The typical operation applied to sets of functions is composition, so idempotency of a function f is the condition that f(f(x)) = f(x) for all x in the domain of f. I don't think that applies meaningfully to GET.
It does apply to HTTP idempotency. `x` is the state of the server. `f` is the change to the state of the server that ensues when one makes such-and-such an HTTP call. So taking PUT as an example, `x` is the state before the PUT, `f(x)` is the state after one PUT, and `f(f(x))` is the state after that single PUT is sent twice. Of course in a RFC7231-compliant server, `f(x) = f(f(x))`. Taking GET (or any other nullipotent method) as an example, we also see that in a RFC7231-compliant server, `x = f(x) = f(f(x))`.
Ah yeah that makes sense.
Technically speaking, idempotency as defined by RFC7231 only requires f(x) = f(f(x)).
Yes, and nullipotency requires x = f(x) = f(f(x)), and four of the methods defined in RFC7231 are expected to be nullipotent, otherwise known as "safe". The point of mentioning that is to highlight the relationship between idempotence and nullipotence.