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Sim glitch re: Halford numbers - the paradox of the WORM and the RUBBER BAND

Suppose that a useless PISSworm crawls along a 1-metre rubbe...
fragrant red garrison
  08/10/15
9245872459877474502487245987457264574572487265
Fantasy-prone bull headed area
  08/10/15
LOL, unmitigated 928374897239847982374923
azure indian lodge roommate
  08/10/15
...
jet native useless brakes
  08/10/15
hard 2 understand this presentation with the rubber band and...
Greedy Motley House
  08/10/15
...
Greedy Motley House
  08/10/15
...
fragrant red garrison
  08/10/15
hmmm...
Violet Halford Corn Cake
  11/18/18
...
Supple dilemma new version
  11/18/18
...
fragrant red garrison
  07/09/25
fantastic bump
aqua deep market incel
  07/09/25


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Date: August 10th, 2015 3:17 AM
Author: fragrant red garrison

Suppose that a useless PISSworm crawls along a 1-metre rubber band at the same time as the rubber band is uniformly stretched. If the worm travels 1 centimetre per minute and the band stretches 1 metre per minute, will the worm ever reach the end of the rubber band?

The answer, counterintuitively, is "yes", for after n minutes, the ratio of the distance travelled by the worm to the total length of the rubber band is

\frac{1}{100}\sum_{k=1}^n\frac{1}{k}

(In fact the actual ratio is a little less than this sum as the band expands continuously). The reason is that the band expands behind the worm also; eventually, the worm gets past the midway mark and the band behind expands increasingly more rapidly than the band in front.

Because the series gets arbitrarily large as n becomes larger, eventually this ratio must exceed 1, which implies that the worm reaches the end of the rubber band. However, the value of n at which this occurs must be extremely large: approximately e100, a number exceeding 10^44.

The exact value of n is 15092688622113788323693563264538101449859497.

Although the harmonic series does diverge, it does so very slowly.

(http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2Reputation#28519125)



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Date: August 10th, 2015 3:44 AM
Author: Fantasy-prone bull headed area

9245872459877474502487245987457264574572487265

(http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2Reputation#28519247)



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Date: August 10th, 2015 6:59 AM
Author: azure indian lodge roommate

LOL, unmitigated 928374897239847982374923

(http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2Reputation#28519429)



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Date: August 10th, 2015 8:44 AM
Author: jet native useless brakes



(http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2Reputation#28519549)



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Date: August 10th, 2015 9:04 AM
Author: Greedy Motley House

hard 2 understand this presentation with the rubber band and the latex. nobody reads latex faggot and after googling this i see that its not a circular BAND but a ROPE with fixed ends. i found this http://www.theproblemsite.com/problems/high-school-math/2002/long-walk

but i still dont get it. why isnt it the case that the distance between the worm and the end of the rope is getting longer and longer over time, so the worm can never reach the end?

(http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2Reputation#28519590)



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Date: August 10th, 2015 1:53 PM
Author: Greedy Motley House



(http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2Reputation#28520692)



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Date: August 10th, 2015 5:07 PM
Author: fragrant red garrison



(http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2Reputation#28522133)



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Date: November 18th, 2018 10:20 PM
Author: Violet Halford Corn Cake

hmmm...

(http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2Reputation#37260869)



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Date: November 18th, 2018 10:21 PM
Author: Supple dilemma new version



(http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2Reputation#37260881)



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Date: July 9th, 2025 4:22 PM
Author: fragrant red garrison



(http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2Reputation#49087353)



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Date: July 9th, 2025 4:23 PM
Author: aqua deep market incel

fantastic bump

(http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2Reputation#49087355)