Math people: Why is n/0 undefined?

[Goosemaster]

The way I understand it is to regard 0 as more of an idea than an actually value.

0 represents and absence of something or all, be it a distance (0= no distance) or a value ( 0=no apples)

The reason why I find it undefineable is because it is a division of a rational or irrational number by an idea

3
_
nothing


=

:thumbsup:

 

[maziwanka]

i was going to say contradiction (the url in gopunk's post affirms it)

 

[TuxDave]

Originally posted by: dullard

Originally posted by: TuxDave
So if you don't want to figure out a definition of a number, then it's undefined? So what's n/0 where n is a real constant not equal to zero. Can I define it as either +infinity or -infinity thus making it defined?

If n >0 then the answer is x is +infinity. Someone then asks what is +infinity equal to. What is your answer? You could say +infinity is undefined, or you could attempt to go into complex philosophies of your thoughts on the infinite universe... But still x is defined to me, it is defined as +infinity. The fact that +infinity may or may not be defined to everyone is their problem.

if n<0 then x is defined as -infinity to me. Same comments apply.

Dullard is an engineer. I give out practical answers. I could care less if some theoretical mathmatician or philosopher comes in and argues against me. In your case, x has an answer, and it has the same answer in each problem if |n|>0. Thus it is defined to me.

So....

n/0 is defined by the solution

(if n > 0 then +infinity)
(if n < 0 then - infinity)
(if n = 0 then indeterminate)

Hence... n/0 is defined?

btw... I'm an engineer too... I try to abuse logic

 

[puffff]

Originally posted by: dullard

Originally posted by: puffff
however, suppose i ask you to solve x - 3 > 0. the answer is x>3. but we dont say the answer is undefined, we just say that x is all real numbers greater than 3.

See the bolded part? That is a definition. Thus x is defined.

I think your problem is that the original poster used the terminology for n / 0 where n is not zero. In that case the answer is undefined (ie infinity). When you talk about 0 / 0 the answer IS DEFINED. But the answer will vary depending on the specific problem. The correct answer is that 0 / 0 is indeterminate. It isn't yet determined until you apply it to your specific problem.

Mathforum.org:
"There's a special word for stuff like this, where you could conceivably give it any number of values. That word is "indeterminate." It's not the same as undefined. It essentially means that if it pops up somewhere, you don't know what its value will be in your case. For instance, if you have the limit as x->0 of x/x and of 7x/x, the expression will have a value of 1 in the first case and 7 in the second case. Indeterminate."

ok, i agree with this... 0/0 = indeterminate.

 

[Goosemaster]

Originally posted by: TuxDave
btw... I'm an engineer too... I try to abuse logic

Isn't that the goal of E's in life ?:evil:

 

[BurnItDwn]

Infinity is not a real/rational number. It is a limit.


EDIT .... corrected spelling of limit.
Thanks for the corrections guys.

 

[Goosemaster]

Originally posted by: BurnItDwn
Infinity is not a real/rational number. It is a limmit.

:thumbsup:

 

[Mathlete]

Originally posted by: BurnItDwn
Infinity is not a real/rational number. It is a limmit.

:thumbsup:

I am a mathematician. I aggree.

edit: except for the spelling of limit

 

[silverpig]

Originally posted by: cquark

Originally posted by: puffff
what about 0/0? i think that should = 0, since you can multiply by 0 to get 0

It could be anything:

Let x = 0/0.

Multiply both sides by zero to get: 0 * x = 0

What number is x? Well, any number satisfies the above equation.

Therefore you could say that x = 0 as you do above, or you could equally correctly say x = 1 or x = 2 ...

Now you have a problem. If x is a number, it can't be 0 and 1 and 2 at the same time. Therefore 0/0 isn't a number and needs to be undefined.

Heh, just for fun, write x as a superposition of all states:

x = 1/sqrt(n) [Psi(1) + Psi(2) + ... + Psi(n)]

 

[AFB]

Wow, I thought this thread would get like 10 posts. Thanks you all for the good explinations and comments. Except you Ameesh

 

[nmcglennon]

I thought dividing by zero would *hypothetically* reach infinity...

 

[AFB]

Originally posted by: Mathlete

Originally posted by: BurnItDwn
Infinity is not a real/rational number. It is a limmit.

:thumbsup:

I am a mathematician. I aggree.

edit: except for the spelling of limit

We can tell

 

[Spencer278]

Originally posted by: Goosemaster

Originally posted by: TuxDave
btw... I'm an engineer too... I try to abuse logic

Isn't that the goal of E's in life ?:evil:

I thought that was physics with there damn cat.

 

[lobadobadingdong]

go get 0 cars, and sell them to 5 people, can you do that? if you can you need to be a car salesman.

 

[DrPizza]

To make a correction to something posted above:

n/0 is NOT infinity..... nor is it "indeterminate" when n=0.

Infinity arises when one attempts to take a limit and the denominator approaches 0. Division by zero is still undefined.

When a limit results in a rational expression such that the numerator is approaching 0 and the denominator is approaching zero, then we call the limit in that form to be "indeterminate"
(other indeterminate forms include infinity minus infinity, 1 to the infinity power, 0 times infinity, and a few others. Yet to call it "one to the infinity" is actually incorrect. It's a matter of laziness, because "we know what you mean" --- yet this "we know what you mean" laziness is the reason for so much of the misunderstanding. It takes too much work to say "the limit is of a form such that a function that is approaching a value of 1 is being raised to a power which is approaching infinity" Writing 1 to the infinity is so much faster.

Anyway, 5/0 is NOT positive infinity. 5/0 is undefined. 5/0=infinity means your calculus teacher blurred the facts to save time and get you to the point of "good enough."
------------------------------------------------
also note:
The limit as x -> 0 of 5/x is neither positive infinity nor negative infinity. The limit does not exist. By definition, the limit must be the same when approached from the left and from the right. Either 1-sided limit does exist, however, and the limit as x->0+ is positive infinity, and the limit as x->0- is negative infinity. Note also that even this isn't correct, as infinity isn't a limit. Infinity isn't a number. To say something approaches infinity is to say it has no limit. So, you're saying "the limit is no limit" which is slightly different from "the limit doesn't exist."

 

[Cerb]

Dr. Pizza's post in a nutshell:
If you can concieve of the large number, infinity just got +1 added to it.

That's basically infinity. Infinity just goes and goes and goes, should you want to capture it as an actual number.
n/0 does not equal infinity on that technicality, as we come to a somewhat philosophical question. If 0/n is nothing, and can be quantified, what is nothing^-1?

 

[ActuaryTm]

Originally posted by: lobadobadingdong
go get 0 cars, and sell them to 5 people, can you do that? if you can you need to be a car salesman.

Alternatively, the same type person could start an internet marketing company (say, like Gratis).

 

[dethman]

Originally posted by: amdfanboy

Originally posted by: Mathlete

Originally posted by: BurnItDwn
Infinity is not a real/rational number. It is a limmit.

:thumbsup:

I am a mathematician. I aggree.

edit: except for the spelling of limit

We can tell

lol

 

[BespinReactorShaft]

Because "n/0" looks like stepping on one's ball and one can't do that without inducing infinite pain.

 

[TheLonelyPhoenix]

Originally posted by: dullard

Originally posted by: TuxDave
So if you don't want to figure out a definition of a number, then it's undefined? So what's n/0 where n is a real constant not equal to zero. Can I define it as either +infinity or -infinity thus making it defined?

If n >0 then the answer is x is +infinity. Someone then asks what is +infinity equal to. What is your answer? You could say +infinity is undefined, or you could attempt to go into complex philosophies of your thoughts on the infinite universe... But still x is defined to me, it is defined as +infinity. The fact that +infinity may or may not be defined to everyone is their problem.

if n<0 then x is defined as -infinity to me. Same comments apply.

Dullard is an engineer. I give out practical answers. I could care less if some theoretical mathmatician or philosopher comes in and argues against me. In your case, x has an answer, and it has the same answer in each problem if |n|>0. Thus it is defined to me.

Infinity isn't even defined. It's just a notation for a number headed off into nowhere. Its not philosophy, its simple definition. Just like n/0 is called 'undefined'.

Saying "the limit as x approaches 0 for n/x" is NOT the same thing as saying "n/0"

And for the record, I'm an engineer too.

 

[Chronoshock]

Originally posted by: TheLonelyPhoenix

Originally posted by: dullard

Originally posted by: TuxDave
So if you don't want to figure out a definition of a number, then it's undefined? So what's n/0 where n is a real constant not equal to zero. Can I define it as either +infinity or -infinity thus making it defined?

If n >0 then the answer is x is +infinity. Someone then asks what is +infinity equal to. What is your answer? You could say +infinity is undefined, or you could attempt to go into complex philosophies of your thoughts on the infinite universe... But still x is defined to me, it is defined as +infinity. The fact that +infinity may or may not be defined to everyone is their problem.

if n<0 then x is defined as -infinity to me. Same comments apply.

Dullard is an engineer. I give out practical answers. I could care less if some theoretical mathmatician or philosopher comes in and argues against me. In your case, x has an answer, and it has the same answer in each problem if |n|>0. Thus it is defined to me.

Infinity isn't even defined. It's just a notation for a number headed off into nowhere. Its not philosophy, its simple definition. Just like n/0 is called 'undefined'.

Saying "the limit as x approaches 0 for n/x" is NOT the same thing as saying "n/0"

And for the record, I'm an engineer too.

Yes, infinity is NOT a limit. It is a concept. Many people have the flawed perception that infinity "grows" or something of that sort and calling it a limit lends to that idea. Additionally, there isn't just infinity, there are different infinities. One example is the size of the set of all natural numbers. Another is the set of all real numbers. The set of all real numbers > the set of all natural numbers even though they are both infinite. Additionally, the set of all real numbers is infinitely greater than the set of all natural numbers. You can't think of them in terms of actual numbers (ie this infinity is 2x as large as that infinity since any real multiple of infinity I will still have 1 to 1 with correspondence with I) but rather in conceptual terms.

 

[silverpig]

Originally posted by: Chronoshock

Originally posted by: TheLonelyPhoenix

Originally posted by: dullard

Originally posted by: TuxDave
So if you don't want to figure out a definition of a number, then it's undefined? So what's n/0 where n is a real constant not equal to zero. Can I define it as either +infinity or -infinity thus making it defined?

If n >0 then the answer is x is +infinity. Someone then asks what is +infinity equal to. What is your answer? You could say +infinity is undefined, or you could attempt to go into complex philosophies of your thoughts on the infinite universe... But still x is defined to me, it is defined as +infinity. The fact that +infinity may or may not be defined to everyone is their problem.

if n<0 then x is defined as -infinity to me. Same comments apply.

Dullard is an engineer. I give out practical answers. I could care less if some theoretical mathmatician or philosopher comes in and argues against me. In your case, x has an answer, and it has the same answer in each problem if |n|>0. Thus it is defined to me.

Infinity isn't even defined. It's just a notation for a number headed off into nowhere. Its not philosophy, its simple definition. Just like n/0 is called 'undefined'.

Saying "the limit as x approaches 0 for n/x" is NOT the same thing as saying "n/0"

And for the record, I'm an engineer too.

Yes, infinity is NOT a limit. It is a concept. Many people have the flawed perception that infinity "grows" or something of that sort and calling it a limit lends to that idea. Additionally, there isn't just infinity, there are different infinities. One example is the size of the set of all natural numbers. Another is the set of all real numbers. The set of all real numbers > the set of all natural numbers even though they are both infinite. Additionally, the set of all real numbers is infinitely greater than the set of all natural numbers. You can't think of them in terms of actual numbers (ie this infinity is 2x as large as that infinity since any real multiple of infinity I will still have 1 to 1 with correspondence with I) but rather in conceptual terms.

All numbers are concepts.