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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...
Buck-toothed slimy toaster codepig
  08/10/15
9245872459877474502487245987457264574572487265
titillating transparent son of senegal
  08/10/15
LOL, unmitigated 928374897239847982374923
multi-colored hall dysfunction
  08/10/15
...
Kink-friendly site
  08/10/15
hard 2 understand this presentation with the rubber band and...
laughsome roast beef dog poop
  08/10/15
...
laughsome roast beef dog poop
  08/10/15
...
Buck-toothed slimy toaster codepig
  08/10/15
hmmm...
unholy national dopamine
  11/18/18
...
excitant public bath
  11/18/18
...
Buck-toothed slimy toaster codepig
  07/09/25
fantastic bump
Maize business firm
  07/09/25


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Date: August 10th, 2015 3:17 AM
Author: Buck-toothed slimy toaster codepig

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...id#28519125)



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Date: August 10th, 2015 3:44 AM
Author: titillating transparent son of senegal

9245872459877474502487245987457264574572487265

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



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Date: August 10th, 2015 6:59 AM
Author: multi-colored hall dysfunction

LOL, unmitigated 928374897239847982374923

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



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Date: August 10th, 2015 8:44 AM
Author: Kink-friendly site



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



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Date: August 10th, 2015 9:04 AM
Author: laughsome roast beef dog poop

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...id#28519590)



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Date: August 10th, 2015 1:53 PM
Author: laughsome roast beef dog poop



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



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Date: August 10th, 2015 5:07 PM
Author: Buck-toothed slimy toaster codepig



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



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Date: November 18th, 2018 10:20 PM
Author: unholy national dopamine

hmmm...

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



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Date: November 18th, 2018 10:21 PM
Author: excitant public bath



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



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Date: July 9th, 2025 4:22 PM
Author: Buck-toothed slimy toaster codepig



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



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Date: July 9th, 2025 4:23 PM
Author: Maize business firm

fantastic bump

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