ok, so it can be any number. but any number shouldnt be the same as undefined. if you take (x-1)(x-2)(x-3)=0 and solve for x, x can be 1, 2, or 3. but we don't say x is undefined in this case?
ok, so it can be any number. but any number shouldnt be the same as undefined. if you take (x-1)(x-2)(x-3)=0 and solve for x, x can be 1, 2, or 3. but we don't say x is undefined in this case?
dullard
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Cquark is correct. In math, 0/0 can be anything at all. The true value depends on the exact problem. Thus it is undefined since it can have many different answers for many different problems.
If Cquark's explanation is too difficult for you to understand, then maybe this is easier:
[*]Think of a line through the origin: y = m*x, where m is a constant slope.
[*]What is y / x? that is obvious, y / x = m.
[*]So at x = 2, y = 2m and y / x = 2. The same goes no matter where you look on the line.
[*]But what about at the origin? What do you do at at x = 0? Well, 0 / 0 = m.
[*]Thus if m = 10, then 0 / 0 = 10 in that problem.
[*]If m = -4, then 0 / 0 = -4 in that problem.
[*]If m = 1.231274241, then 0 / 0 = 1.231274241.
[*]If m = 5, then 0 / 0 does not equal 10, it does not equal -4, it does not equal 1.231274241. 0 / 0 in this specific case equals 5.
See how it has many different values? But in any specific example, 0 / 0 only has one correct value (advanced math people, I'm looking at the limit from one side to simplify the argument). Thus in general it is undefined but in specific problems it has a specific value (in some cases that specific value might be a finite constant or it might even be infinity).
If Cquark's explanation is too difficult for you to understand, then maybe this is easier:
[*]Think of a line through the origin: y = m*x, where m is a constant slope.
[*]What is y / x? that is obvious, y / x = m.
[*]So at x = 2, y = 2m and y / x = 2. The same goes no matter where you look on the line.
[*]But what about at the origin? What do you do at at x = 0? Well, 0 / 0 = m.
[*]Thus if m = 10, then 0 / 0 = 10 in that problem.
[*]If m = -4, then 0 / 0 = -4 in that problem.
[*]If m = 1.231274241, then 0 / 0 = 1.231274241.
[*]If m = 5, then 0 / 0 does not equal 10, it does not equal -4, it does not equal 1.231274241. 0 / 0 in this specific case equals 5.
See how it has many different values? But in any specific example, 0 / 0 only has one correct value (advanced math people, I'm looking at the limit from one side to simplify the argument). Thus in general it is undefined but in specific problems it has a specific value (in some cases that specific value might be a finite constant or it might even be infinity).
Thank you for smashing through the mismash...and giving the correct answer.
Its undefined because the x it should define is ambigous. Good job Cquark.
what about my response to that? (x-1)(x-2)(x-3) = 0 has 3 answers for x, it's ambiguous as well, yet we don't say it's undefined.
when we solve x mod 2 = 0, we say the solution is x is any number divisible by 2, not undefined, even though there are infinite solutions.
so why cant 0/0 = R, where R is the set of all real numbers?
yes, thanks for the clearification (sp).
I didnt take into account the different "speeds" which the numerator, or denominator can approach its value of zero. If the numerator approaches zero faster than the denominator, than you have a 0/n which is clearly zero. However if the denominator approaches zero faster, you have a n/0 example which obviously approaches infinity. And as in my example, if they both approach zero at the same rate, you get 1.
When you divide, using your pile analogy, you do not lose anything. 12 / 4 = 4 piles of three: you still have a total of 12.
What's 12 / 0? You have 0 piles, so what did you do with your 12 items? You can't simply take them off the table and throw them away to make the problem work. If that was acceptable, you could have 12/4 = 1, as long as you take 8 items off the table and discard them, like you did in the 12/0 problem.
DrPizza
Administrator Elite Member Goat Whisperer
I'll just go back to your initial proposition about dividing something into piles.
Lets say you have 63 jellybeans. You're going to divide by 7 - you can look at it 2 different ways.
Either how many piles of 7 jellybeans do you get? -or- 7 piles with how many jellybeans?
First, I'll use the first one to make the most sense out of this.
63 divided by 7. Put 7 jelly beans into a pile. Then start another pile with 7 jellybeans. Then another, and another. When you're done, you'll have 9 piles.
How about 63 divided by 6? 6 in a pile. 6 in a pile... after the 10th pile, you'll have 3 jellybeans. So, you can make 10 1/2 piles.
Now, how about 63 divided by 0? 0 in a pile. 0 in a pile. 0 in a pile. 0 in a pile. When are you going to end?
It might be tempting at this point to say that you'll have an infinite number of piles. But, even if you had a infinite piles, each with 0 jellybeans, you still have 63 jellybeans in your hand. So, you still haven't finished dividing. You just can't do it.
Lets say you have 63 jellybeans. You're going to divide by 7 - you can look at it 2 different ways.
Either how many piles of 7 jellybeans do you get? -or- 7 piles with how many jellybeans?
First, I'll use the first one to make the most sense out of this.
63 divided by 7. Put 7 jelly beans into a pile. Then start another pile with 7 jellybeans. Then another, and another. When you're done, you'll have 9 piles.
How about 63 divided by 6? 6 in a pile. 6 in a pile... after the 10th pile, you'll have 3 jellybeans. So, you can make 10 1/2 piles.
Now, how about 63 divided by 0? 0 in a pile. 0 in a pile. 0 in a pile. 0 in a pile. When are you going to end?
It might be tempting at this point to say that you'll have an infinite number of piles. But, even if you had a infinite piles, each with 0 jellybeans, you still have 63 jellybeans in your hand. So, you still haven't finished dividing. You just can't do it.
Because there are infinite 0's in any finite number....
Using Calculus youll find that the limit approaches infinity!
Kyteland
Diamond Member
- Dec 30, 2002
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It is undefined simply as a notational convenience. Mathematicians have set up the real number system in a certain way that works well in defining operations on numbers in *most* cases, but it simply doesn't behave well in this case. So they say it is undefined as a way to brush it under the rug.
It is not undefined because of some unalterable law of the universe, it is undefined because of limitations in the system we've come up with to describe it. You're welcome to make a new, better system if you would like. As for me, I'm perfectly happy with the one we've got.
It is not undefined because of some unalterable law of the universe, it is undefined because of limitations in the system we've come up with to describe it. You're welcome to make a new, better system if you would like. As for me, I'm perfectly happy with the one we've got.
In (x-1)(x-2)(x-3) = 0 , you are talking about a finite number of solutions.
Also, x mod 2 = 0 has a countably infinite number of solutions. That means that there is a correspondence between the possibilities and the counting numbers. ie the 1st solution is 0, the 2nd is 2, the 3rd is 4...
in the case of dividing by 0 there is an uncountable infinite number of solutions so we call this undifined.
it also could be imaginary numbers
Hope this helps
ArmchairAthlete
Diamond Member
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Traceback (most recent call last):
File "D:\Courses\CS1321\Examples\ch05\fig05_07.py", line 30, in ?
y = 3 / 0
ZeroDivisionError: integer division or modulo by zero
Because the computer said so =)
File "D:\Courses\CS1321\Examples\ch05\fig05_07.py", line 30, in ?
y = 3 / 0
ZeroDivisionError: integer division or modulo by zero
Because the computer said so =)
By reading this thread, it seems like dividing by 0 would be possible if the original number became something else.
IE: If I tell you to turn this pile of 12 apples into groups of 0, you wouldn't be able to compute it. Unless you made applesauce. Then you'd have 0 groups of apples and 1 group of applesauce.
DISCUSS!
IE: If I tell you to turn this pile of 12 apples into groups of 0, you wouldn't be able to compute it. Unless you made applesauce. Then you'd have 0 groups of apples and 1 group of applesauce.
DISCUSS!
DrPizza
Administrator Elite Member Goat Whisperer
the answer is undefined.
just think about it alittle you ass or you can look up some obtuse proof off the internet as well but i doubt that it will be any clearer then using some common sense.
I think the one missing key to some people understanding this is that an equality isn't the same as a limit. Basically,
lim x->0 3/x = inf
is not the same as
3/0
Limits are an approximation, not an absolute.
lim x->0 3/x = inf
is not the same as
3/0
Limits are an approximation, not an absolute.
that does make sense.
however, suppose i ask you to solve x - 3 > 0. the answer is x>3. here, the number of solutions for x is also uncountably infinite. but we dont say the answer is undefined, we just say that x is all real numbers greater than 3. what's the difference between saying all real numbers greater than 3, and just all real numbers?
dullard
Elite Member
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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."
dullard
Elite Member
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Undefined is not undefined.
The answer is that x is all numbers. That is a definition. Undefined is usually another word for "we don't want to go into the details into explaining something you can't understand yet so we give up and say the problem doesn't have an answer".
dullard
Elite Member
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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.
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