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The contents of the Function (set theory) page were merged into Function (mathematics). For the contribution history and old versions of the redirected page, please see its history; for the discussion at that location, see its talk page. |
Text and/or other creative content from this version of Function (mathematics) was copied or moved into History of the function concept with this edit. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists. |
The contents of the Empty function page were merged into Function (mathematics) on 25 July 2017. For the contribution history and old versions of the redirected page, please see its history; for the discussion at that location, see its talk page. |
A mini edit war has started about the paragraph on function evaluation. This paragraph was confusely written, and I rewrote it boldy for clarifiation. Nevertheless, some problems remain, for which I am not sure of the best solution.
In summary, fixing this paragraph of the lead requires more work and more discussion, for which the tag ((cn)) is of no help. D.Lazard (talk) 17:39, 24 March 2024 (UTC)
The redirect Overriding (mathematics) has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2024 April 26 § Overriding (mathematics) until a consensus is reached. Tea2min (talk) 11:59, 26 April 2024 (UTC)
The function as relation or mapping in the single and multiple-valued and in classical functions, continuous functions, smooth functions, and about the language of functions, and domains and ranges and images and codomains, is very overloaded. This article is picking a course of opinion which does not represent its wide and varied usage, function the term. Over time, as other aspects of mathematics solidified, it's "function" the term that is most loosely thrown about, then as with regards to relations that are admitted to various sub-fields, each claiming their own definition of function has those are each distinct and different ant not compatible. This article, which could be called "mappings" instead as that's largely what it defines, does not from the outset affect to describe the development of the definition over time, nor does it very well reflect the most usual sort of arithmetic definition with which most people are familiar, or as with regards to domain and range. Mathematics is not merely differential geometry, and the definition of function is among the very most general and general throughout. So, this article should largely start explaining that "function theory" is its own sort of world, and a history and survey of "this is what is called a function historically or in these various settings", then with regards to an opinion of "this is a function today and in the most usual setting", which it is largely arguable that this article does not reflect, instead expect.
It reminds one of "graph", "chart", and "plot", about diagrams of functions, drawing a function.
Functions are modern, and Cartesian thus including the multi-valued, and not just classical functions, smooth classical continuous functions that are single-valued, and not just differential geometry's functions with neither vertical nor horizontal tangent, "functions" in mathematics are very general, and sub-fields that restrict the definition for their own purpose are presumptious that their definition is implicit, where it is not.
This article is opinionated and needs context in itself why the definition of function is so broad that it's about its own sub-field of mathematics, in matters of relation.
This article needs a brief survey of the development of the term over time, and to point to the many different intended interpretations of the term.
This article needs a thorough introduction detailing the survey of the meaning of the term "function" over time as mathematics has grown, and, specifically not removing what has become its fuller definition, in the interest of su-fields that would restrict its meaning for their own purposes in notation, where instead they should declare their own regions of syntax, because general usage does not agree.
This article has problems and hides them. 97.113.179.80 (talk) 15:03, 19 May 2024 (UTC)
As noted somewhere above, the intent was to introduce something that is usable in schools mathematics courses. Ok, nice. But why not mention it explicitly? Why not say right away (I guess it was before) that this definition is specific for set theories.
Or we could add a section dedicated to the history of the term an the notion. Leibnitz, Newton, Cauchy had no clue about functions being their graphs ("pairs of values").
To me, it's a shame to promote just one specific view of things, the school-level mathematics. It's so XX century, the century were everything was "defined" as sets. These days mathematicians must be familiar with model theory, and see clearly that functions as "sets of pairs of sets" is just a model (in sets).