Timeline for The staircase paradox, or why $\pi\ne4$
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Feb 1, 2024 at 9:29 | history | suggested | user182601 | CC BY-SA 4.0 | Spelling . |
| Feb 1, 2024 at 9:18 | review | Suggested edits | |||
| S Feb 1, 2024 at 9:29 | |||||
| Nov 1, 2021 at 10:40 | comment | added | Maximilian Janisch | To be a bit more specific: The path length as a function from, say, $C^0$ paths equipped with $C^0$-norm to $[0,\infty]$ with the usual topology is discontinuous. But if you change $C^0$ for instance to $C^1$ and equip it with the $C^1$-norm, then the path length becomes a continuous function 😄. | |
| Mar 20, 2020 at 1:36 | comment | added | Luke Collins | @DougSpoonwood You can, if you assume the same reasoning that the OP is assuming, which is basically that $\lim f(x_n) = f(\lim x_n)$ (i.e., continuity). | |
| Nov 5, 2016 at 17:18 | comment | added | Doug Spoonwood | No, you can't conclude that 0 is positive from the first sentence you put in italics. You never actually reach 0 in that sequence. The same for your second sentence. You never reach pi, you only have lower rational approximations at each step. Neither of the conclusions follow and thus those are not paradoxes. The last sentence in italics though does imply that you'll never get there. That is a paradox. | |
| Sep 20, 2016 at 5:03 | comment | added | Eric Wofsey | Not sure why this got downvoted. This answer is better than some of the answers with 50+ score. | |
| Jul 12, 2016 at 0:54 | history | answered | Steve Byrnes | CC BY-SA 3.0 |