless?
I don't see why this is a good argument, or even an adequate one.

The good reason to "believe" that, in the universe, the number of points in a short line is infinite is that physical theories that do a good job of describing reality describe lines as having infinitely many points.
 
In maths, especially the Greek maths in those days, a point has no size only a position in space. So under this, it is reasonable to think that there are infinite number of points in a line.
 
Thinker8921 said:
In maths, especially the Greek maths in those days, a point has no size only a position in space. So under this, it is reasonable to think that there are infinite number of points in a line.

Thanks, makes different sense now.
 

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