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数列是指一串正整数编号的数,人们对数列极限概念的认识是从数列求和开始的。在数列求和问题上产生的悖论使得人们开始探求数列的性质。而数学家们给出由“ε-N”语言描述的严格的数列极限的定义,则意味着分析开始走向严谨。除了标准的“ε-N”语言外,数列极限还具有其它的等价性定义。用“ε-N”定义的数列极限具有唯一性、有界性、保号性、不等式性和夹逼性这五大基本性质。这些性质可运用于常见数列极限的计算和其它性质的证明。
Numbers refer to a series of numbers with positive integers, and people’s understanding of the concept of number limits begins with the summation of numbers. The paradox that arises on the issue of the summation of series has led to the search for the nature of the series. The mathematicians, given the definition of a strict numerical limit by the “ε-N” language, mean that the analysis is beginning to be rigorous. In addition to the standard “ε-N” language, the column limits also have other definitions of equivalence. The numerical limit defined by “ε-N ” has five basic properties of uniqueness, boundedness, preserving sign, inequality and entrapment. These properties apply to the calculation of common series limits and to the proof of other properties.