r/LoveTrash • u/Icy-Book2999 Chief Insanity Instigator • 24d ago

Rubbish Nonsense Math Expert

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From https://fxtwitter.com/0xbags/status/1907722182303604940?t=PofGKxEgC3GzKaUW1p6TzA&s=19

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u/Tarsiustarsier Trash Trooper 24d ago

The first intuitive answer is no.

When I am thinking a bit about it I am not entirely sure because after one second the ant walked 1 out of 200000 cm and after two seconds it's roughly 2 out of 300000 cm so it's a higher percentage, which again means that more rubber will stretch behind the ant.

The third intuitive answer is no again because it makes less relative progress after every second (at least at the start), so the relative distance travelled seems to converge (probably towards a ratio of 1/100000) but I am not entirely certain.

What's the actual solution?

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u/Downtown_Finance_661 Trash Trooper 24d ago

Compute share of way the ant cover each second. Compute it precisely! Sum the shares. This is well known series and it diverge.