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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...
Cerebral drab theater
  08/10/15
9245872459877474502487245987457264574572487265
charismatic soggy private investor meetinghouse
  08/10/15
LOL, unmitigated 928374897239847982374923
misanthropic boltzmann
  08/10/15
...
Haunting Exhilarant Pisswyrm Den
  08/10/15
hard 2 understand this presentation with the rubber band and...
gaped business firm
  08/10/15
...
gaped business firm
  08/10/15
...
Cerebral drab theater
  08/10/15
hmmm...
Cruel-hearted electric turdskin
  11/18/18
...
Laughsome queen of the night
  11/18/18
...
Cerebral drab theater
  07/09/25
fantastic bump
purple abode tattoo
  07/09/25


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Date: August 10th, 2015 3:17 AM
Author: Cerebral drab theater

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: charismatic soggy private investor meetinghouse

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: misanthropic boltzmann

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: Haunting Exhilarant Pisswyrm Den



(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: gaped business firm

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: gaped business firm



(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: Cerebral drab theater



(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: Cruel-hearted electric turdskin

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: Laughsome queen of the night



(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: Cerebral drab theater



(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: purple abode tattoo

fantastic bump

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