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[Pad 4) L'F8:09 n math.edu (5} 19%EH 7/12 7 3. (15 pts) A sequence (36,, : n E N) of real numbers is said to "converge to L"...

A sequence (xn : n ∈ N) of real numbers is said to "converge to L" if for all M ∈ R and M > 0, there is an N ∈ N such that n > N ⇒ |xn − L| < M. Here N = {0,1,2,3,...} is the set of natural numbers and R is the set of real numbers. (a) (5 pts) Write the statement "(xn : n ∈ N) does not converge to 2" in mathe- matical form (with all quantifiers appropriately placed). (b) (10 pts) Show that the sequence ( 1/(n+1)2 : n ∈ N) converges to 0. (c) (5 pts) Are the following statements logically equivalent? Explain your an- swer. (a) ∀x∈R,∃y∈Rxy
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