Let D be a subset of R. Let x0 ∈ D such that x0 is not an accumulation point of D. (a) Use the formal negation of the definition of “accumulation point” to prove that there exists a µ > 0 such that (x0 − µ, x0 + µ) ∩ D = {x0}. (b) Let f : D → R. Prove1 that f is continuous at x0.

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