Out of curiosity, if you took 0, and divided it by 0, what would you get? A number divided by itself gives you 1, a number divided by 0 is undefined, but 0 divided by a number gives you 0. So which one is it? Or is it neither of them?

It's undefined. Even using limits, it's undefined. Note that a non-zero devided by zero is infinity (using limits).

If 0 is null, then there is exactly 1 null part in zero.

Thats how I see it

How many times can you put nothing into nothing?

"Once" seems like the logical answer.

Division by zero is not possible, just thinking about. If i have nothing and divide it into nothing groups, what do i get? That statement is meaningless. I really dont feel like getting into the math, but in our ordinary number system (you can get funky and create a system where you can divide by zero), division by zero is meaningless and thus undefined.


Even with limits, 0/0 is an indeterminate form, there is simply not enough information to define the value, hence, it is also undefined


Zero and Null are two similar but different concepts.

That's not actually true, only when the denominator 0 refers to an infinitesimal and not 0 itself.

lim x->0 3/x = inf
lim x->0 3/0 doesn't exist

You solve for it by solving it as x approaches 0 from the left, and from the right. If the two answers are equal, then you can say that the limit where x=0 is the answer. I taught myself calculus in high school.

y = lim (x->0) (1 / x)
1 / -0.0001 = -10000

1 / 0.0001 = 10000

-10000 ≠ 10000

y = 1 / x
(-infinity, 0) & (0, infinity)

Yeah, the second part isn't REALLY using the limit.

Ahh but any number ^0 = 1.
And if you look at it logically, that means there are two trains of thought defending 0/0=1
Therefore, it is for most intents and purposes, 1.

No.

4/2 = 2 because 2*2 = 4
14/7 = 2 because 2*7 = 14
60/5 = 12 because 12*5 = 60

0/5 = 0 because 0*5 = 0
5/0 = not defined because no number times 0 = 5
0/0 = not defined because any number times 0 = 0

My Trigonometry teacher once said there was a way to divide zero by itself.

I would guess it requires an equation using imaginary numbers. There's no way reals could be involved.

It depends on what you're doing with it. For instance, in the equation (X^2/X), at X=0 the value is 0 if you take the limit. In sin(x)/x, however, the limit is 1. 0/0 by itself is undefined; it depends on what function and context it's being used in.

Imaginary numbers aren't involved. Just calculus

True zeros can never be divided. He was probably talking about limits, where what you divide are two expressions which fastly approach zero. And that can result in any value (inf, -inf, a number or undefined).

0 represents nothing. Simply therefore you cannot divide something by 0 because you aren't dividing by anything. 0 -diviby- 0 = 0. So if you don't get it... You have nothing, you divide by nothing <-thats important. So your dividing by nothing (same thing as not dividing) leaving you with the original value unaffected. Nothing, which is 0.

So that means 0/0 equals 0?

Just something to note, is that the imaginary number is the square root of -1.

stickynote, 0/0 is undefined.

And the square root of -1 isn't imaginary, it's a not real number.

What do you think imaginary means?

SQRT(-1) or i is called the imaginary unit, a complex number is basically a real number plus a multiple of i.

Division by zero is undefined in the complex number system as well as our real number system.