What does "a function takes on" mean? Hey! I'm currently learning Picard's theorem, but I don't quite understand it because of difficult words.. In the text, it uses the term "takes on", ie "If f(z) is analytic and has an isolated essential singularity at a point z_0, it takes on every value, with at most one exceptional value in an arbitrarily small ε-neighbourhood of z_0". What does "take on" mean? Are they talking about the function's range? And what do they mean with "exceptional value"?