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.

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. 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.

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...
[b]
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.

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

so 0 groups of six is 6. How is that the case?

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'

:( 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' :)

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.

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.

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.

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.

SciBoy,

This process seems to yield "Infinite" number of divisions of a "Finite" number.

You still have a "Finite" quanity that is being divided an "Infinite" number of times. That does not seem to indicate "Infinite" base quantity.

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.

NO, this idea of Absolute Nothing(or being exclusive of existence) is a paradox. For, there is no THING that can be exclusive of existence. And any THING that can be descibed, imagined or conjured has its place as a possbility. No thing can BE exclusive of existence, because the word "BE" is defined as "existing as".

So it is an outright contradiction to say something can truly be this paradoxical Absolute Nothingness.

A=Some thing
B=Not that thing

A=1
B=0

As for this....



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.

0/6 then????

ChrisCunningham,

I think it is a misapplication of the term "Be". I would not so describe "0", zero or nothing.

But Nothing I believe does exist beyond the mathematical.

While it may not yet be undestood the folloiwng mathematical expression offers the origin of Everything from Nothing:

1 - 0---------->(+n)+(-n) creation from nothing to something

2 - (+n)+(-n)-------->0 Returning something to nothing.

You do not see "Be" stated nor implied here. It is a mathematical proposition which holds the key to our existance without invoking Gods or Miracles.

We simply need to continue to find how that is jpossible since it appears that is how the Universe works.

Before you answer let me suggest you explore "Particle Entanglement" and the "Chiral Condensate" studies.

They strongly suggest the above formulation.

The Big Bang relates to a singularity (0) becoming the universe, case number (1) above.

Black Holes returning matter and energy from something to a singularity or "Something back into Nothing", case (2) above.

The sequence of numbers 1 + -1 + 1 + -1...
is not even a number! The reason is that the sequence doesn't converge... this means that because we can't determine if the final number is a 1 or a 0 then we can't give the number any value. To clarify the point you were trying to make because I found it hard to read... 1 + -1 + 1 + -1... is the same as saying (1 + -1) + (1 + - 1)... or 1 + (-1 + 1) + (-1 + 1). Which is true although none of those three sequences are actually even numbers.
Hope that isn't too hard to handle because it sounded important to you.

Cybermorphic,

The sequence is simply + and - any equal number. That is the purpose of (n). It isn't a series for convergence. It is infact a divergence from 0 into opposite enities.

Something from Nothing mathematically.

A series that is plus and minus any equal number is not divergent. Divergent means that at the end of that infinite sequence you have a infinite number. Convergent means they are finite. If you add a number n and then subtract it by n on to infinity it will not converge or diverge but is called non-convergent because the final value is not a finite number or an infinite one. Thats a math fact for your series, and the fact is that series does not have a mathmatical value because it is non-convergent. I'm not going to say it again, corect me if I don't understand your series.

n + -n + n + -n + n.... like so.
Or you could say... 0 + n + -n + n + -n + n...
If this is the case, no it doesn't equal anything.
I would like to hear your reasoning for why it does equal something and make the universe!
Are you saying that the a great addition created the universe and where the addition came from is a mistry then a great subtraction destroyed the universe again a mistry and the pattern keeps repeating again and again?

When we think of division of two numbers we tend to get a single number back. 20/4 = 5 (note: 20/4 does not equal -5)*. However consider the following sequence...

1/(1) , 1/(1/2), 1/(1/3), 1/(1/4),..., 1/(0)
= 1, 2, 3, 4,..., +infinity

In this simple demonstration we find that as the fractions in the denominator are getting smaller and smaller. They will continue to do this forever. The quotient (1, 2, 3, 4,...) will continue to get larger as long as the denominator continues to get smaller. In fact it will go to infinity, there is nothing stopping it. Since infinity is not a number and there is no such number to represent infinity the limit of the sequence is undefined (ie. no such number to represent it).

But lets say there is such a number that represents infinity. Infinity would equal 1/0. Now lets change the sequence to...


1/(-1) , 1/(-1/2), 1/(-1/3), 1/(-1/4),...1/(-0)
= -1, -2, -3, -4,... - infinity

Once again the denominators are going to zero (but this time from the negative side). However this time the quotients are going to negative infinity!!

So the question becomes which would we assign to 1/0? +infinity or -infinity?

Obviously we can't choose both (see *) we tend to say 1/0 is undefined.

Cheers. Ben

Originally posted by Shawn34m
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.

thus, do blind people see nothing, or do they see everything?

oh, and can division by zero be valid for a single case? 0/0 = 1 ?

0/0 is called an indeterminate form

0/0 would equal 1 right? :m:

No, 0/0 is "undetermined" just as "On Radioactive Waves" said!

We cannot say that 1/0= x for any number x because that is the same as saying 1= 0*x which is not true for any x. That's why we say "1/0 is undefined".

With 0/0 it's the opposite problem. 0/0= x is the same as saying
0= 0*x which is true for EVERY x. Certainly 0= 0*x so we COULD say 0/0= 1 but 0=0*2 is also true. Why not 0/0= 2?

This is the situation we call "undetermined".

yet before, any number divided by 0 would be classified as 'undetermined'. 0 is not a number, and therefore cannot be used in division. Just as infinity or negative numbers, it cannot be interpreted by the human mind or used in any probable situation. :m:

Originally posted by hotsexyangelprincess
0 is not a number, and therefore cannot be used in division.

of course zero is a number, and of course it can be used in division.

heres an example:

0/7 = 0


(x+0)/7=x/7=x/(7+0-0+0+(0x/7))

whats so hard about that?

Cybermorphic,

I think you have misunderstood my meaning here:


[quote]
0-------(+n)+(-n)
The sequence is simply + and - any equal number. That is the purpose of (n). It isn't a series for convergence. It is infact a divergence from 0 into opposite enities.
Something from Nothing mathematically.[unquote]


I did not mean a sequence of +,- operations were divergent only that "n" meant one could have divergent quantities +/- around "0". That is different magnitudes of +/-.

Try this one:

1 - Start with an identity: a=b
2 - Multiply both sides by variable "a": a^2=a*b
3 - Subtract b^2 from both sides: a^2-b^2=a*b-b^2
4 - Factor both sides: (a-b)(a+b)=b*(a-b)
5 - Cancel the common term: a+b=b
6 - But a=b, so: b+b=b
7 - Divide both sides by b: 2=1

if a=b then a-b = 0 ; step 4 is nothing but 0 = 0 .;)
in effect multiplying by 'a' and subtracting b^2 both sides of a=b already yielded 0. no nedd to have steps 4,5,..

I said that you may be able to divide a number into 0, but not able to see how many 0 in a number. So, 0/7=whatever, but 7/0=undeterminable. :m:

Everneo,

Close, a-b is 0 but if you carry out operation rather than cancel like factors you divide by 0 and the results becomes 2 Inf = 1 Inf.

step 7 divide by Inf (cancelling like terms) still yields 2 = 1

Originally posted by CHRISCUNNINGHAM
0/6 then????

Coming back to counted subtractions...

In this case your answer that you carry forward is already 0<= and <1. So then you have no counts. Which is clearly the answer. 0. (ie. you stop counting subtractions when your answer you bring forward 0<= and <1). Once again hlreed, great way of explaining!

So the question becomes which would we assign to 1/0? +infinity or -infinity?

I liked this idea by oxymoron. Seems true. Since 0 has no quantity it is neither + or - and hence when we divide something by 0 its could be +inf or -inf. So it is undefined?

We cannot say that 1/0= x for any number x because that is the same as saying 1= 0*x which is not true for any x. That's why we say "1/0 is undefined".

Another good idea! Oww my head :P

Question: Is the "opposite" (inverse) of 0, infinity??

MacM:
Okay I think I hear what you are saying. You are saying that when you have the number zero it may turn into n for no reason. I would like to see what proof you offer for that. Sounds intresting but I don't see the math!
I can tell you right now that if 0 doesn't undergo some kind of addition to get to n it can't happen because it would be a contradiction 0=n n!=0 which isn't possible in math. If it does undergo an addition then it really isn't something from nothing, so I am having trouble understanding your logic.

Originally posted by MacM
Everneo,

Close, a-b is 0 but if you carry out operation rather than cancel like factors you divide by 0 and the results becomes 2 Inf = 1 Inf.

step 7 divide by Inf (cancelling like terms) still yields 2 = 1

Infinity could not be determined. Can't say 1 infinity, 2 infinity as if infinity is a number or entity. Its a state of indeterminable quantity, as i understand.

Cybermorphic,

Let me direct you to another topic line where this process is discussed in greater detail.

"Make it Finite if you can".

It seems a little like the sqrt(-1) situation.... but just because we can't find an answer hasn't stopped us from defining it as i or j and then using the whole concept in the real world to solve real problems. So it seems that just because something doesn't exist doesn't mean that it can't be useful - could the same apply here ?

I imagine that all sorts of arguments could be laid down for proof of the non-existence of the quantity sqrt(-1) but there it is, like it or not.... imaginary it may be, but then again - what isn't ?

What would happen if we just accepted (for a moment) that 1/0 is called # and it belongs to the set of....I dunno...how about 'fantasmagorical numbers'....... well now that it has a label and belongs to a family, can we make any use of it ? - like, can it help solve problems ? - isn't that the important bit ?

Hilarion,

I think you have a good view. But I find the topic more accademic than useful.:)

Cybermorphic,


[quote]MacM:
Okay I think I hear what you are saying. You are saying that when you have the number zero it may turn into n for no reason. I would like to see what proof you offer for that. Sounds intresting but I don't see the math!
I can tell you right now that if 0 doesn't undergo some kind of addition to get to n it can't happen because it would be a contradiction 0=n n!=0 which isn't possible in math. If it does undergo an addition then it really isn't something from nothing, so I am having trouble understanding your logic.[unquote]

Ans:
No big breakthrough here, just a possibility I think deserves some thought.

We have assumed (without proof) that energy cannot be destroyed nor created. That premis, if false, ties our hands to understanding our existance.

It occured to me (and I have found other research papers that suggest a simular view) that it may be possible that "Nothingness" can be split into +/- components and still maintain conservation.

IF that is the case there seems no reason to reject the idea that our existance (+n) physical Universe may have arisen from the Big Bang which was an event of O------->(+n)+(-n) where the "O" is the Chiral Condensate or vacuum of space which seperates (+n) from (-n).

That is there may be a resovoir of (-n) componets in a (-n)Universe. That isn't to suggest that (-n) is a mirrow image of the (+n) Universe but it wouldn't exclude it.

As daffy as the idea seems to be at first glance I like it better than miracles, Gods or infinite existance without an initial creation.

It also seems to fit with the possibiities we see in such things as Particle Entanglement, electron orbit jumping in zero time (tunneling) etc., where (+n)+(-n)----->O is the other aspect of the idea.

The Big Bang is O----->(+n)+(-n) creation of energy.

Black Holes stuffing energy and matter back into "O" by (+n)+(-n)----->O

If one views "O" "Nothingness" as being timeless, without energy, mass or dimension, it means "O" is in contact with all spatial ordinates in the entire volume of the universe simultaneously and (+n) enities being returned to "O" therefore would be felt instantly throughout the Universe not delayed by v = c time later as is other information in physics.


"O" should not be looked upon as the equivelent of "0". "O" is not an integer of mathematics.

Any fraction with 0 in the numerator is 0 by definition. 0/0 should not be undefined, it is 0.

Originally posted by wesmorris
Any fraction with 0 in the numerator is 0 by definition. 0/0 should not be undefined, it is 0.

right and wrong

its not undefined, but said to be "indeterminate"

Originally posted by On Radioactive Waves
right and wrong

its not undefined, but said to be "indeterminate"

How can it be "indeterminate" if there are zero of them? I would say it's self defined.

indeterminate forms are: 0/0 , inf/0 , 0/inf and inf/inf

well maybe not o/inf I cant remember exactly

when you say zero of them do you mean that there is zero zero's? without going into calculus, its a contradiction. if i have zero zero's dosn't that make it possible to be something since I don't have zero?

in calculus its possible to turn an equation that ends up as 0/0 to inf/inf..... its indeterminate. we must change the form into one which is determinable.

if you want me to explain this further I'm going to have to dig back into some notes.... as I can't pull it off the top of my head right now.:mad:

ORW,

Why the frown? You know this is fun.:D

I like the view that "0" and Infinity are one and the same. Calculus tends to agree with that view but it seems to drive others crazy.

Maybe that is why I like it.:m:

Originally posted by On Radioactive Waves
indeterminate forms are: 0/0 , inf/0 , 0/inf and inf/inf

well maybe not o/inf I cant remember exactly

when you say zero of them do you mean that there is zero zero's? without going into calculus, its a contradiction. if i have zero zero's dosn't that make it possible to be something since I don't have zero?

in calculus its possible to turn an equation that ends up as 0/0 to inf/inf..... its indeterminate. we must change the form into one which is determinable.

if you want me to explain this further I'm going to have to dig back into some notes.... as I can't pull it off the top of my head right now.:mad:

I'm only saying that as soon as you put zero in the numerator you've established how many of the items in the deminator there are. In terms of "order of operations" you don't have to perform any more if you have zero in the numerator, because you've already said there are zero of whatever is in the denominator.

*shrug*

I realize mathemeticians might argue, I'm just trying to make a practical point.

MacM:

<i>I like the view that "0" and Infinity are one and the same.</i>

You may like it, but it isn't true.

<i>Calculus tends to agree with that view but it seems to drive others crazy.</i>

Calculus does not agree with that view.


wesmorris:

<i>I'm only saying that as soon as you put zero in the numerator you've established how many of the items in the deminator there are.</i>

No you haven't.

If I have 8 ducks and I take them 2 at a time, how many groups of ducks do I have? Answer: 8/2 = 4.

If I have no ducks and I take them 2 at a time, how many groups of ducks do I have? Answer: 0/2 = zero.

If I have 8 ducks and I take them none at a time, how many groups of zero ducks do I have? Answer: 8/0 = infinity. I can have as many groups of zero ducks as I want.

If I have no ducks and I take them none at a time, how many groups of ducks do I have? Answer: 0/0 = indeterminant. If I have no ducks to start with, can I really make groups from them? Maybe, maybe not.

Originally posted by James R
wesmorris:

<i>I'm only saying that as soon as you put zero in the numerator you've established how many of the items in the deminator there are.</i>

No you haven't.

If I have 8 ducks and I take them 2 at a time, how many groups of ducks do I have? Answer: 8/2 = 4.

Of course.
Originally posted by James R

If I have no ducks and I take them 2 at a time, how many groups of ducks do I have? Answer: 0/2 = zero.

You've got a valid point, but I'm just arguing that technically, you can't take zero ducks two at a time because you don't have any ducks to take because you just said you have zero of them.
Originally posted by James R

If I have 8 ducks and I take them none at a time, how many groups of zero ducks do I have? Answer: 8/0 = infinity. I can have as many groups of zero ducks as I want.

Of course.
Originally posted by James R

If I have no ducks and I take them none at a time, how many groups of ducks do I have? Answer: 0/0 = indeterminant.

I was just saying that I disagree because of...
Originally posted by James R

If I have no ducks to start with, can I really make groups from them? Maybe, maybe not.

I was taking the stance: "you can surely make te groups but the groups are only valueless placeholders until you put something there.. thusly.. you can think it... but it doesn't matter really. Thusly, zero over anything is just zero as I've previously stated.

I'm not all that attached to it really, just thinking about it a bit and that's what I came up with.

Maybe it's indeterminant if you only think about it, but if you really want to DO it... then it's zero. *shrug* thoerizing.

James R.,

[quote]I like the view that "0" and Infinity are one and the same.

You may like it, but it isn't true. [unquote]


Re-reading what I wrote I would have to agree "0" does not equal "infinity". But my meaning was more in the light of they are alike. That is they bear many of the same burdens reference proof and physical reality.

The frown because I couldn't remember.....

Isn't dividing by zero the same as multiplying by it's reciprocal ?

That means

0/1 = 0 * (1/0)
= 0

If a Volkswagon is better than nothing
And nothing is better than a Rolls Royce,
Then does that mean that a Volkswagon is better than a Rolls Royce ?

Seems as though 0 is the unmanifest form of number..........

x/0 = x/(-y) + x/(+y)

indeterminable ? - yep, and then some, methinks.

could zero be the mirror in which all other numbers are viewed ?
If so, then we should be able to construct a "numerical laser" ;)
that utilizes bugger all at one end with near-enough to bugger all at the other end of a cavity that is pumped with random numbers. The result, I imagine, would be a highly collimated beam of intense nothingness.

How did that smiley face get there ?...... I was serious !:)

my apologies......

I meant

1/0 = 1/(-y) * 1/(+y)

that should help..... and here was me tring to figure out why I was getting nothing but anti-nothingness out of this stupid laser!

Well, it certainly explains why nothing seemed to be working right...

whoooo....deja vu ! - I can clearly remember doing nothing like this before........must be my imagination.... it's probably nothing.

don't worry, nothing I say means *anything*

1/(-y) * 1/(+y) = 1/-y^2

how do you know what the denominator is?

0/1=0/2=0/3.......what number do we choose?
you cant say the denominator is 1 in this case, because other values will also work.

also, look what happens if we flip the equation(which should still hold true for an equality)

1/0=2/0=3/0

if zero was a valid denominator, then 1=2=3 which we know is not true... the values are undefined in this case.

Originally posted by MacM
Re-reading what I wrote I would have to agree "0" does not equal "infinity". But my meaning was more in the light of they are alike. That is they bear many of the same burdens reference proof and physical reality. [/B]
In someway they r alike in the sense one is infinitely small (0) and the other one is infinitely large (infinity) - infiniteness is common. But in the case of 'infinitely small' we can apply the limit 0. In case of infinity we can't apply any limit. But we take both as sufficiently small / sufficiently large for the given purpose.

Thats It!

By Jove, I think you've got it!!!!!!

This whole (hole?) thing (holething?) is the price we have to pay in return for being able to calculate anything else that doesn't matter....

Originally posted by Hilarion
If a Volkswagon is better than nothing
And nothing is better than a Rolls Royce,
Then does that mean that a Volkswagon is better than a Rolls Royce ?
implied nothings..!

first nothing --> having-no-car
second nothing --> no-other-car

u r using 'nothing' dubiously..!

could zero be the mirror in which all other numbers are viewed ?
If so, then we should be able to construct a "numerical laser" ;)
that utilizes bugger all at one end with near-enough to bugger all at the other end of a cavity that is pumped with random numbers. The result, I imagine, would be a highly collimated beam of intense nothingness.
nothing is better at sometimes.. ;)

Originally posted by Hilarion
my apologies......

I meant

1/0 = 1/(-y) * 1/(+y)

that should help..... and here was me tring to figure out why I was getting nothing but anti-nothingness out of this stupid laser!

Well, it certainly explains why nothing seemed to be working right...

whoooo....deja vu ! - I can clearly remember doing nothing like this before........must be my imagination.... it's probably nothing.

don't worry, nothing I say means *anything*

Dude, that was sweet. Right on.

Hilarion:

<i>Isn't dividing by zero the same as multiplying by it's reciprocal ?

That means

0/1 = 0 * (1/0)
= 0</i>

What is the reciprocal of zero? Is it 1/0 (as you claim), or is it 27/0, or 345000/0 or something else entirely?

In fact, all of these expressions are indeterminate.