Zero

Nylex

I thought it was undefined.

Yes it is undefined, as is anything /0.

Basically the reason for this is that many functions have an 'answer' for when the function returns something/0.

An example is the 'sinc' function - this is (sin(x))/x=sinc(x)

when x=0 sinc(x)=0/0 but in this case sinc(0)=1.
f(x)=sin(2x)/x will have a different value for when x=0. (I think but it might actually =1 as well now that I think about it).
But anyway, 0/0 cannot be defined as a value because it depends on the function.

Hope this mindless jibbering helps someone.

Reply 3

elpaw

15

davey_boy

when x=0 sinc(x)=0/0 but in this case sinc(0)=1.
f(x)=sin(2x)/x will have a different value for when x=0. (I think but it might actually =1 as well now that I think about it).

i think it's 2 (if you use l'hopital's rule, = 2cos(x)/1 = 2)

Reply 4

elpaw

i think it's 2 (if you use l'hopital's rule, = 2cos(x)/1 = 2)

Yep I'd go along with that - I have to learn to trust my instincts.

Reply 5

Hoofbeat

OP

davey_boy

Yes it is undefined, as is anything /0.

But I thought anything divided by zero was infinity? Or is it undefined?

Reply 6

Hoofbeat

But I thought anything divided by zero was infinity? Or is it undefined?

But infinity is undefined... I think at any rate.

Reply 7

GH

13

1) Whats this "Flysoc" in your sig?

2) Lets not get into an argument just yet. Let the warm wisdom of Fermat bathe over us like the sun.

Reply 8

material breach

12

Hoofbeat

But I thought anything divided by zero was infinity? Or is it undefined?

infinity could be an number and every number as far as i understand and thus is undefined

Reply 9

2776

1) Whats this "Flysoc" in your sig?

2) Lets not get into an argument just yet. Let the warm wisdom of Fermat bathe over us like the sun.

1) "Flysoc" appears as "Fyzsoc" in my browser which is a shortened (maybe perhaps 'wacky' or even 'zany') version of the "Physics Society" that appears in your signature.

2) Why not? Got to think by yourself every now and again. :wink:

Reply 10

john !!

Hoofbeat

But I thought anything divided by zero was infinity? Or is it undefined?

It's just undefined. Picture y=1/x. At x=0, is y equal to infinity? Or negative infinity? Two such seperate numbers can't be the same, which is one reason division by 0 is undefined.

Or think of a curve x=4. What is the gradient? The x-value of the curve is independant of y, so again it might seem like infinity, but it's not.

Different things point to different answers. Basically you have to avoid it.

Reply 11

DC_1234

x/x = 1 where x does not equal 0, E or something else I can't remember.

Reply 12

john !!

Although yesterday I did realise:

the line x=m
can be written
x=my^0
differentiated,
dx/dy = 0
and then the gradient (equal to 1/(dx/dy))
dy/dx = 1/0

so no matter what the line is, as long as y is independant the gradient is always 1/0, and therefore undefined. :cool:

Reply 13

elpaw

15

mik1a

Although yesterday I did realise:

the line x=m
can be written
x=my^0
differentiated,
dx/dy = 0
and then the gradient (equal to 1/(dx/dy))
dy/dx = 1/0

so no matter what the line is, as long as y is independant the gradient is always 1/0, and therefore undefined. :cool:

you dont need to put y^0 in, because dx/dy of a constant is 0 anyways.

Reply 14

fishpaste

I think I can show a contradiction from 0/0 being defined

Assume 0/0 is defined

x = 0/0 ---(*)

1/x = 0/0

x = 1/x

x^2 = 1

x = +/- 1 ---(+)

(as if that wasn't ambiguous enough), then consider (*) again, multiply both sides by 2

2x = 0/0 = x => x = 0
but this contradicts (+) which says that 2x = +/- 2

=> 0/0 must be undefined.

I think I've read that it's not absolutely criminal to select a value for 0/0 for some very practical situations though, as its value won't be ambiguous confined to that problem. But it's not the sort of thing you're ever going to want to write on your exam papers ever I'd imagine =P

Reply 15

Fermat

8

Division by zero is (defined as) undefined. Hence, zero/zero is undefined.

As for infinity, here's my opinion, and I think it's right.
Infinity is not a number. It is a mathematical and/or philosophical concept.
You can't do arithmetic with infinity.
In other words you can't do "infinity + 1 = infinity" because infinity isn't a number.
Whren you do things like that it's just to give the idea that infinity is (like) a very large number!
You can only do mathematical arguments using the concept of infinity provided you don't actually do arithmetic with it.

For example, f=1/x
The simple way of saying it is: when x = infinity, then f=0. The mathematical argument is: as x tends to infinity f tends to zero.
It can be simpler, and easier to underdstand, dealing with infinity as a very large number rather than as a mathematical concept that infinity is an entity of unlimited bounds - or something like that!

Another example, f=sinx/x
You can't let x=0 here because division by zero is undefined. What you can do though is to say that,
The limit of f as x tends towards zero is 1.

Reply 16

figgetyfig

2

I know this sounds stupid, but isn't anything divided by itself one?

I'm guessing some of your maths rules that I dont understand rules override that. I just thought I'd put in the thick person's contribution.

Reply 17

Hoofbeat

OP

Thanks for everyone's replies. It's been very interesting to read your thoughts and I always knew I could count on Fermat to say something! :smile:

The reason this all got started was when I was having to find an equation of a tangent on a curve and at that particular point dy/dx=-17/0 ie. dy/dx=infinity. And that got me thinking, as any no. divded by zero is infinity, what is zero divided by itself? So then I lay in bed thinking about this and after an hour I got up and got a calculator just to see what 0/0 gave. Then after about another hour I drifted off to sleep but kept thinking about it all night. Then in the morning in assembly I thought well 1 x 0 =0, so if you re-arrange it that gives 0/0 = 1. However, then realised that was a terrible proof as 5 x 0 = 0, so did that mean 0/0=5 etc etc. So asked my maths teacher and he just laughed at me asking silly questions and then my mate asked what infinty divided by infinity was! lol Anyways, so that's how this whole discussion came about. Sad really i known! I really must get a life! oh well! lol :smile:

Reply 18

Hoofbeat

OP