# We should think of S as containing all the points OI S anu all putsas limits of convergent sequences of points of S. A slightly different formulation of thnotion is given in Exercise 8.an be obtaineEXERCISES 2.21. Which of the following subsets of R" is open? closed? neither? Prove your answer.(a) x : 0x < 2} C R(b) {x x 2- for some keN orx= 0} C R(g):y=xCR: X =y(h) x: 0 x |1}C R"(i) x x 1} C R"j x |x 1} C R"(k) the set of rational numbers, Q CRX(c)C R2yX(d)y 2уCR21(1)X: ||X||хУC R2(m) (the empty set)X(f): ху 2УCR22. Let {x} be a sequence of points in R". For i = 1, .. . , n, 1let xi denote the ith coordinate of thevector Xk. Prove that xk a if and only if xk,iai for all i = 1, .. . , n.3. Suppose {x} is a sequence of points (vectors) in R" converging to a.(a) Prove that |Xk |l a . (Hint: See Exercise 1 17.)

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I need help for problem 1c. Thanks!

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