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> Elementary functions typically include arbitrary polynomial roots Admittedly this may be above my math level, but this just seems like a bad definition of el
by bawolff 7mo ago
> Elementary functions typically include arbitrary polynomial roots
Admittedly this may be above my math level, but this just seems like a bad definition of elementary functions, given the context.
- deleted 7mo ago[deleted]
- js8 7mo agoI would agree, it makes them anything but elementary. I am honestly not even sure if there is a finite constructible basis of the functions that can express any solution of single-variable integer polynomials. And for multivariate polynomials, the roots are uncomputable due to MRDP theorem.
- reikonomusha 7mo agoIt is not known, and the model problem for this is Hilbert's 13th [1]. Nonetheless, "elementary function" is a technical term dating back to the 19th century; it's very much not a general adjective whose synonym is "basic". [1] https://en.wikipedia.org/wiki/Hilbert%27s_thirteenth_problem https://en.wikipedia.org/wiki/Hilbert%27s_thirteenth_problem
- js8 7mo agoThanks, actually https://en.wikipedia.org/wiki/Elementary_function https://en.wikipedia.org/wiki/Elementary_function confirms your claim. Nevertheless, it is a horrible definition. Mathematicians have often taken care to define things as close to everyday intuition as they could (and then proving an equivalence). The "elementary function" in this definition is just a weird mix of concerns.
- NetMageSCW 7mo agoElementary function is also a general English phrase that can very much be used to represent the functions on a scientific calculator.