This is a real analysis proving question. It is 100% complete. Please skip if you are not sure. Please do not comment incomplete question. Thanks

(a) [10] points. Prove that for every v = (x, y) E R2 there exists a sequence Un = (In, Un ) E R2, where En, Un are rational numbers for all n E NV, and such that limn +0o Un = v. (b) [20] points. Let (an), be a bounded sequence of real numbers. Define the set S = {x E R :