为什么所有有理数都不是整数？
数字是用于测量或计算数量的数学值或数字。它由 2、4、7 等数字表示。数包括整数、整数、自然数、有理数和无理数等。在数系中，数有几种类型，如素数、奇数、偶数、有理数、整数等。这些符号和短语可以用来表达这些符号和词。像 40 和 65 这样的整数，当作为数字给出时，也可以写成 40 和 65。
数字系统有时称为数字系统，是表示数字和图形的基本基础。它是在算术和代数框架中表示数字的一种独特方式。
有理数和整数
有理数的形式为 p/q，其中 p 和 q 是整数，q 等于 0。由于数字的基本结构 p/q 形式，大多数人很难区分分数和有理数。当一个有理数被除法时，结果是十进制形式，它可能是结束的，也可能是循环的。有理数的示例有 3、4、5 等，它们可以用分数形式表示为 3/1、4/1 和 5/1。
整数是一类整数，包括所有正数、零和从负无穷到正无穷的所有负数。它不包括分数和小数。整数集由字母“Z”表示。 Z = 表示整数集。 -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, … 就是例子。
负数和正数集合中的数字（包括零）没有小数部分或小数部分。整数包括数字 -8、-7、-5、0、1、5、8、97 和 3,043。
整数类型
整数分为两种类型，
- 正整数：正整数是大于零的一。例如：1、2、3、4、5、6。
- 负整数：负整数是小于零的一。例如，-1、-2、-3、-4，……因此在这种情况下，零既不是负整数也不是正整数。它是一个偶数。 -8, -7, -5, -4, -3, -2, -1, 0, 1, 2, 3,... 是示例。
为什么所有有理数都不是整数？
回答：
Rational numbers are not integers because as per their definition. Integers are a class of integers that include all positive counting numbers, zero, and all negative counting numbers that count from negative infinity to positive infinity. It does not include fraction and decimal. The set of integers can be represented as Z = …,-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5,…
Rational numbers have the form p/q, where p and q are integers and q equals zero. Most people have difficulty distinguishing between fractions and rational numbers because of the underlying structure of numbers, p/q form. They can be expressed in fraction and decimal form as 3/1, 4/1, and 5/1, 8.99, 0.90…
Therefore Rational numbers includes all fractions and decimals whereas integers does not include fractions and decimals value only include set of positive counting numbers.
Hence Rational numbers are not integers. Examples of numbers which are rational as well as integer: 2, 3, 4, 56, 88, 89, …
示例问题
问题1：以下数字的身份，这些数字既是有理数又是整数？
7.88, 6, 3/4, 1890, 65.8989
回答：
Here 6 and 1890 are both rational and integer numbers as it can be written as 8/1, 1890/1.
And 7.88, 3/4, 65.8989 are only rational numbers .
问题2：从以下数字中识别整数？
75、88.09、4/9、1898、-4、-878
解决方案：
Integers are the set of numbers including all the positive counting numbers, zero as well as all negative counting numbers which count from negative infinity to positive infinity. The set doesn’t include fractions and decimals.
Hence 75, 1898, -4, -878 are integers.
问题3：5.89是有理数还是无理数？
回答：
Here, the given number, 5.89 can be expressed in the form of p/q as,
5.89 = 589/100
Hence, 5.89 is a irrational number.
问题 4：确定 8.44848… 是有理数还是无理数。
回答：
Here, the given number 8.44848… is an irrational number as it has non terminating and non recurring digits. Observing the digits after the decimal, they are neither terminating nor recurring.
问题5：判断√4×√4的乘积是有理还是无理？
解决方案：
Given: √4 × √4 both are irrational numbers but it is not necessary that the product of two irrational number will be irrational.
Therefore √4 × √4 = √16
But here square root of 12 is 4… which is terminating after decimal.
Hence the product of √4 × √4 is rational.