This assignment concerns a recursively dened set ROD. Begin with the unit interval RU. = [0,1]; at the next step remove from Re the open centered interval of radius 3 to obtain set R1. Then one has produced R1=wam(%-%(%)=%+%())was?)=[ululll a union of two closed intervals. In the next step, to obtain R2, remove from each of the previous two intervals an open centered interval of radius 52, to produce 9 11 2 3 39 41 R2' [0'50] U [50'5] U [5'50] U [50'1]' a union of four closed intervals. One may continue in this way to obtain at step in + 1 a set 1%...1, a union of 2"+1 51:1 from each of the 2\" closed intervals closed intervals, obtained by removing a centered open interval of radius comprising the previous set HR. The set Rm is then dened as Roe = 127:. 11:0 the intersection of this indexed family of sets. 1. Write down explicitly what is the sets R3. Prove that Rm C [0, 1]. Prove that R00 is a nonempty sct. P99.\" Prove that ROD is an innite set by constructing a surjective function f : Rm > Ru (Hint: try to express numbers in [0,1] as numbers in base 5, What does it mean to belong to Rm when expressed in base 5? Use this fact to construct your function, it will not be injective.) 5. Write down a formula in terms of n computing the length of the set Rn (Hint: at each step how much of the unit interval have you removed?) 6. Using your formula from the previous step to compute the length of R00