Could someone please check my work

1. Prove that x is an accumulation point of a set S iff there exists a sequence (Sn ) of points in S\\{x} such that (Sn) converges to x . . ( # ) x is an accumulation point of a set S => there exists a sequence (Sn) of points in S\\ {x } such that (Sn ) converges to a . Suppose a is an accumulation point of a set S , # VE > ON (x; 6) n S # 0 by the definition of accumulation point Let & = => 3N E N such that Vn > N , Sn EN ( 2; - n S for all n EN . This means Sn * x and Sn E S. It also means, # By the Archimedean property, Theorem 3.3.10(c), Isn - 2 0. Since Sn converges to x , IN E N such that Vn > N , Isn - 2|