In this article,the authors study the self-similarity of the union of Cantor sets.By the Cantor expressions they get a basic relationship between Cantor sets and iterated function systems:T ∪ (T+ α) is a self-similar set iff there exists a natural number n ≥ 0,such that α=±(k2-k1)d n.Moreover,if T ∪ (T+ α) is a self-similar set,it satis...