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I'm not disagreeing with you. Yes, an infinite series can have a finite sum, no argument there but what I am arguing with is that people are saying the ball sto
by greenlblue 16y ago
I'm not disagreeing with you. Yes, an infinite series can have a finite sum, no argument there but what I am arguing with is that people are saying the ball stops bouncing after time t = whatever. Everyone is confounding two things here, air time and bouncing. Yes, the air time is finite but the bouncing isn't. So you can't say it stops bouncing after time t = whatever if you calculate t = whatever by assuming infinitely many bounces which is what everyone is doing because they are summing a geometric series where the terms of the series represent the air time of each bounce.
- cperciva 16y agoThere is a time t such that after time t the height of the ball's bounces is zero. Personally, I call that "not bouncing".
- greenlblue 16y agoOk, now we are in agreement because my definition of "stops bouncing" was finitely many bounces.
- paulofisch 16y agoBzzt Still wrong. If you have infinite bounces, and I ask you "Which number bounce in the series happens at exactly time X?", there is a time for X for which you will not be able to give an answer. This is because there is a limit for the latest time at which bounces happen. Yes, even with infinite bounces.
- greenlblue 16y agoWhatever. I got it sorted out so go bother someone else.