Dividing by zero

Have you ever wondered what happens if you divide by zero? Everyone keeps saying it's impossible, but has anyone actually tried to understand what would happen? Maths is a very abstract and arcane science, but sometimes using practical examples is more helpful when trying to understand a seemingly unresolvable situation.

So here's my take on it - dividing by zero results in infinity.

There are two things that show this (at least the two that I'm aware of):

1. Black holes. Density = mass / volume. The singularity at the centre of a black hole is an infinitely small point with infinite density. For a black hole, the formula is density = mass / 0 and the result is infinity.

2. Divide a number by a divisor that is 0, for example 0.5 ... Note the result. Then decrease the divisor by half (to 0.25) and note what happens to the result. Keep halving the divisor, and you'll see that as it approachers zero, the result approaches infinity.

For me, the two examples are quite enough to conclude that dividing by zero results in infinity.

The problem of dividing by zero reminds me of the impossibility of having square root of -1. Yet we have found a way to deal with it by using imaginary numbers. Perhaps dividing by zero is not as scary as the academia makes it to be.

The reason maths has such trouble with division by zero is because a) the result of a calculation is expected to be a number (and infinity is not a number), and b) because in algebra, division is the inverse of multiplication, and multiplying any number by zero results in zero.

So sometimes it's good to think outside the box.

I watched this a while back and found it pretty interesting. This kind of weird math has always interested me.



DC

reply to post by wildespace


Zero isnt really a number , it more like the absence of numbers.

Originally posted by PhoenixOD
reply to post by wildespace

 

Zero isnt really a number , it more like the absence of numbers.

Right. Zero is immeasurable, so it has no value. It can indicate a process, as in n^0=1, but it never has a value.

Also, a black hole doesn't have zero mass, it approaches zero mass, so it approaches infinite
density. We say it is 'infinite' because its potential is limitless, but it's density doesn't actually equal infinity.

Zero is always a fun subject though. It's amazing how much we are entertained by nothing

Originally posted by wildespace
Perhaps dividing by zero is not as scary as the academia makes it to be.

The reason maths has such trouble with division by zero is because a) the result of a calculation is expected to be a number (and infinity is not a number), and b) because in algebra, division is the inverse of multiplication, and multiplying any number by zero results in zero.

I don't hear mathematicians complaining about it as much as I do physicists, like Michio Kaku.

Kaku has stated that in general when physicists calculate things like "infinite density", they have reason to question the result, and I have to agree with him.

My take is our math probably works with black holes outside the event horizon.

However, we may need some better math to describe what occurs inside the event horizon. There are possibly insurmountable obstacles to experimental verification of the existing math or any new math inside a black hole, since light can't escape. Even if we managed to send a probe into a black hole, there's no way for us to ever get the measurements it takes inside. Therefore, I'm not sure if the question will ever be resolved experimentally.

If we ever come up with a theory of everything, or at least a theory of quantum gravity, that may hold some sort of resolution to the issue.

en.wikipedia.org...

The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory. This breakdown, however, is expected; it occurs in a situation where quantum effects should describe these actions, due to the extremely high density and therefore particle interactions. To date, it has not been possible to combine quantum and gravitational effects into a single theory, although there exist attempts to formulate such a theory of quantum gravity. It is generally expected that such a theory will not feature any singularities.

Originally posted by wildespace
Have you ever wondered what happens if you divide by zero? Everyone keeps saying it's impossible, but has anyone actually tried to understand what would happen? Maths is a very abstract and arcane science, but sometimes using practical examples is more helpful when trying to understand a seemingly unresolvable situation.

So here's my take on it - dividing by zero results in infinity.

There are two things that show this (at least the two that I'm aware of):

1. Black holes. Density = mass / volume. The singularity at the centre of a black hole is an infinitely small point with infinite density. For a black hole, the formula is density = mass / 0 and the result is infinity.

2. Divide a number by a divisor that is 0, for example 0.5 ... Note the result. Then decrease the divisor by half (to 0.25) and note what happens to the result. Keep halving the divisor, and you'll see that as it approachers zero, the result approaches infinity.

For me, the two examples are quite enough to conclude that dividing by zero results in infinity.

The problem of dividing by zero reminds me of the impossibility of having square root of -1. Yet we have found a way to deal with it by using imaginary numbers. Perhaps dividing by zero is not as scary as the academia makes it to be.

The reason maths has such trouble with division by zero is because a) the result of a calculation is expected to be a number (and infinity is not a number), and b) because in algebra, division is the inverse of multiplication, and multiplying any number by zero results in zero.

So sometimes it's good to think outside the box.

On B,

Dividing by zero isn't supposed to be possible, but if it was, and I agree Infinity would be the outcome, it would make perfect sense and fit into your idea because the opposite of zero is infinity.

divide by zero is infinity.

the opposite is multiply, by zero equals zero. Makes sense and I think you are correct that dividing by zero isn't impossible or non existent, it's just too hard to explain with our current mathematics.

reply to post by wildespace

Have you ever wondered what happens if you divide by zero?

The way I see it, nothing can be divided by zero. It's like saying you need to cook something for supper when you have no food to cook. Supper times no food equals no supper. Five people that need to eat, divided by no food = no food. You don't even turn on the oven for this.

Originally posted by wildespace
2. Divide a number by a divisor that is 0, for example 0.5 ... Note the result. Then decrease the divisor by half (to 0.25) and note what happens to the result. Keep halving the divisor, and you'll see that as it approachers zero, the result approaches infinity.

Try that with a divisor > -1 and

Originally posted by jiggerj
The way I see it, nothing can be divided by zero. It's like saying you need to cook something for supper when you have no food to cook. Supper times no food equals no supper. Five people that need to eat, divided by no food = no food. You don't even turn on the oven for this.

Try dividing the amount of food by the number of people, with say 2 pounds of steak, or something perishable like that.

2 pounds/5 people= 0.4 pounds per person
2 pounds/4 people= 0.5 pounds per person
2 pounds/2 people= 1.0 pounds per person
2 pounds/1 person= 2.0 pounds per person
2 pounds/0 people= ? pounds per person

It's conceivable nobody will want to eat the steak, if say the people have already eaten and aren't hungry.
So if nobody is hungry and you divide the 2 pounds of food among everyone that is still hungry (nobody), you get a strange result, mathematically.

I entered the math on 2 different calculators and got 2 different answers.
The simple calculator told me I just can't do that.
The scientific calculator told me that the result is too big to display (overflow error).

Zero is a paper-friendly object, a place holder, a bigger dot. In my world, there is no such thing as zero. Put a dot in the middle of the zero, make new my zeros, then you can divide by everything, or just the big one.

As the statement 4 divided by 2, asks you to take 4; x x x x .. and divide them into 2 groups or there are 2 even groups of 2 in 4; x x ......x x

Wouldnt the statement 4 divided by 0 also be interpreted as; x x x x .... divided into 0 groups. Which can be interpreted as either, dont do anything, or I dont want 4 divided at all or by anything (which would mean 4 divided by 0 is 4? because 4 divided by nothing will leave you with 4). Or I want you to cram a real quantity of 4 into 0, so what can you do to make 4, disappear and equal 0. You would have to infinitely divide the 4, which is where you get your OP idea from.

Originally posted by SandalphonIn my world, there is no such thing as zero.

There are plenty of real things which are zero.

I have zero Ferraris.
I know zero reptile people.
Most people in this thread have zero understanding of math.
etc.

Originally posted by wildespaceEveryone keeps saying it's impossible, but has anyone actually tried to understand what would happen?

No, in the ten-thousand year history of math, no one, especially not the smartest people on the planet, have ever considered this issue. This post on the conspiracy forums is the first discussion of this idea ever in this history of mankind.

It is especially not discussed in any grade-school level textbook on elementary arithmetic.

Imaginary numbers work because one can define symbols which obey all of the properties of arithmetic, and additionally have the property that they may square to negative numbers. As can be easily demonstrated, no such symbol can be written which represents the results of dividing a number by zero.

Originally posted by ImaFungi

As the statement 4 divided by 2, asks you to take 4; x x x x .. and divide them into 2 groups or there are 2 even groups of 2 in 4; x x ......x x

Wouldnt the statement 4 divided by 0 also be interpreted as; x x x x .... divided into 0 groups. Which can be interpreted as either, dont do anything, or I dont want 4 divided at all or by anything (which would mean 4 divided by 0 is 4? because 4 divided by nothing will leave you with 4). Or I want you to cram a real quantity of 4 into 0, so what can you do to make 4, disappear and equal 0. You would have to infinitely divide the 4, which is where you get your OP idea from.

x x x x is already 1 group (which is why 4 / 1 = 4). To have it occupy zero groups, it either has to disappear, or become infinity. The experiment with the ever-decreasing divisor leads me to conclude it becomes infinity.

Zero is a real number, because to have negative numbers, there has to be a zero separating them from positive numbers. en.wikipedia.org...

reply to post by wildespace


It's all about logical conventions used to define the limits in our 'linear' mathematics IE +/- infinity at the outer limits and zero in the middle.
Zero divided by any value (including zero) = zero
Any number divided by zero = infinity
Zero is indivisible so 0/0 = 0
Infinity is divisible but the result is still infinity

Complex numbers based on the impossible SQRT(-1) were only introduced to have unique numbers for defining a 2nd axis allowing easier use of 2 dimensional graphical methods so we now have zero as common to both axes (the crossing point) and 4 actual infinities to deal with, identified as + & - infinity and + & - jinfinity. This allows us to describe and process 2D graphical values without even using graph paper.

It's just numbers, follow the rules and you'll get the right answers.

reply to post by Pilgrum

Any number divided by zero = infinity

No.
The result of division by zero is undefined. Undefined does not equal infinity.

reply to post by Phage


Thought about that after I posted it and yes, it indicates we've hit or even attempted to exceed the boundaries so undefined is a good word for it. My calculator tells me I stuffed up somewhere when I attempt it

reply to post by Pilgrum

And if you try coding it you'll get a NOP exception.
Translation: It don't mean a thing.

Zero makes a lot more sense when you put in the axes. The number line is positional, each space takes a unit, zero allows you to use all 10 positions from the decimal system etc. It allows you to use the same set of numbers for negative and positive on the same line.

Anyone invoking black holes here should be ashamed of themselves.

Originally posted by yampa
Zero makes a lot more sense when you put in the axes. The number line is positional, each space takes a unit, zero allows you to use all 10 positions from the decimal system etc. It allows you to use the same set of numbers for negative and positive on the same line.

Anyone invoking black holes here should be ashamed of themselves.

I don't think Michio Kaku has anything to be ashamed of regarding his black hole observations. (Though perhaps he should be ashamed of his claim that people would freak out if they learned aliens were visiting Earth...since so many people seem to think that's happening anyway...I don't agree they would freak out in general...maybe just a handful.)

The sun is a pretty large object, and 17 billion times as much mass as that is quite a bit. Zero looks fine on a number line, but 17 billion masses having zero volume gives Kaku and some other physicists reason to question the math. He mentions it in this video:


Time index 4:30, Kaku says: "Here is the problem: When r is equal to zero. The point at which physics itself breaks down".

He then continues by apparently contradicting Phage to say 1/r=1/0=Infinity (as opposed to undefined).

I'm not really thrilled with this clip in its entirety, but I think the part around 4:30 and the point that Kaku makes about dividing by zero does frame the black hole density calculation problem when you divide the mass by a volume of zero radius, alluded to in the OP, which I elaborated on in a previous post.

I have no interest at all in listening to Michio Kaku. He is basically a propagandist.

Black holes are completely tenuous, totally abstract mathematical theories. They have nothing to say about the simple and natural division of the number line.

People like Michio Kaku are not helping you understand.