Timeline for What is an instant of time?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 4, 2016 at 15:08 | comment | added | james | @Schwern thank you very much for your answer and your useful links! | |
| Nov 2, 2016 at 19:23 | comment | added | Schwern | @Hurkyl It's not intended to. It's intended to give an intuitive understanding, with a mathematical basis, of how "a sum of instants add up to something that has a duration" that the OP requested. I don't even know what nonstandard analysis is. | |
| Nov 2, 2016 at 18:29 | comment | added | user5174 | @knzhou: This answer isn't describing nonstandard analysis either. (or if it is, its demonstrating a severe misunderstanding) | |
| Nov 1, 2016 at 23:00 | comment | added | Schwern | @MartinArgerami I agree, but I'm not sure why this is relevant. The answer isn't intended as a rigorous proof and discussion of infinitesimals. The OP wanted an illustrative example of how you can sum up infinitely many "instants" and get something finite. I chose infinitesimals as a way to define an "instant of time" that's a pretty good combination of basic math and intuitive understanding. Are your comments the "mathematicians might look at you a bit funny if you talk about 'an infinitely small number'" that knzhou warned about? :) | |
| Nov 1, 2016 at 22:34 | comment | added | Martin Argerami | @Schwern: precisely. The same way you don't have a largest integer, there is no smallest positive real number. You can create the infinitesimals, which are not numbers; they have to be created carefully, and it is usually not immediately obvious which reasonings you can translate from $\mathbb R$ to your extension of $\mathbb R$. In the particular case of continuously dividing by 2, what kind of infinitesimal do you get? And why? | |
| Nov 1, 2016 at 21:24 | comment | added | Schwern | @MartinArgerami To actually slice something infinitesimally you'd need infinite time but you'd run up against the Planck Length first. The wonderful thing about math is you don't have to explain how to do it in the real world, you do it conceptually. Just as infinity is a consequence of the integers, infinitesimals are a consequence of the real numbers. As for any "largest" integer $n$ you can get a larger one with $n+1$, for any "smallest" real number $n$ you can always get a smaller one with $n/2$. But I think you know all that so I'm puzzled. | |
| Nov 1, 2016 at 11:21 | comment | added | Martin Argerami | -1 for "You can go on doing this infinitely many times and you'll get an infinitely small number: an infinitesimal". For that to make sense you would have to explain how to do it "infinitely many times". | |
| Nov 1, 2016 at 3:34 | history | edited | user36790 | CC BY-SA 3.0 |
added 6 characters in body
|
| Nov 1, 2016 at 2:23 | comment | added | knzhou | Word of warning for the OP: this answer is describing non-standard analysis. It's a perfectly good way to think about calculus, but it's, well, non-standard; mathematicians might look at you a bit funny if you talk about "an infinitely small number". | |
| Nov 1, 2016 at 0:52 | history | edited | Schwern | CC BY-SA 3.0 |
added 109 characters in body
|
| Nov 1, 2016 at 0:46 | history | answered | Schwern | CC BY-SA 3.0 |