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Let A, B be two sets and f: A→ B amap. The iterates fn: An→ B,n = 1,2,... Aredefined inductively byA1 = A, f1 = f andAn = f-1(An-1 ∩ B), fn = fn-1(f) for n ≥ 2.Note that A2 = f-1(A1 ∩ B) A = A1 and thus An An-1 A for n ≥ 2.