精选优质文档-倾情为你奉上实数完备性定理的证明及其应用摘要：实数集的完备性是实数集的一个基本特征，它是微积分学的坚实的理论基础，可以从不同的角度来描述和刻画实数集的完备性，因此有多个实数集的完备性基本定理，包含六个实数集完备性基本定理.本文通过证明这六个基本定理的等价性，来对实数集完备性基本定理等价性进行系统的论述，让我们对实数集完备性的基本特征有进一步的认识和理解.关键词：完备性；区间套；连续性Completeness of the system of real numbers and applicationsAbstract : Completeness of the set of real numbers is its basic character , and it is stable background of calculus .It can be described and depicted in different anles , so there are considerable fundamental theorems about it
