I'm assuming a lot of people click on it to see what the word Idempotence means. From the article: "Idempotence is the property of a software that when run 1 or more times, it only has the effect of being run once." And the example is, instead of a chron job just running a process once a month or on some other schedule, it runs more frequently but checks if the change has already been made. (From the latin Idem which…
Mathematically, it's x^2 = x, which implies x^n = x for all positive integers n. Nilpotence (x^2 = 0) is also very helpful some times: it's a process which is self-reversing. Like the discrete Fourier transform (if you set up the constants properly).
Also you may be confusing it with x^n = 1 (which I'm not sure how to name, 'root of unity' perhaps). This would be the case for the Fourier transform (with n=4).
If x^2 = 0 then applying the Fourier transform twice would null your function, which isn't the case.