Timeline for Integration in the surreal numbers
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Jul 28 at 21:09 | comment | added | Anixx | @StevenStadnicki look here, it addresses the issue: mathoverflow.net/questions/475902/… I thought I gave you this link already... | |
| Jul 28 at 21:07 | comment | added | Steven Stadnicki | I wasn't one of the downvotes, but I feel like the point in my initial comment still holds strongly. | |
| Jul 28 at 11:05 | comment | added | Anixx | Why are the downvotes? | |
| Jul 28 at 0:32 | comment | added | Anixx | @StevenStadnicki as you can see, if only at one point the function takes value $2\omega/\pi$, the whole integral is $2$. But on the interval $[0,1)$ there are $\omega_1$ such points. So, the whole integral should be $2\omega_1$. | |
| Jul 26 at 21:18 | comment | added | Anixx | @StevenStadnicki also here: philosophy.stackexchange.com/a/112762/796 | |
| Jul 26 at 21:10 | comment | added | Anixx | @StevenStadnicki see more here: math.stackexchange.com/questions/4627326/… Also, notice, these infinite values have non-zero derivations while finite constants have derivations $0$ | |
| Jul 26 at 21:07 | comment | added | Anixx | @StevenStadnicki they are "constants" but they are infinite constants. For instance, $2\omega/\pi$ is the derivative of the function $\text{sgn}(x)$ at 0, at this point the function makes a jump of 2, so $\int_{-1}^1\left( {\begin{cases}2\omega/\pi,&{\text{if }}x=0\\ 0,&{\text{if }}x\ne 0\end{cases}}\right)\,dx=2$ | |
| Jul 26 at 21:01 | comment | added | Steven Stadnicki | Maybe I'm confused, but aren't all of the values inside your example integrals 'constants'? I would expect, for instance, that $\int_0^1\omega\ dt=\omega$ for any 'reasonable' definition of integration... | |
| Jul 26 at 20:53 | history | edited | Anixx | CC BY-SA 4.0 |
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| Jul 26 at 19:30 | history | edited | Anixx | CC BY-SA 4.0 |
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| Jul 26 at 19:09 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
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| Jul 26 at 17:17 | review | Low quality posts | |||
| Jul 26 at 19:09 | |||||
| Jul 26 at 16:58 | history | answered | Anixx | CC BY-SA 4.0 |