Recent content by rvadd

When discussing the second partial derivative test in multivariate calculus, a reference is usually made to an elusive "higher order test" that one must defer to in the case that the second partial derivative test fails. Does anyone know the general form of these higher order test? My first...

I think you are right, I misread the definition. It says an operation only stays on set S if the set S is considered closed under the operation. Perhaps, then, I am overly philosophical because it is precisely these fundamental terms that I believe need to be nailed down the most. Is there a...

Wonderful, thank you Best Pokemon. Such concision and clarity should be on Wikipedia. So operations are performed within the same domain, whereas functions map a domain to a codomain. So, the corresponding difference between a function operator and a function must be that while a function...

You are correct, I should be more specific. The question is in a strictly mathematical sense (no computer language syntax). I'll give more examples of what I mean: Basic Operations: arithmetic, logical, set Functions: polynomial, transcendental Operators: differential, integral...

This question is fairly simple: what is the difference between functions and operations. Both seem to have inputs and outputs. Both can input/output scalars, vectors, functions, functionals, etc. I think the sticking point might be mapping, but I'm not sure. E.g. f=a+b vs. f(x,y)=x+y

Thank you for the responses. The Spivak reading was especially helpful. So, correct me if my interpretation is incorrect: The generalized cross product in n dimensions has arity n-1, but its operands are all 1-vectors and thus the output will also be a 1-vector. I guess this might be a...

I'm taking multivariate calculus and my teacher just introduced the concept of cross products a week ago. Reading the Wikipedia page, I see that cross products only work in three and seven dimensions, which is puzzling. One use of the cross product for our class is to find the vector...