Linked Questions

10
votes
6answers
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 $\frac{a}{0} = \infty_a$ ...
6
votes
4answers
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. ...
5
votes
2answers
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)?
4
votes
4answers
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 ...
0
votes
2answers
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 ...
0
votes
2answers
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 ...
1
vote
3answers
132 views

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 ...
-7
votes
1answer
207 views

Does 0/0 = a new branch of numbers? Have I made a mistake in the equation? [duplicate]

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 = \...
0
votes
1answer
161 views

Why do we have a symbol for root of -1, but none for divide by zero? [duplicate]

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 ...
-2
votes
1answer
135 views

Are there number systems that fix divide-by-zero? [duplicate]

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 ...
-1
votes
2answers
67 views

If ‘i’was invented to take the square roots of negatives, why can’t we invent a concept to divide by zero? [duplicate]

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 ...
1
vote
1answer
58 views

A problem with 0/0=0 [duplicate]

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
-2
votes
1answer
28 views

Divison by Zero [duplicate]

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?
1
vote
0answers
35 views

Changing the zero product property and defining division by zero [duplicate]

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 ...
474
votes
25answers
163k views

How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?

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 ...

15 30 50 per page