毕业论文摘要部分的翻译

实数的完备性也即实数的连续性、稠密性，是实数集合的一个基本的特征。它是数学各个原理证明的基础，同时它也是微积分学坚实的理论基础。大部分的教材都是采取了循环的证明方式，同时也改变了定理证明的顺序，对于初学者来说，或许需要的是依据定理的介绍顺序、难易顺序进行证明。
Real number completeness of real Numbers of continuity, denseness, is a basic feature of real number set. It is the basis of the mathematical principle of various proof, at the same time it is also a calculus solid theory foundation. Most of the textbooks adopted circulation way of proof, but also to change the order of theorem proving, for starters, maybe need is based on the theorem of sequence, difficulty in order to prove that.
跪求把以上三行文字翻译成英文啊，毕业论文要用到的，不让用百度翻译也不让用谷歌翻译，还必须得符合语法，还要能够读的通，唉，真是心累。
The genuflect is begged the above three lines of text translated into English, graduation thesis will use, not to use baidu translation also not let use Google translation, must also conform to the grammar, but also to be able to read, alas, really tired heart.