数列极限直观顺向描述定义的数学刻画

Mathematical Characterization of the Perceptual Forward Description for Limits of Sequences

现有教材关于数列极限的定义从“当n→+∞时x n→x”的直观顺向描述直接过渡到用于反向刻画的ε-N语言的讲法令初学者难以短时间理解消化.本文利用数学语言给出数列极限直观顺向描述定义的精确表示,并利用下确界定义证明其与ε-N语言等价,进而搭建数列极限从直观顺向描述性定义到ε-N语言精确定义的桥梁.

The current textbooks from the perceptual forward description‘x n→x whenever n→+∞’directly to the reverse characterization inε-N language for the notion of limits of sequences is challenging to some beginners.In this paper,we propose an intuitive mathematical definition for the limits of sequences and prove its equivalence to theε-Nlanguage based on the notion of infimum of sets of real numbers.