Timeline for Is there any work related to Hypertype Theory? [closed]
Current License: CC BY-SA 4.0
46 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 24, 2019 at 21:29 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
deleted 22 characters in body
|
| Jan 14, 2019 at 20:11 | vote | accept | Ismael Ghalimi | ||
| Jan 7, 2019 at 18:20 | review | Reopen votes | |||
| Jan 8, 2019 at 4:47 | |||||
| Jan 7, 2019 at 18:04 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 221 characters in body
|
| Jan 7, 2019 at 15:59 | history | edited | Andrés E. Caicedo |
edited tags
|
|
| Jan 7, 2019 at 15:49 | history | closed |
abx YCor Chris Godsil Andy Putman Harry Gindi |
Needs details or clarity | |
| Jan 7, 2019 at 15:48 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
deleted 83 characters in body
|
| Jan 7, 2019 at 15:33 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 19 characters in body
|
| Jan 7, 2019 at 15:25 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 19 characters in body
|
| Jan 7, 2019 at 15:16 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 204 characters in body
|
| Jan 6, 2019 at 20:20 | answer | added | Ismael Ghalimi | timeline score: 4 | |
| Jan 6, 2019 at 18:48 | comment | added | Ismael Ghalimi | @AlexKruckman Regarding the notion of convergence, this is a much more open question at this point. I have yet to settle on a satisfactory definition for it. I am currently studying the theory of hyperoperations and hope to come back with something soon. | |
| Jan 6, 2019 at 18:39 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 69 characters in body
|
| Jan 6, 2019 at 18:33 | comment | added | Ismael Ghalimi | @AlexKruckman Great question! They will be introduced in the traditional way as solutions to equations like $f(a+b)=f(a) × f(b)$ and $g(a×b)=g(a)+g(b)$ with $e=f(1)$. Doing that properly will certainly stretch my algebraic skills, but it should be a fruitful exercise. | |
| Jan 6, 2019 at 18:27 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 113 characters in body
|
| Jan 6, 2019 at 18:27 | comment | added | Alex Kruckman | Regarding defining $\mathbb{H}_n$ without any reference to $\mathbb{R}$: How do you define the functions $e^x$ and $\ln(x)$ (in order to define $\otimes^n$ and $\ominus^n$) without reference to $\mathbb{R}$? | |
| Jan 6, 2019 at 18:24 | comment | added | Ismael Ghalimi | @AlexKruckman No, I won’t tell you that infinite sets don’t make sense, but I will tell you that I prefer using types rather than sets whenever possible. I hope this is acceptable. Also, I understand that Prof Wildberger is a controversial figure, but I like to give credit when credit is due. That being said, please be assured that I am keeping a wide open mind. My goal is to build things as simply and as precisely as possible. And let me assure you that I have the utmost level of respect for the attention and patience you are blessing me with. I will not waste your time. | |
| Jan 6, 2019 at 18:19 | comment | added | Ismael Ghalimi | @AlexKruckman Sorry for all the shortcuts I took. $\mathbb{H}_1$ Is defined in a coinductive manner, as described in this article (now linked from the original question). As far as defining $\mathbb{H}_n$ Is concerned, I believe that using a closure is the way to go, but I would like to express it without any reference to $\mathbb{R}$ if at all possible. | |
| Jan 6, 2019 at 18:16 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 149 characters in body
|
| Jan 6, 2019 at 18:15 | comment | added | Alex Kruckman | Oops, in my comment above, I meant to write "[set] $\mathbb{H}_{n+1}$ equal to the closure of $\mathbb{H}_n\cup \{i_{n+1}\}$ (inside $\mathbb{R}$) under the operations $\oplus^k$ and $\ominus^k$ for $k\leq (n+1)$." | |
| Jan 6, 2019 at 18:14 | comment | added | Alex Kruckman | Based on the reference to Wildberger at the end of your question, I'm worried there's a real danger you're going to come back and tell me that this argument is invalid because infinite sets "don't make sense". (Just a tip: linking to Wildberger is not the best idea if you want to be taken seriously by mathematicians.) | |
| Jan 6, 2019 at 18:09 | comment | added | Alex Kruckman | Regarding Questions 2 and 3: It's also not totally clear what you mean by "$\mathbb{H}_n$ converges to $\mathbb{R}$". The most natural meaning is $\bigcup_{n} \mathbb{H}_n = \mathbb{R}$. If this interpretation (and the definition of $\mathbb{H}_n$ in my previous comment) is correct, then the answer is no: each $\mathbb{H}_n$ is countably infinite, so $\bigcup_{n} \mathbb{H}_n$ is countably infinite, while $\mathbb{R}$ is uncountable. | |
| Jan 6, 2019 at 18:06 | comment | added | Alex Kruckman | The precise definition of $\mathbb{H}_n$ is not clear to me. Is it an inductive definition, where you set $\mathbb{H}_1 = \mathbb{Z}$, and then $\mathbb{H}_{n+1}$ equal to the closure of $\mathbb{H}_n\cup \{i_n\}$ (inside $\mathbb{R}$) under the operations $\oplus^{n+1}$ and $\ominus^{n+1}$? | |
| Jan 6, 2019 at 17:59 | history | edited | YCor |
edited tags
|
|
| Jan 6, 2019 at 16:32 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
deleted 1801 characters in body
|
| Jan 6, 2019 at 16:01 | comment | added | Ismael Ghalimi | @AntonFetisov Thank you very much for the feedback. I have clarified the introduction and added a few specific questions. I hope this will help keep the question open for a while. If it is not sufficient, please let me know how I can improve it further. Many thanks in advance for your help. | |
| Jan 6, 2019 at 15:54 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 348 characters in body
|
| Jan 6, 2019 at 15:47 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 348 characters in body
|
| Jan 6, 2019 at 13:06 | comment | added | Anton Fetisov | I don't think this is a good question for MO. This posts basically asks for open-ended discussion without any specific problem, while MO (and StackExchange in general) are suited for well-defined problems with verifiable solutions. This post is more of a research article posted on a forum. Regarding your question, I find missing in your observations any theorems that would connect your hyperoperations at different level. It's not hard to make up a new group, a family of groups with some strong connections is a much more interesting (a recursive definition on its own is too weak a connection). | |
| Jan 6, 2019 at 4:26 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 3 characters in body
|
| Jan 6, 2019 at 4:21 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 3 characters in body
|
| Jan 6, 2019 at 4:13 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 751 characters in body
|
| Jan 6, 2019 at 4:02 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 751 characters in body
|
| Jan 6, 2019 at 3:51 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 751 characters in body
|
| Jan 6, 2019 at 2:50 | review | Close votes | |||
| Jan 7, 2019 at 15:50 | |||||
| Jan 6, 2019 at 2:13 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 4 characters in body
|
| Jan 6, 2019 at 2:07 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 4 characters in body
|
| Jan 6, 2019 at 2:00 | comment | added | Ismael Ghalimi | Thank you for the pointers. | |
| Jan 6, 2019 at 1:57 | comment | added | Gerhard Paseman | Somewhat related are hyperidentities. You are looking for similar identities holding for certain terms, but interesting things happen when you ask them to hold for all terms, or for certain closed subsets of terms. Start with work of Denecke, Schweigert, and Wismath. Gerhard "Can Provide Some More Names" Paseman, 2019.01.05. | |
| Jan 6, 2019 at 1:54 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 371 characters in body
|
| Jan 6, 2019 at 1:42 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 8 characters in body
|
| Jan 6, 2019 at 1:24 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 422 characters in body
|
| Jan 6, 2019 at 1:11 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 422 characters in body
|
| Jan 6, 2019 at 0:55 | history | edited | Ismael Ghalimi | CC BY-SA 4.0 |
added 325 characters in body
|
| Jan 6, 2019 at 0:50 | review | First posts | |||
| Jan 6, 2019 at 2:33 | |||||
| Jan 6, 2019 at 0:46 | history | asked | Ismael Ghalimi | CC BY-SA 4.0 |