Is There a Limit On How Fast the Olympic 100 Meters Can Be Ran?

Yes, there is. Call the sequence of Olympic World Record times since the games' inception: {tn, n in N}, with tn being a given Olympic Game's 100 meters World Record and tn+1 being the next Olympic Game's World Record (after 4 years).

Some facts about {tn}:

  1. The sequence of times is strictly decreasing, by the very definition of what "World Record Time" means. In particular: tn+1 < tn, for all n in N.
  2. The sequence of times is obviously bounded below, since no athlete can run the 100 meters in 0 seconds. In particular: tn > 0, for all n in N.

Since {tn} is strictly decreasing and bounded below by 0, it converges to a limit. What is this limit? Nobody knows, of course, but assuming a relatively small variation on the body type, (i.e., if humans don't develop wings any time soon) it certainly looks like a positive number, very close to the current World Record.


japanese 100 meter world record
"Mr. Fujichi Yokohama, Mr. Yokoshi Nakamitsi and Mr. Takishi Takahashi are awarded the gold, silver and bronze medals for 100 meters after breaking Usain Bolt's world-record time while trying to exit their buildings during the 2011 9-magnitude Sendai earthquake. Mr. Takahashi did not make it"[1]

Notes

  1. From Cartoons.

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