One divided by zero.

Question

What is one(or any other number) divided by zero? I have tried to find this out, but the only answer I could think of is infinity, due to the fact that zero is worth nothing. Nothing can fit into anything infinite times, so this is my logic. I repeat: What is one (or any other number) divided by zero?

take a look here. In the standard algebraic structure of $\Bbb R$ the division by zero is not defined. — Masacroso, Aug 01 '17 at 00:35
It's undefined. It just doesn't really mean anything by itself. — AJY, Aug 01 '17 at 00:35
Division by zero is impossible - division is the inverse operation of multiplication. There is no number that multiplied by zero is one. — smb3, Aug 01 '17 at 00:35
$\frac 10$ is undefined. For any real number $x \neq 0,;; \frac x0$ is undefined. — amWhy, Aug 01 '17 at 00:35
We have that $$\lim_{x\to 0^+}\frac{1}{x}=\infty$$and$$\lim_{x\to 0^-}\frac{1}{x}=-\infty$$however, $\frac{1}{0}$ is undefined. — Dave, Aug 01 '17 at 00:40

score 1 · Answer 1 · answered Aug 01 '17 at 00:35

It's undefined. Division by zero leads to different contradictions in math so many have chosen to simply leave it as undefined. See this Wikipedia article, division by zero is "meaningless" and "undefined".

It is often confused to be infinite, because $\frac 1 x \to \infty$ as $x\to 0$ or if we defined division on $a\div b$ as the number of times you subtract $b$ from $a$ to get to $0$. Both of these cases produce infinite results, however division is defined as inverse multiplication, which makes division by zero meaningless.

score 1 · Answer 2 · answered Aug 01 '17 at 00:35

There are lots of questions on this site about division by zero.

Here is the answer that I find best.

The definition of "$1/x$" is "the number you multiply $x$ by to get $1$ for an answer". Since there is no such number when $x=0$, the expression $1/0$ is meaningless.

This definition works nicely when you get to modular arithmetic.

score 1 · Answer 3 · answered Aug 01 '17 at 00:36

$$1 \div 0$$

It is undefined.

So we define division based on multiplication. We define

$$a = b \div c$$

If we could find a unique value $a$, such that $$a \times c =b$$

And you'll find in the case of $1\div 0$, there is no such value exists, because every value multiply by $0$ is $0$, but can never be $1$.

One divided by zero.

3 Answers3