设数列{a[n]}收敛于a,由定义知存在正整数M,使得当n>M时|a[n]-a|<1,或者说a-1于是min{a[1],a[2],...,a[M],a-1}<=a[n]<=max{a[1],a[2],...,a[M],a+1},即{a[n]}有界.