Division by zero

[brokenbin]

I think that any number divide by zero would equal to infinite. Here is how I think about it. Becaue of time dialation, light travels from one place to the other without taking anytime. So the speed of light would be C=x/0. Although the light speed as we know it is 300000 km/s, it is infinite due to time dialation. Therefore everything divided by zero would be zero. It sort of make sense.

[dan19_83]

When you divide by a small number e.g. (6/0.5) you get a larger number, 12. as the number get smaller under the line, the answer gets bigger and bigger until you eventually reach infinity. any number divided by zero is generally accepted as being infinity.

If the number above the line is negative then the answer just becomes -infinity.

[Callipygous]

When you divide by a small number e.g. (6/0.5) you get a larger number' date=' 12. as the number get smaller under the line, the answer gets bigger and bigger until you eventually reach infinity. any number divided by zero is generally accepted as being infinity.

If the number above the line is negative then the answer just becomes -infinity.[/quote']

 

 

thats only if your talking about limits. its not that the answer IS infinity, its "as x approaches 0, the answer approaches infinity." anything divided by zero is undefined.

[brokenbin]

Except 0 divided by 0, which would be either 0 or 1, unsure because. x/x always equals to one, but when the denominator is 0, i have no idea.

[Nicoco]

0/0 isn't defined if I'm correct. The same for 0^0.

[Dave]

There's loads of threads already on this. Have a look around before posting a new thread on it

[Johnny5]

There's loads of threads already on this. Have a look around before posting a new thread on it

 

Dave, I have a question. When using quaternions, can you divide by zero?

[matt grime]

No, of course not. Division by zero is not defined in any division ring for obvious reasons. Though why the quarternions?

[Johnny5]

No, of course not. Division by zero is not defined in any division ring for obvious reasons. Though why the quarternions?

 

Matt, do you know what a quaternion is?

 

Regards

[bascule]

How do you divide things into groups of nothing? You can claim there's infinite groups, but even with infinite groups of nothing you wouldn't have accomplished anything, as all are empty and what you originally tried to divide is still waiting to be divided. It's simply a physical impossibility...

[matt grime]

Matt' date=' do you know what a quaternion is?

 

Regards[/quote']

 

 

You are kidding, right?

 

But the question still remains: why did you ask about the quaternions in particular? I genuinely am curious as too why the quartenions should be different from any other division ring, for example, the reals.

 

 

Anyway, do you know what a division ring is?

 

Should I demonstrate I know about them? Ok, the unit quarternions and D_8 are the smallest groups with the same character table that are not isomorphic. OK?

[Johnny5]

Anyway' date=' do you know what a division ring is?

[/quote']

 

I don't know what a division ring is, why don't you tell me.

[ecoli]

are known as indeterminate, becasue we don't know whether they are 0, 1 or undefined.

[Johnny5]

are known as indeterminate' date=' becasue we don't know whether they are 0, 1 or undefined.[/quote']

 

Take a limit of something then you know.

[matt grime]

Ok, the reason why dividing by zero isn't allowed algebraically is becuase 0*x=0*y for all x and y. this holds in a division ring too, as well as a field.

 

a division rnig is one where for all non-zero elements x there is a y such that xy=1, it is a field if it is commutative (wrt *)

 

i just wondered what made you think of quaternions - the simplest example of a division ring that isn't a field.

[ecoli]

Take a limit of something then you know.

 

It doesn't matter if you take the limit... a situation like finding the limit as the function x/x approaches 0...you find what it approches, but not the actual value.

[Johnny5]

Ok, the reason why dividing by zero isn't allowed algebraically is becuase 0*x=0*y for all x and y. this holds in a division ring too, as well as a field.

 

Prove 0*x=0*y for all x and y.

[Johnny5]

a division rnig is one where for all non-zero elements x there is a y such that xy=1' date=' it is a field if it is commutative (wrt *)

[/quote']

 

[math] \forall x[ \neg (x=0) \Rightarrow \exists y [xy=1]] [/math]

 

A ring becomes a field, if it is commutative with respect to multiplication.

 

You left out the multiplication symbol.

 

[math] \forall x[ \neg (x=0) \Rightarrow \exists y [x*y=1]] [/math]

 

 

What are the axioms of a ring?

[jordan]

I looked up quaternions on mathworld (since this thread isn't going anywhere else), but I don't follow what that means. Could anyone explain it in simpler terms?

[Guest olaan]

I looked up quaternions[/url'] on mathworld (since this thread isn't going anywhere else), but I don't follow what that means. Could anyone explain it in simpler terms?

 

There is a rather nice entry for quaternions on Wikipedia.

 

-o

[matt grime]

You left out the multiplication symbol.

What are the axioms of a ring?

 

Yes, it is perfectly acceptable and very common practice to write the compositoin wrt to * as juxtaposition. In fact I can think of no one who uses * except in basic undergrad texts.

 

The axioms of a ring are easily googlable, wolfram will have them.

[Johnny5]

Why were quaternions invented, does anyone know?

 

Regards

[matt grime]

Hamilton upon noting that the complex numbers are a 2-d vector space over the reals (this isn't actualyl how he'd've stated it, but it is how we say it now) wanted to find a 3-dimensional version. HE struggled, then infamously, and probably apocryphally in a flash of insight saw that you need to make it 4-d, and the quaternions were born and he carved in to the underside of a bridge in dublin. there are 8-d things to called octonians, and even sedonions. thoguh you have to drop commutativity for the quaternions and associativity for the others.

 

We can show there is no 3-d version.