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Curtis

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- Thread starter curt291
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Curtis

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Though that wouldn't make a lot of sense, because any length per infinite amount of time will be the same.

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Zero.

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Zero.

HAHA, you beat me to it! Yes, zero is the slowest possible. I think what the person wanted to ask is what curt291 wanted to ask is what the next slowest possible velocity. I would assume it would be L

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zero v is not/ no velocity, and what about L... zero is the slowest possible. ...it would be L_{planck}per sec.

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That was a puzzle (not a true paradox) 2500 years ago. Zeno didn't have the mathematical tools to resolve his paradoxes of motion. Nowaday saying that Zeno's paradoxes are anything but a simple lack of descriptive tools it is pretty much nonsense.

Yeah, it's called zero.

Though that wouldn't make a lot of sense, because any length per infinite amount of time will be the same.

There's nothing special about a velocity of exactly zero (with respect to

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A less snarky answer is that Zeno did not have the necessary mathematical tools to explain his puzzles. That Zeno could not explain how a faster runner could overtake a slower one was understandable 2500 years ago. The concept of an infinite series was a ways off into his future. Now we know that 1/2+1/4+1/8+1/16+... is a uniformly convergent series. The arrow paradox is fully explained by the concept of a derivative. One again, Zeno did not have those tools on hand. That would have to wait for Newton, Leibniz, Weierstrass, and others.

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Well to clarify, when an object is slowing down, theoretically it must hit every velocity between its initial velocity and zero, so it could never stop, it would just slow down forever. There is an infinite number of velocities between an arbitrary velocity and zero. So what is the slowest velocity before it is defined as having zero velocity? Or could it be that it never has zero velocity but it is just moving so slow that we can't detect any movement?

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That is Zeno's arrow paradox, and it is nonsense.Well to clarify, when an object is slowing down, theoretically it must hit every velocity between its initial velocity and zero, so it could never stop, it would just slow down forever. There is an infinite number of velocities between an arbitrary velocity and zero. So what is the slowest velocity before it is defined as having zero velocity? Or could it be that it never has zero velocity but it is just moving so slow that we can't detect any movement?

There's nothing special about zero here. Any two distinct speeds will do. Suppose you're moving along at 1 m/s and want to speed up to 2 m/s. But in between those two speeds are an infinite number of other speeds, so therefore it takes an infinite amount of time to accomplish this goal. Motion itself is impossible by the same twisted notion. There are an infinite number of points between any two points on a trajectory. Therefore it takes an infinite amount of time to go from point A to point B. Diogenes was right. His response of standing up and walking out showed that motion is possible.

The resolution is with calculus. As you split the distance (or velocity) into finer and finer increments, it takes less and less time to move from one point to another / accelerate from one velocity to another. In the limit of infinitesimally small increments, you have the Lebesgue integral.

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Zeno's paradox is nonsense.

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Zeno's paradox is nonsense.

Could you

The first thing a junior learns, when he starts algebra, is to prove that 2=1. Is that a paradox, is it different from Zeno['s], is it generic "nonsense" too, [

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russ_watters

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We've advanced enough in 2500 years to call what might have been (moderately?) puzzling at the time a silly misunderstanding of a simple mathematical principle today."nonsense" is so generic that carries very little sense, meaning itself; same as "humbug" [Scrooge says] or"fiddlesticks" [Diogenes sayswith body language].That is onlyemotional reaction of disbelief or disdain. You dismiss with one generic word what a most reputable logician and mathematician defined "immeasurably subtle and profound"

As said, the "paradox" assumes constant steps of time. But each time you cut the distance in half, the time it takes to make the step gets cut in half as well. A simple examination of the equation for distance at constant speed will show this - I wouldn't even bother using calculus for it.Could yourationally, analytically defineyour disbelief, or disdain? what is really a paradox?

This is my favorite demonstration of it's wrongness, though:

Obviously, even when Zeno proposed the "paradox", he had to know it was false as arrows were already hitting trees and people were already arriving at destinations they were walking to.DH said:The simplest explanation of all was given by Diogenes, a contemporary of Zeno. He got up and walked out of the room.

I'd call it a prank, yes - or today, perhaps "troll math". 2 does not equal 1. Any "proof" that it does must have a flaw.logics said:The first thing a junior learns, when he starts algebra, is to prove that 2=1. Is that a paradox, is it different from Zeno['s], is it generic "nonsense" too, [what do you call it], a schoolboy prank, a joke, or you envisage something else?

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Duplex

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How about 1 Planck length per 13.7 billion years?

Currently 3.7 10^{-53} m/s.

Currently 3.7 10

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