摘要
本文在实数集合的紧致性为已知的前提下,证明算术平均值与几何平均值不等式,Cauchy不等式,不等式,Holder不等式,不等式,三角不等式和Minkowski不等式之间的互相等价性,而旦它们都等价于一个实数的平方不小于零。
In this paper it is shown that the basic inequality G(a)≤A(a),Cauchy inequality,Tchebychef inequality,Holder inequality,Lyapunov inequality,triangle inequality and Minkowski inequality are all equivalent to the simple proposition that a^2≥0 for every a∈R(set of real number),provided the proposition that the closure of the set of rational number equals R is known.
出处
《辽宁师范大学学报（自然科学版）》
CAS
1989年第3期22-28,共7页
Journal of Liaoning Normal University:Natural Science Edition
关键词
不等式
实数集合
紧致性
等价性
inequality
compactness of the set of real number
on the equivalence between inequalities
