摘要
利用实数十进制无限小数表示直接构造性地给出"单调有界数列必有极限"定理的一种简洁的新证明,并且从新视角揭示数学分析中的实数完备性和高等数学中的数列极限存在准则.
A succinct new proof on the theorem of ＂every bounded monotonic sequence has a limit＂ is given directly and constructively by the infinite decimal expression of real numbers. Moreover, the completeness of the real number system in Mathematical Analysis and the limit existence principle in Higher Mathematics are revealed from a new viewpoint.
出处
《大学数学》
2014年第1期104-106,共3页
College Mathematics
基金
北京自然科学基金(1122014)
北方工业大学教改基金
关键词
数列
单调有界
极限存在准则
实数完备性
sequence of numbers
monotonic and bounded
limit existence principle
monotone covergence theorem
completeness of real numbers
