The electromagnetic spectrum does range between (almost) zero and (almost) infinity. It's just that your eyes are sensitive to a very small part of it (from about 380 nm to about 800 nm).
At the lowest frequencies, it becomes difficult to recognize the signal from background fluctuations.
From this site: "Gamma-rays are detected by observing the effects they have on matter." So the upper end of the EM spectrum is probably above 300 EHz, but there are no EM generators at those frequencies.