有理数

The conjugates of an element are the roots of the irreducible polynormial of which the given element is a root. The conjugates of 根号（根号3+1） over the field of rational numbers are

a。题目中的'over the rational numbers'是不是指四次多项式的系数是有理数，怎么能这么表达呢，为什么要强调有理数，系数应是整理罢。

For the case in a dc-bichromatic electric field (wB= 0), when one of the ratios is an irrational number, the other is a rational number, the dynamicallocalization always remains.

在直交流外场下，当其中一个比率是有理数，另一个是无理数时，总是保持动力学局域化；当两个比率都是有理数或无理数时，动力学局域化发生在准能带塌缩点。

With the new matrix, first the inequality in reference [1] was extended to the case of positive rational number n/m, then by taking the limit, the above case was further extended to the case of positive real number.

利用该矩阵，将文献[1]中的不等式推广到正有理数n/m的情形。然后应用极限将正有理数的情形推广到正实数。

The type of input and output are rational, every rational number indicated by two long plastic surgery.

输入输出的类型均为有理数，每个有理数用两个长整形表示。

The chapter, rational number, is the first chapter that students will learn after they go to the junior high school.

有理数》一章是学生进入初中的第一章学习内容，本文主要谈谈有理数学习中几种数学思想的体现及实施过程中要注意的问题。

The first fraction is the smallest rational number in the range, and the second fraction is the largest rational number in the range.

第一个分数是该区域中最小的有理数，第二个分数是该区域中最大的有理数。

"The idea behind Dedekind cuts is that a real number x can be named by giving an infinite set of rationals, namely all the rationals less than x .

Enderton (p.113)形容了这个描述：戴德金分割背后的想法，是每一个实数 x 都可以用一个有理数的无穷集合，也就是所有小于 x 的有理数来命名。

Enderton (p.113)形容了这个描述:The idea behind Dedekind cuts is that a real number x can be named by giving an infinite set of rationals, namely all the rationals less than x .

&（&戴德金切割背后的想法，是每一个实数 x 都可以用一个有理数的无穷集合，也就是所有小于 x 的有理数来命名。

Consider the set of all rational numbers.

当考虑所有有理数的集合时，有些门外汉可能会天真地认为有理数理所当然地多於整数，而有理数又显然少於实数，因此把连续统假设证否。

Taking operation of rational numbers as the carrier, this paper starts the research right from the study on multiplication of decimal, division of fraction and multiplication of rational numbers and studies the "understanding levels of operation of rational numbers and the teaching and learning strategies that matches them."

本论文以有理数运算作为载体，选取小数乘法、分数除法和有理数乘法作为研究的切入点，研究了&有理数运算的理解水平及其教与学的策略&，具体说来，研究了3个问题：(1)学生对有理数运算的理解达到怎样的水平；(2)学生达到某种理解水平的原因是什么；(3)基于学生的理解水平，有效的教与学的策略是什么。

It is also known as one of the most poisonous naturally occurring substances.

它也被称为一个最自然发生的有毒物质。

The greatest stress is found at the location on the cross section where V is the largest.

最大应力出现在横截面上V为最大的地方。