Timeline for Cartesian product of $(k-2)\text{-times } [\text{Interval}_1] \times [\text{Interval}_2] \times [\text{Interval}_2]$
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Jun 23 at 15:25 | comment | added | Iosif Pinelis | @bof : I think $\prod_{i=1}^n S_i$ should not be used, without explaining the notation, to denote the "Minkowski product" $S_1\cdots S_n$ even when the $S_i$'s are subsets of a group. Anyhow, in the OP context, it is not the "Minkowski product", but the cartesian one. | |
| Jun 22 at 8:08 | comment | added | bof | @IosifPinelis So if $S_1,S_2,S_3,S_4,S_5$ are subsets of a group, the notation $\prod_{i=1}^nS_i$ would always be understood to mean $S_1\times S_2\times S_3\times S_4\times S_5$ and never $S_1S_2S_3S_4S_5$? | |
| Feb 1 at 21:50 | comment | added | Marco Ripà | @EmilJeřábek I used that notation in the body of the original paper (see pag. 159 of ejournal2.undip.ac.id/index.php/jfma/article/view/12053/6717), but in the current version for the arXiv I've chosen $[0,2]^{k-3}$, following your kind suggestions. Thank you all! | |
| Feb 1 at 10:20 | comment | added | Emil Jeřábek | @MarcoRipà The exact shape of \varprod is not the problem. The issue is that the standard notation for a Cartesian product of an indexed family of sets is $\prod_{i\in I}S_i$, not \varprod. | |
| Jan 31 at 15:19 | vote | accept | Marco Ripà | ||
| Jan 31 at 15:11 | comment | added | Marco Ripà | I used the mentioned symbol here since the $\varprod$ is not supported (it has been explained in the text of the question). Anyway, I agree that if I use the standard set notation in the abstract (i.e., $[0,2]^{k-3}$ instead of $[0,2]^{\times (k-3)}$), there is no reason to change it in the body of the article, where there are also some Figures. | |
| Jan 31 at 11:02 | comment | added | Iosif Pinelis | @MarcoRipà : In addition, I do not remember ever seeing elsewhere using the nonexistent natively in TeX operator $\mathop{\Large\times}$ to write something like $\mathop{\Large\times}_{i\in I}S_i$ to denote the cartesian product of sets $S_i$ over $i\in I$. Also, I do not remember ever seeing something like $\prod_{i\in I}S_i$ denoting anything except the cartesian product of sets $S_i$ over $i\in I$. As for the dot product, it is only a binary operation and certainly requires a particular symbol to denote it. So, I don't understand your worry about $[0,2]^{k-3}$, especially in the abstract. | |
| Jan 31 at 10:43 | comment | added | David Roberts♦ | @Marco I agree with Iosif, but if you are super worried, then blah$\times [0,2]^{\times (k-2)}$ is another option. | |
| Jan 30 at 23:00 | comment | added | Iosif Pinelis | @MarcoRipà : For a set $S$, the standard way to read $S^m$ is as the $m$-fold cartesian product of $S$. Other ways to read this would be unusual and requiring explicit definitions. Also, not everything has to be completely defined in an abstract. Also, I don't think that an underlining curly bracket would be appropriate for an abstract, where heavy notations should be avoided. | |
| Jan 30 at 23:00 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
deleted 20 characters in body
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| Jan 30 at 22:50 | comment | added | Marco Ripà | P.S. In the "old" abstract, I gave it as $[0,4-\sqrt{3}] \times [0,4-\sqrt{3}] \times [0,2] \times \cdots \times [0,2]$, maybe just adding a long horizontal curly bracket below $[0,2] \times \cdots \times [0,2]$ with "$(k-2)$-times" as its label would be nice for the abstract. No idea if this can be easier to read the first time. | |
| Jan 30 at 22:44 | comment | added | Marco Ripà | It seems nice to look at... my only concern is about writing $[0,2]^{k-3}$ to indicate a cartesian product (I hope that the casual reader does not think of the most common $\prod_{j=3}^{k}$ or even dot product). If there are no risks, this would be a good solution. | |
| Jan 30 at 22:33 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |