TITLE: Do functions really always take only one argument?
QUESTION [7 upvotes]: I am used to $f(x_{1},x_{2})$ or $f(x_{1})$ (and to say this function takes one, two etc arguments). But the more I think about it from a set-theoretic or linear-algebra point of view there is really just a single n-dimensional vector or tuple $\mathbf{x}$, which is our $\mathbf{x} = (x_{1},x_{2},...)$ input. So functions always have one input argument (be it univariate, bivariate or multivariate). Is this correct or gibberish?

REPLY [5 votes]: Yes, they do. But remember that maps like these $(x_1,x_2)\mapsto y$ (that so can be considered as being $x\mapsto y$) have a domain with an implicit structure: it will always be possible to say, given any point of it, what is the first component and so the "first argument" of the map, the second and so on. Otherwise it will make no sense a map like this $x\mapsto y,~y=\frac{x_1}{x_2}$