Timeline for Examples of bad notation and its consequences [closed]
Current License: CC BY-SA 4.0
40 events
| when toggle format | what | by | license | comment | |
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| Aug 20, 2023 at 8:20 | comment | added | Daniel Asimov | I also have a big problem with the math police closing a perfectly interesting and extremely useful question like this one. When that happens, everyone loses. (Except for the math police, who apparently imagine they are doing a good deed. They are not.) | |
| Aug 20, 2023 at 8:18 | comment | added | Daniel Asimov | I have long had a problem with precisely √-1, because it neglects to specify if it should mean i or -i. | |
| Apr 25, 2023 at 7:53 | history | left closed in review |
Alex M. Ivan Izmestiev Chris Wuthrich |
Original close reason(s) were not resolved | |
| S Apr 23, 2023 at 17:28 | review | Reopen votes | |||
| Apr 25, 2023 at 7:53 | |||||
| S Apr 23, 2023 at 17:28 | history | edited | Humberto José Bortolossi | CC BY-SA 4.0 |
tryin to make clear the point of the question.
Added to review
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| Apr 23, 2023 at 17:00 | history | closed |
Moishe Kohan M.G. Benjamin Steinberg Yemon Choi LSpice |
Opinion-based | |
| Apr 21, 2023 at 19:04 | answer | added | Ethan Bolker | timeline score: -2 | |
| Apr 21, 2023 at 18:48 | comment | added | Buzz | Notations fixing a unique square root of something can confuse even people who ought to know better. The Algebra II textbooks that my high school used stated in chapter 8(as an explicit, albeit unproved, theorem) that $\sqrt{ab}=\sqrt{a}\sqrt{b}$ for all real $a$ and $b$. Then in chapter 9, it introduced complex numbers, and I pointed out that the "theorem" actually only held for real $\sqrt{a}$ and $\sqrt{b}$. The teacher did not want to get into it, for fear of confusing the other students. | |
| Apr 21, 2023 at 3:41 | answer | added | Daniel Asimov | timeline score: 2 | |
| Apr 20, 2023 at 19:46 | comment | added | JosephDoggie | In electrical engineering (EE) we use "j" as "i" is reserved for current -- from Wikipedia: French phrase intensité du courant (intesity of current, which we usually just call current). | |
| Apr 20, 2023 at 17:13 | answer | added | Jan Stuller | timeline score: 4 | |
| Apr 20, 2023 at 11:15 | comment | added | Hollis Williams | There are quite a few examples of confusing notation in theoretical physics, like a quantity will be written down as if it were a scalar when it is actually a matrix. | |
| Apr 20, 2023 at 10:38 | comment | added | Bumblebee | $A\xrightarrow{f}B\xrightarrow{g}C$ composition denotes as $g\circ f$ in which the order of maps is reversed. I rather prefer $(x)f,$ over $f(x).$ | |
| Apr 20, 2023 at 6:39 | history | became hot network question | |||
| Apr 20, 2023 at 6:21 | answer | added | Roland Bacher | timeline score: 9 | |
| Apr 20, 2023 at 6:15 | comment | added | Roland Bacher | I think that there are bad notations and confusing notations : Confusing notation often use the same notation for two different things, depending on context.My favourite example of a confusing notation : $f^{-1}$. It can can be $1/f$ or the preimage or the reciprocal of a bijection. All three are perfectly fine. | |
| Apr 20, 2023 at 6:13 | answer | added | Gerald Edgar | timeline score: 3 | |
| Apr 20, 2023 at 4:22 | answer | added | Timothy Chow | timeline score: 15 | |
| Apr 20, 2023 at 4:11 | comment | added | Timothy Chow | Related: Has incorrect notation ever led to a mistaken proof? and What are the worst notations, in your opinion? | |
| Apr 20, 2023 at 2:11 | comment | added | Emily | @LSpice Another choice is $\mathbb{Z}_{/n}$. I think it's a bit ugly/clunky (although this is the notation I personally use), but at least it's kinda convenient | |
| Apr 20, 2023 at 1:34 | comment | added | Nate Eldredge | The use of $\lim$ as an operator is a serious problem for my analysis students. They have trouble remembering that you can't even write $\lim a_n$ until you have first proved that the limit exists. So an equation like $\lim a_n = 5$ may be neither true nor false but actually ill-defined. By contrast, using $\to$ as a relation, the formula $a_n \to 5$ at least has a definite truth value no matter what sequence $a_n$ is. | |
| Apr 20, 2023 at 1:09 | comment | added | LSpice | @Bma, re, I use $\mathrm C_n$ when I can get away with it. That's two of us! | |
| Apr 20, 2023 at 1:02 | comment | added | Bma | @LSpice That was one I had in mind actually. I think $\mathbb{Z} /n$ saves quite a bit of time and angst, although it’s still pretty rough. $\mathbb{Z}_n$ is definitely not an option. I’m almost drawn to using $C_n$ instead ($C$ for cyclic group). | |
| Apr 20, 2023 at 0:51 | comment | added | LSpice | @Bma, re, aside from $\mathbb Z/n$, which is shorter but otherwise surely not much more convenient as a subject of operations and parentheses, what are the superior alternatives to $\mathbb Z/n\mathbb Z$? (Although there is disagreement on this, as a $p$-adicist I regard $\mathbb Z_n$ as taken, at least for $n$ prime.) | |
| Apr 19, 2023 at 23:36 | comment | added | Bma | There are a few notations I find irritating. For one, $\mathbb{Z}/n\mathbb{Z}$ is incredibly inconvenient to write or type. God forbid you have to apply any operations to it and parenthesize it as well. I also dislike $a \equiv b$ (mod $n$). I think $a \equiv_n b$ is much better. Neither of these notations are unclear, but they are just tedious compared to superior alternatives. | |
| Apr 19, 2023 at 21:54 | answer | added | Christophe Leuridan | timeline score: 16 | |
| Apr 19, 2023 at 18:40 | comment | added | M.G. | @JochenGlueck: could well be. My impression is that people tend to use $\sqrt{-1}$ instead of $i$ when they deal with more than 1-2 complex variables (be it analysis or geometry) or an indefinite amount, so that they can have for ex. $z_i$, $1 \leq i \leq n$, or some tensors in coordinates. Replacing $i$ by $\sqrt{-1}$ in single variable complex analysis or Riemann surfaces seems less beneficial. Personally, I prefer to write $i$ instead of $\sqrt{-1}$ whenever possible b/c it's shorter, but I prefer to read $\sqrt{-1}$ rather than $i$ :-) Also, $\sqrt{-1}$ seems perhaps a bit old-fashioned. | |
| Apr 19, 2023 at 18:35 | history | made wiki | Post Made Community Wiki by Asaf Karagila♦ | ||
| Apr 19, 2023 at 18:18 | comment | added | M.G. | @LSpice: my take on $\sqrt{-1}$ vs. multiple roots is that, even though there are multiple different roots, there is no preferred one (having a preferred one being an algebraic impossibility). You pick one, but it doesn't matter which, because any choice works equally well (as long as you are consistent in your choice). | |
| Apr 19, 2023 at 17:46 | comment | added | Loïc Teyssier | @JochenGlueck: that is very likely, in my opinion. Yet, the "problem" in the OP is not a problem as most functional equations involving usual real functions fail for their complex counterparts, which are generally multivalued. This has clearly nothing to do with the rightness of the notation for $\sqrt{-1}$, people just have to forget about (or, better, adapt) the multiplicative law for square roots when going to $\mathbb{C}$. | |
| Apr 19, 2023 at 17:13 | comment | added | Jochen Glueck | @M.G.: I'm wondering whether this might be an analysis vs. algebra cultural thing. | |
| Apr 19, 2023 at 17:10 | comment | added | LSpice | As suggested by @M.G., I think that $\sqrt{-1}$ is just fine. Where I see the problem is with thinking that "$\sqrt{-1}$ is the square root of $-1$", emphasis mine, because there is no such thing as the square root of $-1$ (unless you work in characteristic $2$). If you think that $\sqrt{-1}$ is a square root of $-1$, then you should be untroubled by the suggestion that $\sqrt{-1}\cdot\sqrt{-1} = \sqrt{1}$: it says that the product of two square roots of $-1$ (which need not even be the same!) is a square root of $1$, which is true. | |
| Apr 19, 2023 at 17:08 | history | edited | LSpice | CC BY-SA 4.0 |
TeX
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| Apr 19, 2023 at 16:01 | review | Close votes | |||
| Apr 21, 2023 at 11:48 | |||||
| Apr 19, 2023 at 15:14 | history | edited | gmvh | CC BY-SA 4.0 |
Fixed typo in title, added top-level tags
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| Apr 19, 2023 at 15:14 | comment | added | M.G. | Cont. In a similar fashion we have for example the notation $\mathbb{Q}(\sqrt{-d})$ in Algebraic Number Theory, the meaning of which is immediately clear. | |
| Apr 19, 2023 at 15:12 | comment | added | M.G. | I disagree that $\sqrt{-1}$ is necessarily a bad notation. It might be pedagogically bad for mathematically inexperienced first-timers in complex numbers, but that's not enough to disqualify it. Arguably, it has certain shock value, which has turned it into a symbol on its own, subconsciously burried into every mathematician's mind: it hits you even before you digest the other parts of a formula. Many classical (and even newer) books on SVCs and Complex Geometry use it instead of $i$, which frees the latter to be used as an index, e.g. Donu Arapura's book, Griffiths and Harris' book etc. | |
| Apr 19, 2023 at 14:42 | answer | added | Iosif Pinelis | timeline score: -7 | |
| Apr 19, 2023 at 14:04 | comment | added | Iosif Pinelis | This is a good question for ChatGPT. | |
| Apr 19, 2023 at 13:46 | history | asked | Humberto José Bortolossi | CC BY-SA 4.0 |