Editing Arg max (section)

{{Short description|Inputs at which function values are highest}}
{{refimprove|date=October 2014}}
[[File:Si_sinc.svg|thumb|350px|As an example, both unnormalised and normalised [[sinc]] functions above have <math>\operatorname{argmax}</math> of {0} because both attain their global maximum value of 1 at ''x''&nbsp;=&nbsp;0.<br /><br />The unnormalised sinc function (red) has ''arg min'' of {&minus;4.49,&nbsp;4.49}, approximately, because it has 2 global minimum values of approximately &minus;0.217 at ''x''&nbsp;=&nbsp;±4.49. However, the normalised sinc function (blue) has ''arg min'' of {&minus;1.43,&nbsp;1.43}, approximately, because their global minima occur at ''x''&nbsp;=&nbsp;±1.43, even though the minimum value is the same.<ref>"[http://physics.usyd.edu.au/teach_res/mp/doc/math_sinc_function.pdf The Unnormalized Sinc Function] {{Webarchive|url=https://web.archive.org/web/20170215045226/http://www.physics.usyd.edu.au/teach_res/mp/doc/math_sinc_function.pdf |date=2017-02-15 }}", University of Sydney</ref>]]

In [[mathematics]], the '''arguments of the maxima''' (abbreviated '''arg max''' or '''argmax''') and '''arguments of the minima''' (abbreviated '''arg min''' or '''argmin''') are the input points at which a [[Function (mathematics)|function]] output value is [[Maxima and minima|maximized and minimized]], respectively.<ref group="note">For clarity, we refer to the input (''x'') as ''points'' and the output (''y'') as ''values;'' compare [[critical point (mathematics)|critical point]] and [[critical value (critical point)|critical value]].</ref> While the [[argument of a function|arguments]] are defined over the [[domain of a function]], the output is part of its [[codomain]].