Timeline for Infinite plate of charge - questions about infinity
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jun 14, 2023 at 5:16 | comment | added | naturallyInconsistent | @Chemistry you are looking at "doesn't mean it's 100% correct." In the totally wrong way. The physicist is still using the Leibniz-Newton conception of small quantities, but all of these calculus results should be viewed in terms of Cauchy's epsilon-delta manner: If you give me any error tolerance epsilon, then I can tell you what delta neighbourhood you can pick the initial imprecision to be, and we will still be able to guarantee correctness to the tolerance level. And then you can let the error tolerance go to zero, hence 100% correct. | |
| Jun 13, 2023 at 17:54 | comment | added | Vincent Fraticelli | I'm not sure I fully understand your second question (English is not my native language). But actually, I have the impression that it's the same problem as for the first one.There would still be a lot to say about the infinite uniformly charged plane, but that would be getting off topic. | |
| Jun 13, 2023 at 17:16 | vote | accept | Giorgi | ||
| Jun 13, 2023 at 17:16 | comment | added | Giorgi | Would the same imply for my 2nd question ? As in we would have no error even if f(x) is not an function ? As in ring area is 2px times dx. Integrating this rings would still give us 0 error ? Thus is important because if there is an error that means there is a place on the plane for which we didnt calculate area(small but still) and what if this small area contains a charge ? Then our overal calculation would skip this detail. This is my last question⦠| |
| Jun 13, 2023 at 17:09 | comment | added | Vincent Fraticelli | I have added an edit to precise my answer. For the second point, since $t_0$ is a constant which do not change the order, I have not written it. | |
| Jun 13, 2023 at 17:07 | history | edited | Vincent Fraticelli | CC BY-SA 4.0 |
added 1145 characters in body
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| Jun 13, 2023 at 16:29 | comment | added | Giorgi | By the way, (π‘0/ππ‘)π(ππ‘2)=π(ππ‘) is this correct ? shouldn't it be t0O(dt) ? but I guess, since t0 is some integer (not even close to infinity), it can be negligible | |
| Jun 13, 2023 at 16:21 | comment | added | Giorgi | This is such an amazing answer. I'd love to ask you few questions if you don't mind. 1) from what reference do you say that error is in the second order ? 2) one interesting confusion that I always have is just because dx tends to 0, doesn't mean it's 0, it's still very close to 0, but not exactly 0. Hence error won't be 0, but close to 0. If so, error still should be there. so it shoudn't give us exactly 100% correct area, but 99.999999%, which doesn't mean it's 100% correct. | |
| Jun 13, 2023 at 16:09 | history | answered | Vincent Fraticelli | CC BY-SA 4.0 |