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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...
Fiercely-loyal gas station regret
  08/10/15
9245872459877474502487245987457264574572487265
Thriller Blood Rage Theater
  08/10/15
LOL, unmitigated 928374897239847982374923
Bateful kitchen
  08/10/15
...
Histrionic Thirsty Nursing Home
  08/10/15
hard 2 understand this presentation with the rubber band and...
soggy pink boltzmann becky
  08/10/15
...
soggy pink boltzmann becky
  08/10/15
...
Fiercely-loyal gas station regret
  08/10/15
hmmm...
Talking shivering ratface corner
  11/18/18
...
crystalline frum idea he suggested
  11/18/18
...
Fiercely-loyal gas station regret
  07/09/25
fantastic bump
indigo arousing stead
  07/09/25


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Date: August 10th, 2015 3:17 AM
Author: Fiercely-loyal gas station regret

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=2#28519125)



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Date: August 10th, 2015 3:44 AM
Author: Thriller Blood Rage Theater

9245872459877474502487245987457264574572487265

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



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Date: August 10th, 2015 6:59 AM
Author: Bateful kitchen

LOL, unmitigated 928374897239847982374923

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



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Date: August 10th, 2015 8:44 AM
Author: Histrionic Thirsty Nursing Home



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



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Date: August 10th, 2015 9:04 AM
Author: soggy pink boltzmann becky

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=2#28519590)



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Date: August 10th, 2015 1:53 PM
Author: soggy pink boltzmann becky



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



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Date: August 10th, 2015 5:07 PM
Author: Fiercely-loyal gas station regret



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



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Date: November 18th, 2018 10:20 PM
Author: Talking shivering ratface corner

hmmm...

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



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Date: November 18th, 2018 10:21 PM
Author: crystalline frum idea he suggested



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



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Date: July 9th, 2025 4:22 PM
Author: Fiercely-loyal gas station regret



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



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Date: July 9th, 2025 4:23 PM
Author: indigo arousing stead

fantastic bump

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