618 views

### What is the meaning of $\frac{0}{0}$? [duplicate]

I asked my teacher what is the real meaning of $\cfrac{0}{0}$, and the answer I got was "nobody knows". I can't leave this subject "as is". I need a decent explanation, at least an explanation to why "...
275 views

### Does $\frac{0}{0}$ really equal $1$? [duplicate]

If we agree that $\textbf{(a) }\dfrac{x}{x}=1$, $\textbf{(b) }\dfrac{0}{x}=0$, and that $\textbf{(c) }\dfrac{x}{0}=\infty^{\large\dagger}$, and let us suppose $z=0$: \begin{align*} z&=0&&...
4k views

### Can you show why zero divided by zero does not equal zero? [duplicate]

I was talking about division by zero with my discrete math instructor, and it was explained to me that dividing can be broken down into simpler terms, i.e: Consider 6 divided by 3. To reach the answer ...
132 views

### Why does $0/0$ have to be undefined? [duplicate]

Why can't it no be $\pm$ Infinity? If $x/1$ is $x$ then $x/0$ should be $\pm$ Infinity.
63 views

### Why is $0/0$ ot equal to $1$? [duplicate]

If $3/3=1, 2/2=1, 1/1=1$, then why is $0/0$ undefined? Why is it not $1$?
4k views

### Why is $x^0 = 1$ except when $x = 0$?

Why is any number (other than zero) to the power of zero equal to one? Please include in your answer an explanation of why $0^0$ should be undefined.
5k views

### What is a real number (also rational, decimal, integer, natural, cardinal, ordinal…)?

In mathematics, there seem to be a lot of different types of numbers. What exactly are: Real numbers Integers Rational numbers Decimals Complex numbers Natural numbers Cardinals Ordinals And as ...
19k views

### Can $\frac {100-100}{100-100}=2$?

\begin{align*} \frac{0}{0} &= \frac{100-100}{100-100} \\ &= \frac{10^2-10^2}{10(10-10)} \\ &= \frac{(10+10)(10-10)}{10(10-10)} \\ &= \frac{10+10}{10} \\ &= \frac{20}{10} \\ &= ...
1k views

### why 0=0 is not possible??

Hi one of my friend showed me one proof i.e. $1)$ $2^2 - 2^2 = 10 - 10$ $2)$ $(2+2) (2-2) = 5 (2-2)$ $3)$ dividing both sides by (2-2) $4)$ $(2 + 2) = 5$ I know this is wrong in first line as ...
171 views

### Does $1^i$ and $1^{\frac{0}{0}}$ also give $1$ again? [duplicate]

This is the property of Real number $1$ that, $1^n=1$ does this property only hold $\forall n \in \mathbb R$ or also $1^i=1$ and $1^{\frac{0}{0}}=1$ If it is; explain how? I think that it should ...
216 views

### is $\frac{0}{0}$ indeterminate or undefined? [duplicate]

I know in calculus the form $\frac{0}{0}$ is indeterminate.but if it is not calculus is it still indeterminate or undefined in the real number field? P.S. I know that $\frac{1}{0}$ is undefined ...
48 views

### Is $0 = 0^1 = 0^2 \times 0^{-1}?$ [closed]

Does the above equation follow? Conversely, can you say $0^2 \times 0^{-1} = 0^1 = 0$? I apologize if this is a stupid question but it just popped in my mind.