What are identities in elementary mathematics?  Sergei Akbarov  10/22/10 2:00 PM  Dear colleagues, Who can explain me what people in Calculus (or, I do not know, maybe I f(x)=g(x) on, say, an interval I means that they coinside in each point x\in I. This is the definition for all, not necessarily elementary functions. But People in computer algebra are discussing different ways to teach computer http://www.math.upenn.edu/~wilf/AeqB.html and the identities they consider are "analytical identities", i.e. to study Were there any investigations in this field? Does such approach indeed has a I would greatly appreciate any references, suggestions, etc. Sergei Akbarov 
Re: What are identities in elementary mathematics?  Norbert Marrek  10/23/10 9:00 AM  In Z/2Z the polynomial functions f(X)=X+1 and g(X)=X^2+1 Aloha 
Re: What are identities in elementary mathematics?  tc...@lsa.umich.edu  10/23/10 9:00 AM  In article <i9su0g$m6b$1...@news.acm.uiuc.edu>,
I think the top two Google Scholar hits on "recognizing zero" should 
Re: What are identities in elementary mathematics?  David Hobby  10/24/10 2:00 PM  On Oct 23, 12:00�pm, "tc...@lsa.umich.edu" <tc...@lsa.umich.edu> wrote: > In article <i9su0g$m6...@news.acm.uiuc.edu>, ... As an aside, I'd expect axiomatizing the theory of elementary functions to be tricky. Compare this to Tarski's High School Algebra Problem, which considered a small subset of all elementary functions and was still quite difficult. http://en.wikipedia.org/wiki/Tarski%27s_high_school_algebra_problem David Hobby 
Re: What are identities in elementary mathematics?  Dan Luecking  10/25/10 5:00 PM  I certainly would, because surely x^2 = x is one of the Similarly, I would consider e^x e^y the same as e^{x+y}

Re: What are identities in elementary mathematics?  mjc  10/28/10 1:00 AM  > I would consider both of these to be theorems, not axioms (the first 
Re: What are identities in elementary mathematics?  Ilya Zakharevich  10/28/10 12:00 PM  On 20101028, mjc <mjc...@acm.org> wrote: > I would consider both of these to be theorems, not axioms (the first I doubt it. In F_4, 1+1=0, but x^2 is not equal to x. > the second from the definition of e^x and properties of I do not know what is a "limit". And I wonder which "property of Ilya [P.S. Is it my imagination, or had the quality of moderation 
Re: What are identities in elementary mathematics?  Dan Luecking  10/29/10 4:30 AM  I was referring to the original poster's discussion: axioms For example, the algebra of elementary functions (over C) Over C, sin z can be defined in terms of e^z, and various Finally, if our elementary functions are going to be My main point was that the set of identities (or axioms)
