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**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"?