Timeline for What happens when a car starts moving? The last moment the car is at rest versus the first moment the car moves
Current License: CC BY-SA 4.0
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| Oct 15 at 17:43 | history | edited | Nuclear Hoagie | CC BY-SA 4.0 |
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| Oct 15 at 17:37 | history | edited | Nuclear Hoagie | CC BY-SA 4.0 |
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| Oct 15 at 17:29 | comment | added | Nuclear Hoagie | @Peter-ReinstateMonica Two values separated by an infinitesimally small difference are exactly equal to each other (matheducators.stackexchange.com/questions/26934/…) For any non-zero duration time period we could suppose between "stops resting" and starts moving", we can observe there is no transition period that takes that long - the time difference between "stops resting" and "starts moving" is infinitesimal, therefore, the times at which the car "stops resting" and "starts moving" are indeed the same. | |
| Oct 15 at 15:58 | comment | added | Peter - Reinstate Monica | Yes, I was imprecise. The limit is indeed zero, that is what it means; my fault. x is never zero though, which in this case means the points in time never coincide (even if we assume non-granular time which is probably wrong). | |
| Oct 15 at 15:52 | comment | added | Nuclear Hoagie | @Peter-ReinstateMonica The limit does exist, and the limit (not x) is indeed equal to exactly zero. A limit doesn't tend toward a value, a limit is a value. The limit of x as x approaches zero is exactly zero, not some number arbitrarily close to zero, or something that "tends toward zero". It's just zero. There is nothing "between" the left-handed limit as x approaches 0 and the right-handed limit as x approaches 0, since both of those are equal to exactly 0. | |
| Oct 15 at 13:53 | comment | added | Peter - Reinstate Monica | And yet, the car being at standstill and the car being in motion seem like two fundamentally different things. Also, and relatedly, I contest your notion that $\lim_{x\to 0} x$ is zero. What we have here is a procedure which allows us to get as close as we desire. $\lim_{x\to 0} x = 0$ is a simplified notation for that. | |
| Oct 14 at 19:49 | history | edited | Nuclear Hoagie | CC BY-SA 4.0 |
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| Oct 14 at 19:43 | history | answered | Nuclear Hoagie | CC BY-SA 4.0 |