i dont no... i can draw like a hundred of those... and id ont think there are more than that...There are as many as you can draw. And more.
For one-dimensional functions [itex]f(x): \mathbb{R}\to\mathbb{R}[/itex], there areWe know that the function f(x) = sin(2*pi*x) vanishes at all integers, are there other functions like that and what is the appropriate generalization to higher dimensions?
Suppose we had two such real valued functions on the reals. What new function could you create such that its restriction on Z^2 is identically zero and nonzero on R^2/Z^2?Maybe I wasn't specific, I'm looking for the formula of a function f(x,y) that would vanish at integers, could anyone help?
Before there's any confusion, the "hundred" comment is mine (in jest).If you don't think there are more than "hundreds" of such functions (or if you think of functions as limited to "formulas") then you have a very restricted idea of "function".