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Why does 13 divided by 0 not equal infinity?
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Original post by Felix Felicis
Do not worry, I am a professor Emeritus from Harvard in mathematics, therefore the mathematical validity of my statement supercedes that of your mathematics teacher's. 
Either you are misquoting him and he said something like "as x gets really small, 13/x tends to infinity" or he shouldn't have a PhD in maths if he makes a mistake like this.
13/0 just like 1/0, 2/0, ... , a/0 is undefined.
Either you are misquoting him and he said something like "as x gets really small, 13/x tends to infinity" or he shouldn't have a PhD in maths if he makes a mistake like this.
13/0 just like 1/0, 2/0, ... , a/0 is undefined.
I don't believe you are a professor, what are you doing on TSR. I'm not as stupid as you think I am, so don't even try it
I think the best description I ever read as to why any number divided by zero is undefined was that you could let n/0 = infinity but you'd lose many of the laws of algebra that you take for granted such as the ability to times out by a common factor. The simplest way to see this is:
1 * infinity = infinity (basic)
1 / 0 = infinity (allegedly)
1 / 0 = 1 * infinity (axiomatically)
1 = 1 * infinity * 0 i.e. infinity * 0 = 1, this is a whole different can of fish but even if we can't agree on the product of infinity and zero I think we can all agree it ISN'T one
edit: the best you can say is that the limit as x approaches 0 for n/x tends to infinity
1 * infinity = infinity (basic)
1 / 0 = infinity (allegedly)
1 / 0 = 1 * infinity (axiomatically)
1 = 1 * infinity * 0 i.e. infinity * 0 = 1, this is a whole different can of fish but even if we can't agree on the product of infinity and zero I think we can all agree it ISN'T one
edit: the best you can say is that the limit as x approaches 0 for n/x tends to infinity
(edited 10 years ago)
Original post by tazmaniac97
I don't believe you are a professor, what are you doing on TSR. I'm not as stupid as you think I am, so don't even try it
I was merely pointing out the appeal to authority fallacy.
There is no reason that his statement is any more mathematically valid than your friend's simply because he has a PhD in mathematics (in fact, his statement is actually incorrect) unless he provides you rigorous proof, which has been peer-reviewed by other mathematicians (at least for a statement that is as controversial as this - you're still young so may not know about this, but dividing anything by 0 is widely regarded to be undefined and to define it obliterates the current framework we have for mathematics - both for algebra and analysis - your teacher cannot simply get away with nonchalantly stating 13/0 = infinity and avoiding the burden of proof that lies on him in doing so). Your teacher is wrong. 13/0 is not infinity. 13/0 is undefined, as is dividing anything by 0 - it's a big no-no in general.
(edited 10 years ago)
As far as I know all real numbers which are divided by 0 are undefined, as there is nothing what can be divided. Its the same as if a cake should be divided by 0 people - how to divide a cake, if there is no one to divide? the quantity of the pieces is undefinable.
(edited 10 years ago)
You have £1000 to give away to anyone who tells you a code word today. At the end of the day, nobody give you the code word. How much did each person get?
Now, you'll answer nobody got anything, but that doesn't answer the question. The question cannot be answered, because it is a ridiculous thing to ask. This is why n/0 is undefined. It is ridiculous.
Now, you'll answer nobody got anything, but that doesn't answer the question. The question cannot be answered, because it is a ridiculous thing to ask. This is why n/0 is undefined. It is ridiculous.
I think there's something to do with hyperreals that lets you divide by zero (sorta) but hyperreal numbers are way above my level so I don't know how much that can achieve. I'm guessing this professor was talking in terms of reals though, are you sure he didn't say as the denominator tends to zero? Because that would be infinity. (Edit: except it wouldn't.)
(edited 10 years ago)
Original post by justanotherposter
I think there's something to do with hyperreals that lets you divide by zero (sorta) but hyperreal numbers are way above my level so I don't know how much that can achieve. I'm guessing this professor was talking in terms of reals though, are you sure he didn't say as the denominator tends to zero? Because that would be infinity.
No it wouldn't.
Don't believe the people on this forum, they clearly aren't mathematics majors. One thing you will find out when you begin a phd in mathematics, is that 13/0 actually equals 4.
People always give this really unsatisfactory answer that it's "undefined", but never explain why we don't define it as infinity. Here's why:
Consider the graph of 1/x:
Now imagine you start approaching the origin from the right hand side. As you get closer and closer to 0, you tend to infinity.
Now imagine you start approach the origin from the left hand side. As you get closer and closer to 0, you get -infinity.
The question then becomes whether we should say 1/0 is infinity or -infinity. There's no logical way to decide between these two, so it's best to call it undefined. Essentially, the limit as you tend to 0 is undefined here, which is the real problem. This problem doesn't exist for something like the function (sinx)/x, where again you have division by 0, but both the right hand and left hand limits tend to the same thing (they both tend to +1), so we can define (sin0)/0 = 1 quite happily.
It also makes sense to call it undefined because algebra often breaks down with division by 0 (Google "division by zero fallacies" or something). This is totally separate from my point above though - even if the limit from both sides tended to +infinity, I don't think we could modify algebra to include infinity because infinity is not a number.
These are the two main reasons why you can't define division by zero.
Consider the graph of 1/x:
Now imagine you start approaching the origin from the right hand side. As you get closer and closer to 0, you tend to infinity.
Now imagine you start approach the origin from the left hand side. As you get closer and closer to 0, you get -infinity.
The question then becomes whether we should say 1/0 is infinity or -infinity. There's no logical way to decide between these two, so it's best to call it undefined. Essentially, the limit as you tend to 0 is undefined here, which is the real problem. This problem doesn't exist for something like the function (sinx)/x, where again you have division by 0, but both the right hand and left hand limits tend to the same thing (they both tend to +1), so we can define (sin0)/0 = 1 quite happily.
It also makes sense to call it undefined because algebra often breaks down with division by 0 (Google "division by zero fallacies" or something). This is totally separate from my point above though - even if the limit from both sides tended to +infinity, I don't think we could modify algebra to include infinity because infinity is not a number.
These are the two main reasons why you can't define division by zero.
(edited 10 years ago)
Original post by james22
No it wouldn't.
Second year maths undergraduate and I'm getting basic stuff like this wrong... you're right of course, it would tend to infinity from the positive axis and negative infinity from the negative axis
(edited 10 years ago)
"It is undefined" is a convenient semi-fiction to cover up the fact that maths basically doesn't work. 13/0 "is" infinity in a very meaningful sense, but then if you take that at face value and use it to make other assumptions about infinity other things don't work and the system breaks down, the simplest example is that if 13/0 = infinity = 2/0 then 13 = 2, so that all finite numbers equal each other.
In relation to infinity, all finite numbers DO equal each other: they are all infinitesimal. But essentially what it means is that infinity, insofar as it can be said to exist, must work on a different logic from the finite numbers.
So you either say there are two systems, which is iffy because you just derived one from the other, or you say infinity doesn't exist, which is also iffy because maths is supposed to be an entirely theoretical system defined on its own terms only.
Personally I think it's because the universe is a (necessarily) simplified simulation of itself running within (maybe any number of times removed) some true reality.
It is also true that a system cannot fully define itself using its own axioms, since the axioms are part of the system too. This is the same reason why we can never fully observe the universe and I also consider quantum logic to be another instantiation of the simulation thing.
In relation to infinity, all finite numbers DO equal each other: they are all infinitesimal. But essentially what it means is that infinity, insofar as it can be said to exist, must work on a different logic from the finite numbers.
So you either say there are two systems, which is iffy because you just derived one from the other, or you say infinity doesn't exist, which is also iffy because maths is supposed to be an entirely theoretical system defined on its own terms only.
Personally I think it's because the universe is a (necessarily) simplified simulation of itself running within (maybe any number of times removed) some true reality.
It is also true that a system cannot fully define itself using its own axioms, since the axioms are part of the system too. This is the same reason why we can never fully observe the universe and I also consider quantum logic to be another instantiation of the simulation thing.
Original post by scrotgrot
"It is undefined" is a convenient semi-fiction to cover up the fact that maths basically doesn't work. 13/0 "is" infinity in a very meaningful sense, but then if you take that at face value and use it to make other assumptions about infinity other things don't work and the system breaks down, the simplest example is that if 13/0 = infinity = 2/0 then 13 = 2, so that all finite numbers equal each other.
In relation to infinity, all finite numbers DO equal each other: they are all infinitesimal. But essentially what it means is that infinity, insofar as it can be said to exist, must work on a different logic from the finite numbers.
So you either say there are two systems, which is iffy because you just derived one from the other, or you say infinity doesn't exist, which is also iffy because maths is supposed to be an entirely theoretical system defined on its own terms only.
Personally I think it's because the universe is a (necessarily) simplified simulation of itself running within (maybe any number of times removed) some true reality.
It is also true that a system cannot fully define itself using its own axioms, since the axioms are part of the system too. This is the same reason why we can never fully observe the universe and I also consider quantum logic to be another instantiation of the simulation thing.
In relation to infinity, all finite numbers DO equal each other: they are all infinitesimal. But essentially what it means is that infinity, insofar as it can be said to exist, must work on a different logic from the finite numbers.
So you either say there are two systems, which is iffy because you just derived one from the other, or you say infinity doesn't exist, which is also iffy because maths is supposed to be an entirely theoretical system defined on its own terms only.
Personally I think it's because the universe is a (necessarily) simplified simulation of itself running within (maybe any number of times removed) some true reality.
It is also true that a system cannot fully define itself using its own axioms, since the axioms are part of the system too. This is the same reason why we can never fully observe the universe and I also consider quantum logic to be another instantiation of the simulation thing.
Maths works fine, 13/0 does not equal infinity becuase the limit does not exist. The reeason you cannot divide by 0 is not because it causes contradicts, but because it can be proven that in any field, 0 has no inverse.
There is nothing wrong with saying that infinity doesn't exist. From the definition of the real numbers you cannot deduce the existance of any numbers staisfying the typical properties you would want infinity to have.
Original post by Swayum
People always give this really unsatisfactory answer that it's "undefined", but never explain why we don't define it as infinity. Here's why:
Consider the graph of 1/x:
Now imagine you start approaching the origin from the right hand side. As you get closer and closer to 0, you tend to infinity.
Now imagine you start approach the origin from the left hand side. As you get closer and closer to 0, you get -infinity.
The question then becomes whether we should say 1/0 is infinity or -infinity. There's no logical way to decide between these two, so it's best to call it undefined. Essentially, the limit as you tend to 0 is undefined here, which is the real problem. This problem doesn't exist for something like the function (sinx)/x, where again you have division by 0, but both the right hand and left hand limits tend to the same thing (they both tend to +1), so we can define (sin0)/0 = 1 quite happily.
It also makes sense to call it undefined because algebra often breaks down with division by 0 (Google "division by zero fallacies" or something). This is totally separate from my point above though - even if the limit from both sides tended to +infinity, I don't think we could modify algebra to include infinity because infinity is not a number.
These are the two main reasons why you can't define division by zero.
Consider the graph of 1/x:
Now imagine you start approaching the origin from the right hand side. As you get closer and closer to 0, you tend to infinity.
Now imagine you start approach the origin from the left hand side. As you get closer and closer to 0, you get -infinity.
The question then becomes whether we should say 1/0 is infinity or -infinity. There's no logical way to decide between these two, so it's best to call it undefined. Essentially, the limit as you tend to 0 is undefined here, which is the real problem. This problem doesn't exist for something like the function (sinx)/x, where again you have division by 0, but both the right hand and left hand limits tend to the same thing (they both tend to +1), so we can define (sin0)/0 = 1 quite happily.
It also makes sense to call it undefined because algebra often breaks down with division by 0 (Google "division by zero fallacies" or something). This is totally separate from my point above though - even if the limit from both sides tended to +infinity, I don't think we could modify algebra to include infinity because infinity is not a number.
These are the two main reasons why you can't define division by zero.
+1. And there is your answer OP.
Original post by tazmaniac97
Yeah but if I applied your logic to this situation, then...
13 x 0 = 0
so why doesn't 0 divided by 0 equal 13
13 x 0 = 0
so why doesn't 0 divided by 0 equal 13
is even more wildly undefined than the others. It doesn't even have a coherent limit.
Original post by tazmaniac97
But if he said that then there must be a good reason for it, so I would believe him
Perhaps you misunderstood him?
lim(x->0) of 13/x tends to infinity - that should be true.
13/0 certainly isn't equal to infinity.
Original post by BlueSam3
is even more wildly undefined than the others. It doesn't even have a coherent limit.
Neither does 1/x
Original post by Elcano
Perhaps you misunderstood him?
lim(x->0) of 13/x tends to infinity - that should be true.
13/0 certainly isn't equal to infinity.
lim(x->0) of 13/x tends to infinity - that should be true.
13/0 certainly isn't equal to infinity.
That is not true.
Original post by tazmaniac97
But if he said that then there must be a good reason for it, so I would believe him
Anyone can say that. Doesn't mean they're right..but it should be your right to ask him why and to prove it.
Original post by tazmaniac97
Why does 13 divided by 0 not equal infinity? I really don't understand why?
My Maths teacher who has a PhD. in Mathematics told us. So basically I told my friend in another class, and she said it doesn't. So we both decided to have a bet on here on which one of us is right.
My Maths teacher who has a PhD. in Mathematics told us. So basically I told my friend in another class, and she said it doesn't. So we both decided to have a bet on here on which one of us is right.
Original post by tazmaniac97
but my maths teacher who has a PHD said it would, why should I believe you and not him?
Because you are capable of independent thought and are willing to read the evidence we can provide
Original post by james22
That is not true.
O rly?
Try this: http://www.wolframalpha.com/input/?i=lim%28x-%3E0%29+13%2Fx
It tends to +inf if approached from x>0 and to -inf if approached from x<0.
(edited 10 years ago)
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