Dividing By zero

can some one explain to me how it is (or is not) possible to divide by zero? i have had this conversation with many people and none of them could give a decent answer.

How can you divide nothing into nothing and get something from nothing?

Cheers!!!

"Division: 0/x = 0, for nonzero x. But x/0 is undefined, because 0 has no multiplicative inverse, a consequence of the previous rule; see division by zero. In the real numbers, for positive x, as y in x/y approaches 0 from the positive side, the quotient increases indefinitely toward positive infinity, but as y approaches 0 from the negative side, the quotient tends toward negative infinity."

Straight from Wikipedia.

I always look at division problems how I first learned them as a child.

Imagine having no toffees but 5 kids. Divide the sweets between the kids, and nobody gets any, obviously.

But if there is 5 toffees and no kids.. that would be 5 divided by 0. Obviously nobody gets any, because nobody is there.
Them 5 toffees just sit there. They don't disappear, or turn negative, or enter a parallel universe. They just sit there.
A pretty low-tech way of looking at it, but its clear at least.

now i have had people tell me that dividing by zero is possible, because zero cannot exists, as anything that exists cannot not exist. (if that makes any sense) so therefore, zero is just so small we cannot "comprehend' it, therefore we cannot divide by it.

what is your take on this?

Obviously, I would get the toffees, so this disproves the whole dividing by zero thing. I mean, come on, who's going to let 5 toffees just sit there undisturbed just because imaginative kids aren't there to devour them?

Originally posted by spaceweasle7
now i have had people tell me that dividing by zero is possible, because zero cannot exists, as anything that exists cannot not exist. (if that makes any sense) so therefore, zero is just so small we cannot "comprehend' it, therefore we cannot divide by it.

what is your take on this?

Zero is a representation of no quantity. It exists as a symbol, just as everything we write is a symbol. 1 is a symbol for quantity 1. You can "theoretically" divide by zero, but as stated above, the answer is undefined.

Technically, 0 doesn't exist.

The number 0 is the mathematicians' way of explaining a complete absence of whatever they're referring to.
Originally, when the Arabic numeral system was devised (ie numbers we use today) they used to leave a gap instead of writing a 0.

Of course, if your tried buying 300 camels by writing to someone, you might end up with 3, because thats all it looked like.
Hence the number 0.

Technically it does exist. Like I said, it is a symbol representing no quantity just as every letter and number are agreed upon symbols with agreed upon meanings. Otherwise the word "nothing" would not exist, which it clearly does.

[edit on 9-9-2008 by ninthaxis]

Nah.

I'd say it exists as a symbol to represent nothing, but technically, nothing can't exist, because by its own definition, it isn't there.

Or you could extrapolate that and say nothing exists, and your just a figment of your own imagination.

42!!!!

Originally posted by selfisolated
42!!!!

Do you mean 42 aforementioned toffees???? Because if you do, 42=0 as I just ate them all!!!

You have to realize the relationship between multiplication and division. Look at it this way, 10 / 2 = 5 because 5 x 2 = 10, right? But if 12 / 0 = n, that would mean that 0 x n = 12 and we know that isn't right.


However zero can be in the numerator (ie 0 / 5) because zero of something split into 5 stacks would still zero just like multiplying zero 5 times would still equal zero.

It's all about the relationship between multiplication and division.

ITT: Trolled by a /b/tard.

Originally posted by spaceweasle7
can some one explain to me how it is (or is not) possible to divide by zero? i have had this conversation with many people and none of them could give a decent answer.

Well how about you show us your formula to explain how it is possible to divide by zero. Maths and hence science must rely on certain assumptions or else it wouldn't work.

0 is the first number btw. It's 0-9, not 1-10.

When you make an array or hash in programming, which is a sequence of variables(hashes have key names), the first variable is indexed at 0.

So, if you make an array of animals (dog, cat, turtle, pig, horse) named animals. If you want to get the value of dog, you would grab the index of 0 from the animals array, not 1 - which would be cat.

@animals = (dog, cat, turtle, pig, horse);
animals[0] = dog;
animals[1] = cat;

etc. All counting starts at 0. People just don't count it because it represents having none of the item/whatever. But it is the first number.

You get use to it after awhile.

Dividing by Zero is not impossible for humans. It just represents a logical fault for computers.

Most computers cannot computer a divide by zero.

If you can't divide by zero but want to - make it up:

e.g. Anything divided by zero = "symbol formerly known as squiggle."

That's how negative numbers and sqr root -1 were invented

Originally posted by selfisolated
Them 5 toffees just sit there. They don't disappear, or turn negative, or enter a parallel universe. They just sit there.

That depends on the type of toffees.
If they were nutty toffees I agree.. BUT..
If they were caramel toffees they would indeed disappear..as soon as whoever was guarding them turned their back. ..They're my fave.


I like the explanation of..
"Into how many groups of 0 could you divide those five toffees.?"

It makes it a little more straightforward.


If toffees were used in school I'd have enjoyed maths a lot more.. and been a lot fatter

Originally posted by zephyrs
You have to realize the relationship between multiplication and division. Look at it this way, 10 / 2 = 5 because 5 x 2 = 10, right? But if 12 / 0 = n, that would mean that 0 x n = 12 and we know that isn't right.


However zero can be in the numerator (ie 0 / 5) because zero of something split into 5 stacks would still zero just like multiplying zero 5 times would still equal zero.

It's all about the relationship between multiplication and division.

I think this is the most illustrious explanation why calculators get upset and refuse to divide by zero. However, the calculator doesn't acknowledges the only option where a / 0 is possible, and that's the case when a = 0.

IF a x b = c THEN c / b = a

and therefore

IF 0 x 0 = 0 THEN 0 / 0 = 0

Any calculator returns the result of 0 x 0 but considers its algebraic reciprocal 0 / 0 as an erroneous entry. Why is it so?

My guess is that the result of 0 / 0 can be any number:

0 / 0 = 1 and 1 x 0 = 0
0 / 0 = 2 and 2 x 0 = 0
0 / 0 = 3 and 3 x 0 = 0

and so on.

I clearly remember one of my math teachers saying that borders the bounds of advanced calculus. Clearly remember.
Full of theoretical gobbledy gook I'm sure.
Mrs. Cantolon. God rest her soul.

[edit on 9/10/2008 by jpm1602]