出三个题考考吧友的数学能力：
（1）1除以0等于几？
1/0 = ?
（2）任何非0数除以0等于几？
X/0 = ? (其实X不等于0)
（3）0除以0等于几？
0/0 = ?
答不出来，小学不过关呦

小学定义证明法：
（1）任何非0的数除以0是不存在的；因为a X 0 = 0; 任何数乘以0只能等于0； a X 0 不能等于 a (如果a 不等于0）。 所以a/0 = 不存在的。 也就是小学数学老师说的无意义。
（2）同理任何数乘以0等于0. 所以0/0 = 任意数。 这是一个无穷尽的集合。 可以是1， 可以是0， 可以是1和0； 可以是1，2，3， 也可是无穷尽。。

我们小学老师说0不能做分母原因是： a/0 = 不存在； 而0/0=任意数 违背了商是唯一性原则。注意，四则运算中的除法运算有个人定义的性质就是商是唯一的，而0/0违背了这一点。所以老师才说无意义。

总之，
(1) a/0 = 不存在，未定义，也无意义；
（2）0/0 = 任意数，一个不定式无穷尽的集合

想看高等数学证明，自己百度吧。哈哈。

@静候轮回_

你说的正高阶无穷大是早起婆罗摩笈多尝试，现已证明是错误的。

婆罗摩笈多（598–668年）的著作《Brahmasphutasiddhanta》被视为最早讨论零的数学和定义涉及零的算式的文本。但当中对除以零的论述并不正确，根据婆罗摩笈多，“一个正或负整数除以零，成为以零为分母的分数。零除以正或负整数是零或以零为分子、该正或负整数为分母的分数。零除以零是零。”
830年，摩诃吠罗在其著作《Ganita Sara Samgraha》试图纠正婆罗摩笈多的错误，但不成功：“一数字除以零会维持不变。”
婆什迦罗第二尝试解决此问题，设，虽然此定义有一定道理，但会导致所有满足该条件的n值都相同的悖论。

不想钻研的只需要理解

In ordinary (real number) arithmetic, the expression has no meaning, as there is no number which,multiplied by 0, givesa (a≠0), and so division by zero is undefined

Since any number multiplied by zero is zero,the expression 0/0 has no defined value and is called anindeterminate form.

最简易的理解方法：

Division as the inverse of multiplication

The concept that explains division in algebra is that it is the inverse of multiplication. For example,


since 2 is the value for which the unknown quantity in


is true. But the expression


requires a value to be found for the unknown quantity in


But any number multiplied by 0 is 0 and so there is no number that solves the equation.
The expression


requires a value to be found for the unknown quantity in


Again, any number multiplied by 0 is 0 and so this time every number solves the equation instead of there being a single number that can be taken as the value of 0/0.

In general, a single value can't be assigned to a fraction where the denominator is 0 so the value remains undefined (see below for other applications). 0/0 is known as indeterminate.

这些给想钻研的阅读

Extended real line

At first glance it seems possible to define a/0 by considering the limit of a/b as b approaches 0.
For any positive a, the limit from the right is


however, the limit from the left is


and so theis undefined (the limit is also undefined for negative a).
Furthermore, there is no obvious definition of 0/0 that can be derived from considering the limit of a ratio. The limit


does not exist. Limits of the form


in which both ƒ(x) and g(x) approach 0 as x approaches 0, may equal any real or infinite value, or may not exist at all, depending on the particular functions ƒ and g (see l'Hôpital's rule for discussion and examples of limits of ratios). These and other similar facts show thatthe expression 0/0 cannot be well-defined as a limit.

Formal operations

A formal calculation is one carried out using rules of arithmetic, without consideration of whether the result of the calculation is well-defined. Thus, it is sometimes useful to think of a/0, where a ≠ 0, as being. This infinity can be either positive, negative, or unsigned, depending on context. For example, formally:


As with any formal calculation, invalid results may be obtained. A logically rigorous (as opposed to formal) computation would assert only that


Since the one-sided limits are different, the two-sided limit does not exist in the standard framework of the real numbers. Also, the fraction 1/0 is left undefined in the extended real line, therefore it and


aremeaningless expressions.

The setis the real projective line, which is a one-point compactification of the real line. Heremeans an unsigned infinity, an infinite quantity that is neither positive nor negative. This quantity satisfies, which is necessary in this context. In this structure,can be defined for nonzero a, and. It is the natural way to view the range of the tangent and cotangent functions of trigonometry: tan(x) approaches the single point at infinity as x approaches eitherorfrom either direction.

This definition leads to many interesting results. However, the resulting algebraic structure is not a field, and should not be expected to behave like one. For example,is undefined in the projective line.

The setis the Riemann sphere, which is of major importance in complex analysis. Here toois an unsigned infinity – or, as it is often called in this context, the point at infinity. This set is analogous to the real projective line, except that it is based on the field of complex numbers. In the Riemann sphere,, butis undefined, as is.Extended non-negative real number line

The negative real numbers can be discarded, and infinity introduced, leading to the set [0, ∞], where division by zero can be naturally defined as a/0 = ∞ for positive a. While this makes division defined in more cases than usual, subtraction is instead left undefined in many cases, because there are no negative numbers.

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