>>11135267>>11135271it's literally just a way of rewriting your function.
instead of writing how big the function is at every point in SPACE, we write how PERIODIC a function is. that is, when you slide around by a specific number, how similar is the function?
they're two different perspectives - one talks about a function as having a set of values, and the other talks about the function as having certain regularity/periodicity. the first helps you if you want to know what a function actually says, but the second helps you a lot if your function is relatively regular or well behaved (say, it obeys some differential equation) but you want to know more about its behavior.