数学英语句子翻译
2.1
1. 数学来源于人类的社会实践，包括工农业的劳动，商业、军事和科学技术研究等活动。
Mathematics comes from man’s social practice，for example，industrial and agricultural problem，commercial activities《海底两万里》读后感，military operations and scientific and technological rearches.
2. 如果没有运用数学，任何一个科学技术分支都不可能正常地发展。
No modern scientific and technological branches could be regularly developed without the application of mathematics.
3. 符号在数学中起着非常重要的作用，它通常用于表示概念和命题。苏醒的近义词
Notions are a special and powerful tool of mathematics and are ud to express conceptions and propositions very often.
4. 17世纪以前，人们局限于初等数学，即几何、三角和代数，那时只考虑常数。
Before 17th century, man confined himlf to the elementary mathematics, i.e., geometry, trigonometry and algebra, in which only the constants were considered.
5. 方程与算术的等式不同在于它含有可以参加运算的未知量。
6. 方程又称为条件等式，因为其中的未知量通常只允许取某些特定的值。
An equation which is true only for certain values of the unknown quantities is also called an equation of condition.
7. 方程很有用，可以用它来解决许多实际应用问题。
Equations are of very great u and we can u it in many mathematical problems.
8. 解方程时要进行一系列移项和同解变形，最后求出它的根，即未知量的值。
To solve an equation means to find the value of the unknown term stands alone on one
2.3
9. 由于小于10且能被3整除的正整数组成的集是整数集的子集。
The t consisting of tho positive integers less than 10 which are divisible by 3 is a subt of the t of all even integers less than 10.
10. 如果方便，我们通过在括号中列举元素的办法来表示集。
When convenient, we shall designate ts by displaying the elements in braces.
11. 用符号 表示集的包含关系，也就是说，式子A B表示A包含于梦见被骗了钱B。
The relation is referred to as t inclusion. And we write A B whenever every element of A also belongs to B.
12. 命题A B并不排除B A的可能性。
The statement A B does not rule out the possibility that B A.
13. 基础集可根据使用场合不同而改变。
The underlying t may vary from one application to another.
14. 为了避免逻辑上的困难，我们必须把元素x与含有元素x的集｛x｝区分开来。
To avoid logical difficulties, we must distinguish between the element x and the t {x} who only element is x.
15. 图解法有助于将集合之间的关系形象化。
Diagrams often help us visualize relations between ts.
貂蝉和吕布的故事16. 定理的证明仅仅依赖于概念和已知的结论，而不依赖于图形。
种植致富好项目
Proofs of theorems must rely only on the definitions of the concepts and known conclusions and not on the diagrams.
2.4
17. 严格说，这样描述整数是不完整的，因为我们并没有说明“以此类推”或“反复加1”的含义是什么。
Strictly speaking, this description of the positive integers is not entirely complete becau we have not explained in detail what we mean by the expressions “and so on”, or “repeated addition of 1”.
18. 两个整数的和、差或积是一个整数，但是两个整数的商未必是一个整数。
The sum, difference, or product of two integers is an integer, but the quotient of two integers need not be an integer.
19. 这种用几何来表示实数的办法对于帮助我们更好地发现与理解实数的性质是非常有价值的。
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This device for reprenting real numbers geometrically is a very worthwhile aid that helps us to discover and understand better certain properties of real numbers.
补天浴日
20. 几何经常为一些特定的定理提供证明思路（建议），而且，有时几何的论证比纯分析的（完全依赖于实数公理的）证明更清晰。
The geometry often suggests the method of proof of a particular theorem, and sometimes a geometric argument is more illuminating than purely analytic proof(one depending entirely on the axioms for the real numbers).
21. 一个由实数组成的集若满足如下条件则称为开区间。
A t of real numbers is called an open interval if it satisfies the following two conditions.
22. 实数a是-a的相反数，他们的绝对值相等，且当a≠0时，其他符号不同。
The real number is the negative of –a. Their absolute values are equal and their signs are not same when a≠0.
23. 每个实数刚好对应着实轴上的一点，反之，对实轴上的每一点，有且只有一个实数与之对应。
Each real number corresponds to exactly one point on this line and, converly, each point on the line corresponds to one and only one real number.
24. 在几何上，实数之间的次序关系可以在数轴上清楚地表示出来。
The ordering relation among the real numbers has a clear geometric interpretation on the axis.
2.5
25. 计算图形的面积是积分的一种重要应用。
One of the applications of the integral is the calculation of area.
26. 在x-轴上O点右边选定一个适当的点，并把它到O点的距离称为单位长度。
On the x-axis a convenient point is chon to the right of O and its distance from O is called the unit distance.
27. 对xy-平面上的每一个点都指定了一个数对，称为它的坐标。
Now each point in the plane (sometimes called the xy-plane) is assigned a pair of numbers, called its coordinates.
28. 选取两条互相垂直的直线，其中一条是水平的，另一条是竖立的，把它们的交点记作北京省0，称为原点。
Two perpendicular reference lines (called coordinate axes) are chon, one horizontal (called the “x-axis”), the other vertical (the “y-axis”).
29. 当我们用一对书（a,b）来表示平面的点时，商定要把横坐标写在第一个位置上。
When we write a pair of numbers such as (a,b) to reprent a point, we agree that the abscissa or x-coordinate , a , is written first.
30. 微积分与解析几何在它们的发展上已经互相融合在一起。
Throughout their historical development, calculus and analytic geometry have been intimately intertwined.
