Linked Questions

I have looked through some of the previous questions posted on this topic, and I think mine is different. Is there a flaw in defining division by zero? For example, define $\frac{a}{0} = \infty_a$ ...

In regular math, you cannot get the square root of a negative number. Likewise, you cannot divide by zero. Both dividing by zero and taking the square of a negative have no place in real life. ...

Why can't you divide a number by zero? It is possible to say $\sqrt{-1}$ is an imaginary number $i$, but why can't you say $\frac{1}{0}$ is also an imaginary number $z$ (for example)?

Is there any way of treating $\frac{1}{0}$ without breaking maths? I tried just the variable $\lambda$, thinking that it would be easy to manipulate: $$\frac{2}{0} = 2\cdot\frac{1}{0} = 2\lambda$$ But ...

The number $i$ is defined as a solution to the equation $x^2+1=0$. How come no one has yet defined a number $j$ as a solution to the equation $\frac{1}{x}=0$? The purpose of course is to be able to ...

Why 0/0= undefined? We always write $0/x\in\mathbb R$, where $x \in\mathbb{R}\setminus\{0\}$, and this $0/x = 0$. Again $x/0$ is always undefined. Now when it's about $0/0$ why we don't follow the ...

Just out of curiosity, can we make illegitimate operations with $0$, say, division by $0$ legitimate simply by imposing additional axioms? If so, then what consequences may follow? If the answer is ...

So I thought... If $\frac00 = x$... then $0 = x\cdot0$... then $0x = 0$... then its technically possible to divide by $0$ again $\frac{0x}0 = \frac00$ ... since $\frac00 = x$ and $\frac{0x}0 = \...

Even though there is no real answer to the equation √-1, we give it the symbol i. What is the reason that there is a symbol for ...

Natural numbers are closed under addition and multiplication, but not subtraction. Fixed by... Integers are closed under subtraction, but not division. Fixed by... Rational numbers are closed under ...

As explained in the title, if i is used to simplify expressions involving the square root of a negative number, is there another concept which allows us to simplify expressions involving zero on the ...

So what is the problem/contradiction If I state I can divide by 0 but the number will be 0 I tried a few thing but didn't find a problem

I have seen multiple answers on the web, but I can't get my mind around why division by zero outputs an error and not zero. Can anyone explain this in laymen's terms?

I know that defining division by zero is not possible because it violates the zero product property we define, that is, $0\times a=0$ for every $a$. I wonder whether we can somewhat circumvent and ...

How can one prove the statement $$\lim_{x\to 0}\frac{\sin x}x=1$$ without using the Taylor series of $\sin$, $\cos$ and $\tan$? Best would be a geometrical solution. This is homework. In my math ...