Timeline for Suggestions for good notation
Current License: CC BY-SA 3.0
111 events
| when toggle format | what | by | license | comment | |
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| Apr 10, 2023 at 14:52 | answer | added | David E Speyer | timeline score: 3 | |
| Apr 10, 2023 at 3:26 | answer | added | Michael Hardy | timeline score: 0 | |
| Dec 22, 2021 at 4:58 | comment | added | Michael Hardy | If you want an undergraduate to understand why you call a function $x\mapsto x\sin x$ instead of just calling it $x\sin x,$ point out that $x\mapsto(x+2y)^2$ and $y\mapsto(x+2y)^2$ are two different functions. $\qquad$ | |
| Dec 19, 2021 at 9:51 | comment | added | François Brunault | The notation $\delta_P$ is also used for a formula $P$, and if $A$ is a set then $\delta_A$ is the characteristic function of $A$. So $[n]=\delta_{n=0}=\delta_0(n)$. In comparison to $[n]$, this makes it easier to view this as a function. This is also more general than the traditional $\delta$. | |
| Dec 19, 2021 at 5:40 | answer | added | Daniel Sebald | timeline score: 1 | |
| Dec 19, 2021 at 5:08 | answer | added | Dan Ramras | timeline score: 2 | |
| Dec 17, 2021 at 18:28 | answer | added | Mozibur Ullah | timeline score: 0 | |
| Dec 17, 2021 at 0:16 | answer | added | Michael Hardy | timeline score: 4 | |
| Jun 18, 2021 at 0:24 | answer | added | Tom Copeland | timeline score: 1 | |
| May 19, 2021 at 10:03 | answer | added | Ben McKay | timeline score: 3 | |
| Feb 9, 2021 at 15:15 | answer | added | Ben McKay | timeline score: 6 | |
| Sep 4, 2020 at 7:05 | answer | added | Qiaochu Yuan | timeline score: 8 | |
| Nov 20, 2019 at 14:43 | comment | added | firtree | I also don't have enough reputation on this one to post an answer, so I'll do mine as a comment: In basic linear algebra, N.Vavilov suggests $[u\leadsto v]$ for the transition matrix from basis $u$ to basis $v$. That makes much easier and more natural and more memorizable formulas like $u[u\leadsto v]=v$ and for coordinates columns $x,y$: $a=ux=vy=(u[u\leadsto v])y=u([u\leadsto v]y)=ux$. Sure $[v\leadsto u]=[u\leadsto v]^{-1}$, and one never needs a transpose matrix. | |
| May 13, 2019 at 18:59 | answer | added | Dirk | timeline score: 10 | |
| May 13, 2019 at 16:49 | answer | added | k.stm | timeline score: 9 | |
| Mar 5, 2018 at 14:55 | comment | added | johnnyb | I don't have enough reputation on this one to post an answer, so I'll do mine as a comment: 1) The second derivative written so that it can be used as a fraction: $\frac{d^2y}{dx^2} - \frac{dy}{dx}\frac{d^2x}{dx^2}$. See arxiv.org/abs/1801.09553 for more details on this approach. 2) Partial differentials written so that they can be used as a fraction: The partial derivative of $u$ with respect to $x$ where $x$ is the only variable allowed to independently vary written as $\frac{\partial_x u}{dx}$. Both of these allow differentials to more freely be used as fractions. | |
| Jan 27, 2018 at 22:46 | answer | added | Itai Bar-Natan | timeline score: 3 | |
| Jan 27, 2018 at 21:48 | answer | added | Mr Pie | timeline score: -3 | |
| Jan 27, 2018 at 21:11 | comment | added | Mr Pie | I invented my own function $\delta(n, k)$ which simply means the sum of the digits of $n$ in base $k$ since $\delta$ looks like an $S$ in english but corresponds to a $d$ in greek ..... until I read this post and found out there was already a similar delta function (sigh). | |
| Jan 13, 2018 at 20:32 | answer | added | echinodermata | timeline score: 4 | |
| Oct 26, 2017 at 5:53 | review | Close votes | |||
| Oct 26, 2017 at 9:23 | |||||
| Jul 15, 2017 at 11:29 | comment | added | Peter Heinig | Re the comments on $B^A$: like you are likely to know, a useful and usual alternative notation for $B^A$, coming from category theory, is $[A,B]$, often referred to as the "internal-hom". In the category $\mathsf{C}$ of sets, we have $B^A = \mathsf{C}(A,B) = [A,B]$. The notation somewhat clashes with Iverson brackets, of course; and then again...one can perhaps reconcile the two with a suitable interpretation. | |
| Jul 15, 2017 at 3:28 | answer | added | ಠ_ಠ | timeline score: 3 | |
| Jul 15, 2017 at 1:45 | answer | added | k.stm | timeline score: 5 | |
| Jul 18, 2016 at 12:39 | answer | added | Matt Majic | timeline score: 6 | |
| Dec 16, 2014 at 0:57 | answer | added | echinodermata | timeline score: 52 | |
| Dec 13, 2014 at 14:22 | answer | added | Sylvain JULIEN | timeline score: -2 | |
| Dec 13, 2014 at 12:24 | answer | added | Rasmus | timeline score: 0 | |
| Dec 13, 2014 at 11:48 | answer | added | Basil | timeline score: 13 | |
| Dec 1, 2013 at 2:32 | history | edited | Tom LaGatta | CC BY-SA 3.0 |
switched B -> A to A -> B
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| Jul 9, 2013 at 16:41 | history | protected | François G. Dorais | ||
| Feb 2, 2013 at 23:15 | answer | added | Douglas Lind | timeline score: 11 | |
| Jan 24, 2013 at 22:28 | answer | added | Hans Schoutens | timeline score: 0 | |
| Jan 24, 2013 at 21:04 | answer | added | Anton Petrunin | timeline score: 1 | |
| Jan 24, 2013 at 5:25 | answer | added | Anton Petrunin | timeline score: 23 | |
| Dec 10, 2012 at 1:13 | comment | added | Daniel McLaury | Well, if X is a set, then the Cartesian product $X^n$ is the set of functions from $[n] = {1, 2, \ldots, n}$ to X, so naturally $X^A$ is the set of functions $A \to X$. | |
| Dec 9, 2012 at 23:36 | answer | added | Qfwfq | timeline score: 8 | |
| Oct 16, 2012 at 14:34 | comment | added | Hans-Peter Stricker | (1) I only know the Kronecker delta with two indices, yielding $\delta_{ij} = [i = j]$ - but this is better anyhow! (2) I always found the notation $A^B$ useful since the number of functions from $B$ to $A$ is - in the finite case - just $|A|^{|B|}$ (3) I believe it's a matter of taste: for me $A\rightarrow B$ indicates one morphism from $A$ to $B$, not all of them. | |
| Oct 15, 2012 at 19:32 | answer | added | Jonathan Beardsley | timeline score: 9 | |
| Oct 15, 2012 at 19:27 | answer | added | Todd Trimble | timeline score: 5 | |
| Oct 15, 2012 at 19:07 | answer | added | David E Speyer | timeline score: 41 | |
| Sep 20, 2012 at 5:29 | answer | added | 36min | timeline score: 24 | |
| Jun 14, 2012 at 18:48 | comment | added | LSpice |
@Peter LeFanu Lumsdaine, there's no need to do that spacing manually; stmaryrd (ctan.org/tex-archive/fonts/stmaryrd) includes \llbracket and \rrbracket.
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| Feb 5, 2012 at 17:50 | comment | added | timur | I would say the second bullet is completely standard. | |
| Dec 19, 2011 at 1:27 | answer | added | Zeeshan Mahmud | timeline score: 0 | |
| Jul 2, 2011 at 21:35 | comment | added | Noam D. Elkies | How about the notation $x^n$ itself? Initially for positive integers $n$ (and even then Euler still wrote $xx$ and $xxx$ on occasion) but suggesting fruitful generalization where $n$ might be negative, fractional, etc. and eventually even $x$ might "live" somewhere other than the real or complex numbers. | |
| Dec 18, 2010 at 22:12 | answer | added | Andreas Blass | timeline score: -3 | |
| Dec 18, 2010 at 13:49 | answer | added | Zhen Lin | timeline score: 8 | |
| Nov 16, 2010 at 5:56 | answer | added | Alan Guo | timeline score: 89 | |
| Nov 16, 2010 at 1:54 | answer | added | Jérôme JEAN-CHARLES | timeline score: 10 | |
| Nov 9, 2010 at 0:06 | answer | added | Gareth | timeline score: 2 | |
| Nov 8, 2010 at 23:00 | answer | added | David MJC | timeline score: 18 | |
| Nov 8, 2010 at 12:41 | answer | added | Zsbán Ambrus | timeline score: 13 | |
| Nov 2, 2010 at 1:41 | answer | added | John D. Cook | timeline score: 2 | |
| Nov 2, 2010 at 0:13 | answer | added | darij grinberg | timeline score: 12 | |
| Nov 1, 2010 at 23:19 | answer | added | Chris Hardin | timeline score: 3 | |
| Oct 29, 2010 at 5:21 | answer | added | Sándor Kovács | timeline score: 15 | |
| Oct 29, 2010 at 3:26 | answer | added | Chua KS | timeline score: 1 | |
| Oct 27, 2010 at 8:13 | answer | added | Darsh Ranjan | timeline score: 27 | |
| Oct 22, 2010 at 21:20 | answer | added | David MJC | timeline score: 31 | |
| Oct 22, 2010 at 13:24 | answer | added | Qfwfq | timeline score: 5 | |
| Oct 22, 2010 at 8:13 | answer | added | Roy Maclean | timeline score: 2 | |
| Oct 22, 2010 at 8:00 | answer | added | Suvrit | timeline score: 7 | |
| Oct 22, 2010 at 4:59 | answer | added | Cristi Stoica | timeline score: 15 | |
| Oct 22, 2010 at 4:59 | history | edited | timur | CC BY-SA 2.5 |
Hindu-Arabic numerals
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| Oct 22, 2010 at 4:52 | answer | added | Cristi Stoica | timeline score: 31 | |
| Oct 21, 2010 at 17:52 | answer | added | Willie Wong | timeline score: 28 | |
| Oct 21, 2010 at 17:27 | answer | added | Terry Tao | timeline score: 23 | |
| Oct 21, 2010 at 17:05 | answer | added | Terry Tao | timeline score: 49 | |
| Oct 21, 2010 at 16:59 | answer | added | Ryan Reich | timeline score: 14 | |
| Oct 21, 2010 at 13:12 | history | made wiki | Post Made Community Wiki by Ben Webster♦ | ||
| Oct 21, 2010 at 12:00 | answer | added | Qfwfq | timeline score: 42 | |
| Oct 21, 2010 at 11:55 | answer | added | Qfwfq | timeline score: 48 | |
| Oct 21, 2010 at 11:15 | answer | added | John Bentin | timeline score: 2 | |
| Oct 21, 2010 at 8:18 | comment | added | Neel Krishnaswami | @Peter: I've always heard them called "Oxford brackets" -- I've never heard the name Scott brackets before. I wouldn't mind attributing them to Scott though, if he invented them. | |
| Oct 21, 2010 at 5:17 | answer | added | Harry Altman | timeline score: 2 | |
| Oct 21, 2010 at 4:56 | comment | added | J. M. isn't a mathematician | For those who missed the point of Chandan's comment: it's "Hindu-Arabic numerals". ;) | |
| Oct 21, 2010 at 4:33 | answer | added | Quadrescence | timeline score: 42 | |
| Oct 21, 2010 at 3:38 | comment | added | Aleksei Averchenko | Isn't $x \mapsto f(x)$ commonplace? As for homomorphisms, they are not simply maps, and $\mathrm{Hom}(A, B)$ denotes the whole class, while $A \to B$ denotes a single mapping. | |
| Oct 21, 2010 at 3:37 | answer | added | Andrey Rekalo | timeline score: 88 | |
| Oct 21, 2010 at 3:29 | comment | added | Chandan Singh Dalawat | Arabic numerals ? Ah yes, they were transmitted to Europe by the Arabs. | |
| Oct 21, 2010 at 3:21 | answer | added | Jason Morton | timeline score: 13 | |
| Oct 21, 2010 at 3:05 | comment | added | Peter LeFanu Lumsdaine | (a version of) the Iverson bracket notation is common in categorical logic: we write them like $[\![ \mathrm{this} ]\!]$, i.e. [\![ … ]\!], and call them “Scott brackets”. Besides the examples already given, it extends beautifully to more general models with some other lattice of truth-values; but I guess that's of less general interest :-) | |
| Oct 21, 2010 at 2:50 | answer | added | Richard Stanley | timeline score: 105 | |
| Oct 21, 2010 at 2:38 | answer | added | Allen Knutson | timeline score: 19 | |
| Oct 21, 2010 at 2:18 | answer | added | Hsien-Chih Chang 張顯之 | timeline score: 23 | |
| Oct 21, 2010 at 2:06 | answer | added | Karl Schwede | timeline score: 0 | |
| Oct 21, 2010 at 1:30 | answer | added | Dick Palais | timeline score: 20 | |
| Oct 21, 2010 at 0:59 | comment | added | J. M. isn't a mathematician | I still find it terribly annoying that I have to write things like "where $[Q]$ is an Iversonian bracket" every time I use it. I wish it reaches the point where it should only have to be explained in introductory work. On the other hand, since brackets get used a lot for other things as well, maybe someone should develop specific enclosures like what was done for floor and ceiling I suppose... | |
| Oct 20, 2010 at 23:25 | answer | added | Qfwfq | timeline score: 9 | |
| Oct 20, 2010 at 23:20 | comment | added | darij grinberg | Yes, among other things. Also $A^B\times A^C=A^{B+C}$, where $+$ is disjoint union. But all the great reasons for it don't help for our mind thinking that maps start with the source and end with the image, not the other way round. | |
| Oct 20, 2010 at 23:19 | comment | added | Kevin H. Lin | I guess, in terms of lambda calculus, this is called "currying" ... | |
| Oct 20, 2010 at 23:18 | comment | added | Kevin H. Lin | I've always assumed that the notation $A^B$ is because of the "exponential law" $(A^B)^C = A^{B\times C}$ ... | |
| Oct 20, 2010 at 23:13 | answer | added | Qfwfq | timeline score: 24 | |
| Oct 20, 2010 at 23:08 | answer | added | Qfwfq | timeline score: 1 | |
| Oct 20, 2010 at 22:51 | answer | added | Qfwfq | timeline score: 21 | |
| Oct 20, 2010 at 22:29 | answer | added | Mark | timeline score: 73 | |
| Oct 20, 2010 at 21:17 | comment | added | lhf | Knuth made an argument for Iverson's notation in arxiv.org/abs/math/9205211 . | |
| Oct 20, 2010 at 21:02 | answer | added | Bjørn Kjos-Hanssen | timeline score: 43 | |
| Oct 20, 2010 at 20:54 | comment | added | Andrés E. Caicedo | In set theory we write ${}^B A$ for the set of functions from $B$ to $A$. | |
| Oct 20, 2010 at 20:52 | answer | added | Mark Grant | timeline score: 50 | |
| Oct 20, 2010 at 20:48 | answer | added | José Figueroa-O'Farrill | timeline score: 42 | |
| Oct 20, 2010 at 20:44 | answer | added | Michael Lugo | timeline score: 46 | |
| Oct 20, 2010 at 20:39 | answer | added | Joel David Hamkins | timeline score: 6 | |
| Oct 20, 2010 at 20:19 | answer | added | Pietro Majer | timeline score: 121 | |
| Oct 20, 2010 at 20:14 | answer | added | Faisal | timeline score: 19 | |
| Oct 20, 2010 at 20:13 | answer | added | Jan Weidner | timeline score: 59 | |
| Oct 20, 2010 at 20:13 | history | edited | Harald Hanche-Olsen | CC BY-SA 2.5 |
Replaced → by ↦
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| Oct 20, 2010 at 20:12 | answer | added | Suvrit | timeline score: 31 | |
| Oct 20, 2010 at 20:00 | history | edited | Alison Miller |
edited tags
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| Oct 20, 2010 at 19:58 | history | asked | Richard Borcherds | CC BY-SA 2.5 |