VC-dimension of infinite set of triangle wave I am searching for the VC-dimension of the following:
What is the VC-dimension of the infinite set of triangle wave functions with
amplitude 1 and period parameter p on points on the line?
2πarcsin⁡(sin(2πx⁄p))
First of all, presumably you want the VC-dimension of your class of composed with the sign function, which yields a class of Boolean functions (otherwise, VC-dim is not defined). With that out of the way, the answer is: It's infinite. That will be the answer for any periodic function class that contains all possible frequencies and crosses the x-axis. For a concrete proof for this sine wave, see Theorem 9 here:
https://www.cs.bgu.ac.il/~karyeh/fat-add.pdf