Division by Zero

X

Xeroc

Registered Member
I was just wondering...

I was talking with a friend of mine and he said division by zero could be defined!

He said just add a "number" (I'll just use # because he hasn't thought of a good name yet) and call it equal to 1/0!

so 1/0 = #
and # * 0 = 1!

I've heard people say this can't be done, I would like to know if anyone knows why this is the case? I don't see any problems with it, what is wrong:confused:
 
Your # is equal to infinity in most math classes.

Think of it this way. As the number you divide by gets smaller the answer gets bigger. 0 is basically infinitely small, so the answer will be infinitly large.
 
Then how would you define 3/0, which is the same as 3*(1/0) ?

If 1/0 =# then 3*(1/0) = 3*# or 3#

then 3# * 0 = 3.

but...

this is the same as 3 * # * 0 = 3

under the Commutative Law this can be written

3 *0 *# = 3

And then grouped by the Associative Law as

(3*0) * # = 3

0 * # =3

But you've already defined 0*# (or #*0) as equal to 1, so you get

1 = 3?!!

A contradiction.

(which is why division by zero can not be defined, because it leads to contradiction.)
 
Division is also counted subtractions.
To divide 6 by 3
6 - 3 = 3 count = 1
3 - 3 = 0 count = 2

To divide 6 by 0
6 - 0 = 6 count = 1
6 - 0 = 6 count = 2
...
You never can stop this, since result must be 0 or < 0 to stop.
 
Your # is equal to infinity in most math classes.
Click to expand...

Not quite. I had a physics teacher who insisted that undefined was equal to infinity, but it's not that simple, is it?

It's more an infinitely continuing series, if I understand the concept correctly.
 
You're physics teacher may have been trying to make a distinction between "undefined" and "undetermined".
 
Originally posted by Xev
It's more an infinitely continuing series, if I understand the concept correctly.
Click to expand...
Yeah... it's an infinite number of 0s followed by a number. When you start doing limits and stuff though you just take it as 0.
 
Originally posted by Persol
Yeah... it's an infinite number of 0s followed by a number. When you start doing limits and stuff though you just take it as 0.
Click to expand...

Y = X/0
Let a stupid machine do that and allow partial answers and you will get N until it runs out of bits and starts over, creating a saw tooth wave.

You might get one zero at the beginning, depending on the program in the machine.

You can make a smart machine that will detect 0 divisors and return anything you wish. That will lead to contradictions later.

My DIV machine returns 0.
So I guess it does limits.
 
Originally posted by hlreed
Let a stupid machine do that and allow partial answers and you will get N until it runs out of bits and starts over, creating a saw tooth wave.
I'm not seeing how you could get a saw tooth wave...

X/infinity->0
X/0->infinity

6/0 is not 0... it would tend towards infinity.
 
I already said that twice. I just said my own div machine I chose to emit 0 when it is told to divide by 0. Not much used by my robots.
 
Originally posted by hlreed
Division is also counted subtractions.
To divide 6 by 3
6 - 3 = 3 count = 1
3 - 3 = 0 count = 2

To divide 6 by 0
6 - 0 = 6 count = 1
6 - 0 = 6 count = 2
...
You never can stop this, since result must be 0 or < 0 to stop.
Click to expand...

This is going to sound corny but... that was the most beautiful
example possible. I understood before, but this makes it so much
clearer...

:p

It's beautiful... :D
 
YOu had proceeded as

1/0 = #
1 = #*0
This actually means

1/0 * 0 = #*0
1*[0/0] = #*0 .....By assaciative law in the Group of real numbers

i.e., 0/0 = #*0

Surely 0/0 is undefined so any one of the factors in RHS should be undefined.

Since Zero is defined your # must be undefined !

That leads to the fact that 'Division by Zero in undefined'
 
Try this way

:( YOu had proceeded as

1/0 = #
1 = #*0
This actually means

1/0 * 0 = #*0
1*[0/0] = #*0 .....By assaciative law in the Group of real numbers

i.e., 0/0 = #*0

Surely 0/0 is undefined so any one of the factors in RHS should be undefined.

Since Zero is defined, your # must be undefined !

That leads to the fact that 'Division by Zero in undefined' :)
 
there is a definition for this i believe, looky here --;

lim x/n = 0 and
n->Infinity

lim x/n = infinity
n->0
 
Look at what exactly?

Assuming that your x is a constant (at least does not depend upon n) then your limits are both true but that does NOT define infinity as a number nor does it say that "x divided by 0" is infinity.
 
can't we

just say that a number that is devided by 0 is not devided? Is 0 not infinitely small, but simply nothing. The difference between a quirk and a vacume.
 
Divide by 0

Janus58,

Hi again. This thread just made me realise something. In another thread I posted the "Origin of Existance" one of the challenges to the following was:

0---------->(+n)+(-n)

and n/0 = Inf.

The arguement was that "0" was and could never be actually nothing that it was always something.

That being the case then Infinity is also impossible. It seems some people like to have their cake and eat it too.

What is your take on that circumsatnce.
 
my take is

this has been WAY over thought. If you have 10 cats that have 0 homes to go in when it is cold and wet and it's raining: Guess what? 0 has meaning - and can still be nothing. I have known for quite some time that the human brain (mine too) has a very hard time in the concept of nothing. Can you picture seeing nothing? Not even black? Not many people can. To me 0 means no quantity. It is very easy to over think this. So I guess yes and no. Yes 0 has deep meaning, and no it does not have quantity.
 
I agree, overthought. Same works for infinity. If 0 is nothing (no quantity) then the inverse (or oppositve) of 0 is 0^(-1) which is 1/0. Without thinking mathematically about it, the opposite of no quanity is all quantity, which is infinity.

Its always difficult to think of infinity and it should be the same as the concept of 0. It is clear to me that anyting divided by zero is infinity. I still remember my grade 2 teacher teaching me division. eg. if it was 6 divided by 3 she would say "Okay how many times does 3 go into 6".

Whats different? How many times does 0 go into 1?? Infinity, you'll never get back to one.

hlreeds counted substraction idea was good.

eg. 6 / 3
6 - 3 first time
(Take the answer and subtract 3 again)
3 - 3 2nd time
When the answer is <0 or 0 stop.

Answer = 2
eg n / 3
n - 3 first time
(n-3) - 3 second time
[(n-3) - 3] - 3 3rd time

Continue until u get <0 or 0.
So 6/0
is 6 - 0 count 1
take the answer and subtract 0
6 - 0 count 2

As we can see we would continue forever thus infinity. Just trying to clarify hlreeds view. great way of explaining.
 
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