CEdunce Mathematics (Sequences of Real Numbers) 5. LIMIT POINT OF A SEQUENCE Let (a) be any sequence and a e R we say a is limit point of {a} if every neighbour

CEdunce Mathematics (Sequences of Real Numbers) 5. LIMIT POINT OF A SEQUENCE Let (a) be any sequence and a e R we say a is limit point of {a} if every neighbourhood of a contains infinite members of the sequence (a). ie. for any 8> 0 a, e (a-6, a+ 8) for infinite values of n. a,=(-1) a-1 for any 6>0 a, e-1-8, -1+ 8) Vn = 2k - 1, k = 1, 2, .. -1 is a limit point. 1. for any 6 > 0 Ex. 0 a e (1-6, 1+ 8) V n = 2k, k = 1, 2, . 26 1 is a limit point. (a) has two limit points {-1, 1 2; n=1 or prime. p () a pln and p is the least prime doing so. a = 2 for any ö>0 a e (2 - 8, 2+ 8) Vn = 1 or prime ancle 2 is a limit point. Let p be any prime. for any 8 > 0 oa, e (P- 8, p+8) Yn= p', k= 1, 2,. p is the limit point of a Hence, every prime no. is a limit point of fa As set of prime no. are infinite fay has infinite no. of limit points. tha range set of a seguence is limit point of a sequence.