2k views

Defining division by zero [duplicate]

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 $\frac{a}{0} = \infty_a$ ...
5k views

Why does division by zero not have an imaginary number “option”? [duplicate]

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. ...
262 views

Dividing a number by zero [duplicate]

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)?
118 views

Treating $\frac{n}{0}$ as a constant? [duplicate]

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 ...
103 views

A solution to the equation $\frac{1}{x}=0$ [duplicate]

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 ...
507 views

Undefined cases of 0/0 [duplicate]

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 ...
Can we make illegitimate operations with $0$ legitimate by adding a few more axioms? [duplicate]
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 ...