数字种类第1节50%英语版本：整数与自然数

知识点：数字都有哪些分类和包含关系。

学习目标：了解整数的概念，了解自然数的概念。

数学双语学校课程 

同学们好！今天我们来讲一下数字的种类！
Hello everyone, today we are going to talk about types of numbers.
首先，让我们来思考一下，学习数字的种类有什么用途呢？
First of all, let’s think about one question. Why we need to know the types of numbers?
我们都知道，数学作为一门科学和语言，是专门用数字和图像来认识世界的。
As we all know, Math, is a science and a kind of language, is specially working on how to understand our world by using numbers and graphs.
正因为如此，我们想要学习数学，就要和数字们成为最好的朋友。
That’s why we need to becomes best friends of numbers before we learn math.

日常生活中的数字 

在数学领域中，数字有很多的种类、头衔和名称。 There are many different types of numbers with different names.
Let me introduce you some of the types of numbers that we use very often.
现在让我来为大家介绍一些我们在课本和日常学习中最经常使用的数字的种类。

自然数 

我想自然数应该是所有小朋友们接触最多的数字种类了。 I guess Natural Numbers should be the most popular type we use in daily life and study.


It is whole numbers from 1 and up. Please note, the concept of Natural Number in China is a little different from foreign country. The Number zero 零， is included in Natural Number in Chinese Math books, while it is not included by foreign countries.
自然数是指正整数和零的统称。在这里同学们需要注意的是，自然数的概念在中国的教科书中是包括零的，然而在国外，自然数是不包括零的。


Normally, we also cal Natural Numbers the counting numbers, which means we use them very often when we count things.
自然数其实就是我们日常生活中统计数量时所使用的数字，也就是英文中所说的counting numbers.我们在数数的时候，基本一直都在使用自然数！

整数 

As we know Natural Numbers are all Whole Numbers, 整数。 也就是说，所有我们日常生活中所使用的自然数，其实都是整数。然而，整数又可以分为正整数，负整数和零。
The Whole Numbers also can be separated into Positive Whole Numbers, zero, and Negative Whole Numbers.


And normally in foreign countries, Positive Whole Numbers and zero are Named The Whole Numbers, while Positive Whole Numbers are Named Natural Numbers, and Positive Whole numbers, Negative Whole Numbers and zero are called Integers.
在国外，数字的分类和中国略有不同。让我们先来了解一下国外的数字分类体系吧！
在国外，正整数和零被统称为Whole Numbers; 正整数被统称为Natural Numbers; 正整数，负整数和零被统称为整数。
那么在中国，In China, We use Types of Number as Below 我们的归纳法为，正整数和零被统称为自然数，也就是Natural Numbers, Positive Whole Numbers and zero are called Natural Numbers; 正整数被称为正整数也就是Whole Numbers, Positive Whole Numbers are called Whole Numbers; 而正整数，负整数和零统称为整数，也就是Integers, Positive Whole numbers, Negative Whole numbers and zero are called Integers.


Anyway, Whole Numbers include Positive Numbers and zero which are with no fractional or decimal part. Cannot be negative.总的来说，正整数也就是我们小学所说的整数，其实是指的正整数和零，它们是没有小数和分数部分的数字，也就是说，它们的小数部分和真分数部分为零，因此在正常情况下，是省略不写的。


而真正意义上的整数，则指的是正整数，零，和负整数。
Integers are all whole numbers and their negative counterparts.

零是整数吗 

我们来举例说明一下。Let’s take some example.
在中国教科书的定义下：零既不是正整数，也不是负整数，它在整数概念中单独占有一席之位。也就是说，零是虽然整数，但是它既不是正整数，也不是负整数。同时，零也是自然数。
In China, zero is not a Positive Whole Numbers, also is not a Negative Whole Number, but it is a Integer. That’s means that although zero is a Integer, but it is neither a Positive Whole or a Negative Whole, it is a independent part of Integer alone.
At the same time, zero is also a Natural Number.


很好，同学们，今天我们详细的学习了国外与中国教科书中整数与自然数的数字分类体系中常见的分类模式，了解了它们有哪些不同之处，同时，我们也了解了如何使用中英文来表达这些数字种类的名称。
Perfect, today we talked about what’s the difference between Chinese and foreign number system for Whole Numbers, Integers, and Natural Numbers. We already know their Chinese name and English Names.


Next time, I’m going to show you more types of numbers which we use very often in our daily life and math books.
下一次，我会继续和同学们一起来了解更多数的种类，这些数种无论是在我们的日常生活中，还是我们的数学课本中，甚至是考试题中，都是屡见不鲜的。


Today’s math class is over, class dismissed, see you next time.
今天的课就到这里，我们下一次再会！