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Justin Wei

12 years agoPosted 12 years ago. Direct link to Justin Wei's post “What is 0/0 then? Because...”

What is 0/0 then? Because aren't there several rules that yield different answers for example, any number divided by itself is one, zero divided by any number is zero, etc? At

1:00

Sal says, "any non-zero number divided by zero is undefined". What if you divide zero by zero?Thanks!

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(134 votes)

Mr. Millette

12 years agoPosted 12 years ago. Direct link to Mr. Millette's post “The way I explained it to...”

The way I explained it to my 7th graders is this:

If 0/0 is equal to a number, then let's rewrite it as a multiplication.

0/0 = 0 ==> 0 * 0 = 0, so that works...

But wait!

0/0 = 1 ==> 0 * 1 = 0. Oops, that also works.

and so does 0/0 = 2 and 0/0 = 6 and 0/0 = any real number.

This is where it breaks down.Because there are so many (in fact, an infinite number) of ways that this division could be converted into a valid multiplication, we can conclude that this division isn't valid or indeterminate, to use the correct terminology). For any operation, there should only be at most one operation that "undoes" it.

Hope this helps.

(368 votes)

Blaine

12 years agoPosted 12 years ago. Direct link to Blaine's post “Infinity is a strange thi...”

Infinity is a strange thing. What is most strange about it is the fact that it isn't an actual number. Like what is the absolute value of negative infinity. One could argue that the answer is simply infinity, but since infinity doesn't really exist in the first place, can it have an opposite? What actually is an example of negative infinity?

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(87 votes)

Nolan Pudimat

12 years agoPosted 12 years ago. Direct link to Nolan Pudimat's post “You ask for an example of...”

You ask for an example of negative infinity, but what is an example of infinity? Because infinity is not a real number (it basically means 'goes on and on forever') then infinity would be the largest number in existence (this would not be possible because numbers go on forever), so negative infinity would be the smallest number in existence (this is also not possible because number also go on forever in negative numbers) so there is no example of infinity or negative infinity.

(72 votes)

Trurl

11 years agoPosted 11 years ago. Direct link to Trurl's post “Playing a bit of devil's ...”

Playing a bit of devil's advocate, so please take this post as more or a philosophical discussion than a question...

Just wondering why this is not defined as an imaginary number or an "imaginary ratio". Seems to me if we can define the square root of -1, which for real numbers is nonsensical, we could define 1/0.

Also, I am not convinced by the argument that it breaks down because we can have infinity or negative infinity. Why not simply state that infinity is an absolute (perhaps unobtainable) limit and that it is approached from either the positive or negative side? We do not give a sign to zero--we say that 0/-1 is the same is 0/1 so why not define infinity the same way?

I am of course not really trying to argue that 1/0 can be defined. If it could, far, far more brilliant people than me would have figured that out years ago, but I wanted to throw this out for discussion.

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(61 votes)

ArDeeJ

11 years agoPosted 11 years ago. Direct link to ArDeeJ's post “We actually have that: it...”

We actually have that: it's called the real projective line. It's kind of like wrapping the two ends of the real number line and declaring that the point where they meet is the point at infinity.

http://en.wikipedia.org/wiki/Real_projective_line

(38 votes)

maxtn

12 years agoPosted 12 years ago. Direct link to maxtn's post “Sal, is it possible that ...”

Sal, is it possible that 0 is the intersection of positive and negative numbers, since all other division results in some other non zero number and multiplication by zero is zero? Therefore infinity exists as an intersection.

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(46 votes)

Lucas K. Sorensen

11 years agoPosted 11 years ago. Direct link to Lucas K. Sorensen's post “Well.....if you ask me, I...”

Well.....if you ask me, I think 0 is not really an intersection, but a bridge between positive and negative numbers and the 2nd question, 0+-∞.

(18 votes)

Dennis Fisher

8 years agoPosted 8 years ago. Direct link to Dennis Fisher's post “Why couldn't it just be d...”

Why couldn't it just be defined like this:

0=nothing

If i divide something by nothing, I'm left with that something. I simply didn't divide it.

Therefore, x/0=x

If I divide by .0000000001 or -.00000000001, I am then dividing by something again and therefore have an answer that is quantifiable. This could still allow us to hold true that dividing something by nothing simply means you did not divide it at all.

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(18 votes)

Bean Jaudrillard

8 years agoPosted 8 years ago. Direct link to Bean Jaudrillard's post “Okay, let's accept the fa...”

Okay, let's accept the fact the x/0=x but accepting it leads to all sorts of contradictions,

Consider V=S/T (Velocity=displacement divided by time)

say you have to cover 1m in 0 sec,which means in no time,then you ask what is the velocity, according to you it must be 1m/s. Does that make sense?

The contradiction becomes more apparent after you rearrange the equation by solving for time.

T=S/V (Time=displacement/velocity)

Say you have to cover 1 metre,with a velocity of 0m/s,but a velocity of 0m/s means that you are standing still,and if you are standing still how can you cover a given distance?Even if you stand motionless at a fixed point for an eternity you will**never**be able to cover**any**given distance,in this case asking the question 'what is the time if the velocity is 0 and distance 1' does not make sense,the solution is not infinity,the solution is not 1,there**is**no solution.

I guess in this universe dividing by 0 does not make sense but probably in a universe where you could cover distance without moving,it would make sense.(27 votes)

Ronald Das

12 years agoPosted 12 years ago. Direct link to Ronald Das's post “Guys What is square root ...”

Guys What is square root of Zero??

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(15 votes)

saurabhag12

4 years agoPosted 4 years ago. Direct link to saurabhag12's post “if you go and check a cal...”

if you go and check a calculator it will show 0 and if you even think square root means its asking to what number we should put ^2 that the number which is being square rooted will come . so the answer for square root of zero is always=0. hope this helps:)

(6 votes)

Alexander L

5 years agoPosted 5 years ago. Direct link to Alexander L's post “Hi, I'm failing to unders...”

Hi, I'm failing to understand the issue here? It seems to me that 2 different questions are trying to be represented here with the same mathematical formula:

1. What happens when you have nothing to divide?

If you have 7 and you want to divide by nothing then no division is going to happen, so it seems to me that 7/0 = 7

If you owe 1 and you want to divide by nothing then nothing is going to happen either -1/0 = -1 Again, no division is happening because you have nothing to divide.

2. If we are asking the question: How many times can I fit a number into another like how many times can we fit 0.1 into 1 then is obvious that the smaller the number the more times we can fit it, that is what happens when we do:

1/0.1 = 10

Obviously here the smaller the numbers we are using to divide the more times we can fit them and since we know that there are an infinite amount of numbers in between 0.1 & 1, then as long as we have something to divide, no matter how small, we get a result. But the assumption that because we are dividing by smaller and smaller numbers then 1/0=∞ seems wrong to me because the moment we are dealing with 0 we really have nothing to divide, therefore the division doesn't happen.

CONCLUSION:

So I'm failing to see the issue here and why there is a problem determining the value? Where is the problem with this line of thinking and what are the other ways of reasoning that contradict this?•

(14 votes)

MusicWizz

5 years agoPosted 5 years ago. Direct link to MusicWizz's post “I like to think of it thi...”

I like to think of it this way.

When you are dividing say, 7/0, you are dividing it by nothing, but into a number of groups, which in this case would be no groups.

So if you divide 7 items into 0 groups, how many are there in each group? 0.As for your second question. Let's consider factors.

So continuing with 7/0. If 7/0 is a question of how many 0's can we fit into 7, then once again the answer is 0.

Why? Because 0 cannot fit into 7, the only numbers that can are 1, and 7 (the factors of 7).This is a great question, and I hope my answer helps clear it up a little!

(5 votes)

jude.gallagher

a year agoPosted a year ago. Direct link to jude.gallagher's post “anything divided by zero ...”

anything divided by zero is itself. dividing by nothing is leaving everything there

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(2 votes)

Tanner P

a year agoPosted a year ago. Direct link to Tanner P's post “It doesn’t work that way....”

It doesn’t work that way.

You can think of division as finding the missing part to a multiplication problem. For example, 20/4 can be written as 4 x ? = 20. And ? = 5.

Now, say you have 20/0. This can be written as 0 x ? = 20. According to your method, ? = 20. But we know this isn’t possible because 0 x 20 = 0, not 20.

Hope this helps!

(17 votes)

CR_DragoUchiha

10 years agoPosted 10 years ago. Direct link to CR_DragoUchiha's post “If infinity is not a real...”

If infinity is not a real number, what exactly is it?

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(3 votes)

jmascaro

10 years agoPosted 10 years ago. Direct link to jmascaro's post “Hi,Infinity is a concept...”

Hi,

Infinity is a concept. We cannot put a value on infinity because there will always be something bigger that we can come up with.We tend to think of infinity as "the biggest number" but it's not, infinity is just an idea. If I give you my biggest number, you will be able to come up with a bigger number. Then I can come up with a number bigger than yours, and you come up with an even bigger number, and so on and so on forever.

By trying to put a value on infinity, we are limiting infinity which, by definition, is limitless. Hope that helps :-)

(14 votes)

Joseph Fletcher

7 years agoPosted 7 years ago. Direct link to Joseph Fletcher's post “I wonder is you could put...”

I wonder is you could put a fraction inside of a fraction, inside of a fraction, inside of a fraction, inside a fraction, and it just keeps on going on and on and on.

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(6 votes)

Judith Gibson

7 years agoPosted 7 years ago. Direct link to Judith Gibson's post “You have hit upon a field...”

You have hit upon a field of mathematics that is called "continued fractions".

Although I know it exists, it is far beyond my knowledge at this point to be able to understand it well enough to explain it. Some PhD dissertations have covered this topic.(8 votes)

## Video transcript

Comedian StevenWright-- and I guess we can credit him with beinga bit of a philosopher-- once commented that "Black holesare where God divided by zero." And I won't get into the physics of it, and obviously the metaphorbreaks down in certain ways But it is strangely appropriate,because black holes are where our current understanding ofphysics seems to break down and dividing by zero, as simpleof idea as that seems to be, is where our mathematicsalso breaks down. This is "undefined." Sometimes when you see"undefined" in math class it seems like avery strange thing. It seems like avery bizarre idea. But it really means exactlywhat the word means. Mathematicianshave never defined what it must meanto divide by zero. What is that value? And the reason theyhaven't done it is because they couldn'tcome up with a good answer. There's no good answerhere, no good definition. And because of that,any non-zero number, divided by zero, isleft just "undefined." 7 divided by 0. 8 divided by 0. Negative 1 divided by 0. We say all of these thingsare just "undefined." You might say, well ifwe can just define it, let's at least try to comeup with a definition of what it means to take a non-zeronumber divided by zero. So let's do that right now. We could just take the simplestof all non-zero numbers. We'll just do it with one. But we could have done thiswith any non-zero number. Let's take the example of one. Since we don't knowwhat it means-- or we're trying to figure out what itmeans to divide by zero Lets just try out really, really,small positive numbers. Let's divide by really,really small positive numbers and see what happens aswe get close to zero. So lets divide by 0.1 Well,this will get us to 10. If we divide 1 by 0.01that gets us to 100. If I go really,really close to zero. If I divide 1 by0.000001 this gets us-- so this is not a tenth,hundredth, thousandth, ten thousandth,hundred thousandth. This is a millionth. 1 divided by a millionth, that'sgoing to give us 1 million. So we see a pattern here. As we divide one by smallerand smaller and smaller positive numbers, we get alarger and larger and larger value. Based on just this youmight say, well, hey, I've got somewhat of adefinition for 1 divided by 0. Maybe we can say that 1 dividedby 0 is positive infinity. As we get smaller and smallerpositive numbers here, we get super super largenumbers right over here. But then, your friendmight say, well, that worked when we divided bypositive numbers close to zero but what happens when wedivide by negative numbers close to zero? So lets try those out. Well, 1 divided by negative 0.1,that's going to be negative 10. 1 divided bynegative 0.01, that's going to be negative 100. And, if we go all the way to 1divided by negative 0.000001-- yup, I drew the samenumber of zeros-- that gets us tonegative 1 million. So you when we keep dividing1 by negative numbers that are closer and closer andcloser and closer to zero, we get a very different answer. We actually start approachingnegative infinity. So over here we said maybe itwould be positive infinity, but you can make anequally strong argument that it could be avery different number. Negative infinity is goingthe exact opposite direction. So you could make anequally strong argument that it should benegative infinity. And this is whymathematicians say there's just nogood answer here. Especially one that's consistentwith the rest of mathematics. They could have just saidit's equal to 42 or something like that. But that would make no sense. It's neither oneof these values, and it wouldn't be consistentwith everything else we know. So they just left thewhole thing "undefined."