Why start at x, y, z - User contributions [en-gb]

Parentheses are overused

2021-07-31T13:02:11Z

Dginev: add a custom constructor via a parenthetical

[[Category:Ambiguities]]

Parentheses are used to represent all sorts of operations and objects, many of which conflict with each other.

Grouping parts of an expression: \( (x+1)(x+2) \)

Argument of a function: \(f(x)\) is "\(f\) applied to \(x\)". ([[There is no function application symbol]])

Greatest common divisor: \((a,b) = \gcd(a,b)\)

Counting combinations: \( {n \choose k} = \frac{n!}{k!(n-k)!} \)

Repeated differentiation : \( f^{(n)}(x) = \frac{\mathrm{d}^nf}{\mathrm{d}x^n} \)

Vectors or one-column matrices: \( \begin{pmatrix} a \\ b \end{pmatrix} \)

Ideals: \((2)\) is the ideal generated by 2, \((a,b,c)\) is the ideal generated by \(\{a,b,c\}\).

Tuples: \((a,b)\)

Cycle notation for permutations: \((a,b)\) or \((a \; b)\)

Legendre/Jacobi symbol: \( \left(\dfrac{a}{b}\right) \)

[[Intervals]]: \((a,b)\) is open at both ends, \((a,b]\) is open at one end.

== Less standard notations, local to a document ==

These are many and varied, one motivating example
<ref>[https://www.sas.rochester.edu/mth/undergraduate/honorspaperspdfs/caten2017.pdf "The toplogy of magmas", by Charlotte Aten]</ref>:

The set of all 2-faces of the simplex with vertices a,b,c and d: \((a,b,c,d)_2\).

==References==

<ref>[https://karendcampe.wordpress.com/2016/04/28/problems-with-parentheses/amp/ "Problems with parentheses", by Karen Campe]</ref>

Whystartatxyz talk:Organisation

2021-07-13T13:31:46Z

Dginev:

Other attributes to organize by that may be useful as an index could be:

* Fixity: prefix, infix, postfix, circumfix/fenced, scripts, fractional, tabular and compound notations.

* Level of study: it may be helpful to separate which notations are present in 1) early education, 2) K-12, 3) higher education and then 4) active research notations. I've talked to people who like focusing on specific levels, so they may find it easier to navigate the wiki for whichever parts they find important to them.

* Indeed some current pages write about specific examples, and some write about a general ambiguity. To my taste having a page about a conceptual practice is great, and then listing various interesting examples in its body. So, to take a random recent page, [[Prime symbol in variable names]] could be a little more generic, even just "Prime".

* Naming conventions for pages could be nice, so that they're easy to find and add. For instance, I have an external page on the "Many meanings of superscript plus", that I would be happy to transport over but am unsure what name to use in this Wiki so that it fits in naturally.

That's all for some early thoughts from me, it's very fun to see the wiki growing!

[[User:Dginev|Dginev]] ([[User talk:Dginev|talk]]) 13:30, 13 July 2021 (UTC)

Whystartatxyz talk:Organisation

2021-07-13T13:30:45Z

Dginev:

Other attributes to organize by that may be useful as an index could be:

* Fixity: prefix, infix, postfix, circumfix/fenced, scripts, fractional, tabular and compound notations.

* Level of study: it may be helpful to separate which notations are present in 1) early education, 2) K-12, 3) higher education and then 4) active research notations. I've talked to people who like focusing on specific levels, so they may find it easier to navigate the wiki for whichever parts they find important to them.

* Indeed some current pages write about specific examples, and some write about a general ambiguity. To my: taste having a page about a conceptual practice is great, and then listing various interesting examples in its body. So, to take a random recent page, [[Prime symbol in variable names]] could be a little more generic, even just "Prime".

* Naming conventions for pages could be nice, so that they're easy to find and add. For instance, I have an external page on the "Many meanings of superscript plus", that I would be happy to transport over but am unsure what name to use in this Wiki so that it fits in naturally.

That's all for some early thoughts from me, it's very fun to see the wiki growing!

[[User:Dginev|Dginev]] ([[User talk:Dginev|talk]]) 13:30, 13 July 2021 (UTC)

Whystartatxyz talk:Organisation

2021-07-13T13:30:23Z

Dginev: some thoughts on organization

Other attributes to organize by that may be useful as an index could be:

* Fixity: prefix, infix, postfix, circumfix/fenced, scripts, fractional, tabular and compound notations.

* Level of study: it may be helpful to separate which notations are present in 1) early education, 2) K-12, 3) higher education and then 4) active research notations. I've talked to people who like focusing on specific levels, so they may find it easier to navigate the wiki for whichever parts they find important to them.

* Indeed some current pages write about specific examples, and some write about a general ambiguity. To my: taste having a page about a conceptual practice is great, and then listing various interesting examples in its body. So, to take a random recent page, [[Prime symbol in variable names]] could be a little more generic, even just "Prime".

* Naming conventions for pages could be nice, so that they're easy to find and add. For instance, I have an external page on the "Many meanings of superscript plus", that I would be happy to transport over but am unsure what name to use in this Wiki so that it fits in naturally.

That's all for some early thoughts from me, it's very fun to see the wiki growing!

Function application without parentheses

2021-07-09T11:54:19Z

Dginev: add example of "f x" used as function application

[[Category:Ambiguities]]

It's sometimes OK to write a function name followed by its argument, without any parentheses. Because there's [[There is no function application symbol|there is no function application symbol]], this can look like a [[Missing multiplication symbol|multiplication]].

This is an example of [[juxtaposition means combine in the obvious way]].

This is most usually done with the trigonometric functions and logarithms, e.g.

\[ \sin \theta, \ln x \]

So is it only OK to omit the parentheses for well-known functions? Or is it for any function whose name is longer than one letter? Christian Lawson-Perfect asked<ref>[https://twitter.com/christianp/status/1412411447552917515 Tweet by Christian Lawson-Perfect], [https://mathstodon.xyz/@christianp/106534017984381320 toot by Christian Lawson-Perfect]</ref><ref>[https://twitter.com/christianp/status/1036895727442644992 Earlier tweet by Christian Lawson-Perfect]</ref>, and got mixed responses.

Deyan Ginev searched for occurrences of <code>f x</code> in arXiv papers<ref>[https://gist.github.com/dginev/0587ce0264f03f2787503b6e4c14a342 A report on the direct uses of "f x" (without parentheses) in arXiv] by Deyan Ginev</ref> and found about 7,000 papers containing that pattern, containing a wide range of exotic uses. In a handful of which, "f x" was indeed a function application.

[[File:F-x-for-brevity.png|thumb|alt="To simplify expressions we often omit parentheses writing f x = f (x) etc." [math/0201098] |Clear statement of the "f x" shorthand, from arXiv:math/0201098]]
==References==
<references/>

File:F-x-for-brevity.png

2021-07-09T11:51:50Z

Dginev:

[math/0201098] "To simplify expressions we often omit parentheses writing f x = f (x) etc."

MathML Intent

2021-06-30T19:56:51Z

Dginev: offer MathML Intent draft list as a seed for curating/editorializing ambiguity pages

A list of notations curated as an exploratory project in the recent reopening of the [https://www.w3.org/Math/Documents/Charter2021.html Math WG] can be seen at [https://docs.google.com/spreadsheets/d/1EsWou1K5nxBdLPvQapdoA9h-s8lg_qjn8fJH64g9izQ/edit?usp=sharing this Google Spreadsheet]. This sheet is a living document that is going to grow further during 2021.

Concretely, the "Level 1 Ed", "Level 2" and "Level 3" sheets contain a draft organization of notations. For the purposes of this wiki, it's best to imagine these were united as one big flat list of ~1300 notation examples.

As one example for fishing possible ambiguities from the spreadsheet:

* visit the Level 3 sheet
* search for the `{` character
* this results in 15 hits, some of which may have fully or partially overlapping syntax