2. Let (r) be the function defined by V(x) = 1. Let 1+x. In(x) Vovo...(x) n-copies Note that alternate definitions proceed by induction: Let V₁(x) In ((x)) or, equivalently, define Yn+1 = Y(Yn (x)). (x) and define n+1 a) What is the domain of Vn(x) for n = {1,2,3,4}? b) What is your guess for the domain of Vn in general? c) Calculate (x) for n € {1,2,3,4}. Arrange your calculation in a way to make it easily under- standable. There are various approaches here and some are easier to understand than others. Do not be afraid to start on one approach and give it up in favour of another. d) What is your guess for (r) in general. You are not asked to prove this by mathematical induction, but it is a good exercise to give it a try.

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