Function application without parentheses: Difference between revisions
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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. | 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. | ||
Some people interpret \(\sin(x)^2\) to mean \(\sin(x^2)\) rather than \((\sin x)^2\), even though \(f(x)^2\) normally means \((f(x))^2\). | |||
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== | ||
<references/> | <references/> | ||
Latest revision as of 15:01, 21 October 2022
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, this can look like a 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[1][2], and got mixed responses.
Some people interpret \(\sin(x)^2\) to mean \(\sin(x^2)\) rather than \((\sin x)^2\), even though \(f(x)^2\) normally means \((f(x))^2\).
Deyan Ginev searched for occurrences of f x in arXiv papers[3] 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.
!["To simplify expressions we often omit parentheses writing f x = f (x) etc." [math/0201098]](/wiki/File:F-x-for-brevity.png)
