(a) Let A be the subset of R defined by A= {1-:n€N}. Find all cluster points of A and justify your answer. (b) Let ScR and let e eR be a cluster point of S. Prove that for each e> 0 the set...

Extracted text: (a) Let A be the subset of R defined by A= {1-:n€N}. Find all cluster points of A and justify your answer. (b) Let ScR and let e eR be a cluster point of S. Prove that for each e> 0 the set W:=sn(e-t.c+e) has infinitely many elements. Let (z.) be a sequence of real numbers and let B be the subset of R defined by B:= {!:n€N}. Let LE R and let f : B→R be defined by f () = a,-. Prove that lim a, = L if and only if limf(r) = L.