Log in Wilbur Donovan 12 years agoPosted 12 years ago. Direct link to Wilbur Donovan's post “Is 0/0 = 1? Or is it unde...” Is 0/0 = 1? Or is it undefined? Couldnt you say that the numbers are like a dimension where you could join the infinitys'? Like for example, if you wrote a number line on a piece of paper, with positive infinity at the top and negative infinity at the bottom, couldn't you fold the paper so that negative and positive infinity are the same? • (43 votes) Paul Moore 12 years agoPosted 12 years ago. Direct link to Paul Moore's post “0/0 is undefined. If sub...” 0/0 is undefined. If substituting a value into an expression gives 0/0, there is a chance that the expression has an actual finite value, but it is undefined by this method. We use limits (calculus) to determine this finite value. But we can't just substitute and get an answer. Example: the limit as x approaches 0 of x/x = 1, but the expression x/x is undefined at x = 0. In geometry, we do not consider lines to meet at infinity. We consider them to go on forever in opposite directions, never meeting. In physics, of course, space is curved, and a real "line" might, in fact, be a closed figure (which is somewhat like "meeting at infinity")... but not in geometry. Your thinking is great - keep it up. (52 votes) Paulius Eidukas 11 years agoPosted 11 years ago. Direct link to Paulius Eidukas's post “In my opinion, it seems t...” In my opinion, it seems that 0/0 could be equal not only to 0 and/or 1, but actually to any number. Let's say that 0/0 = x Is this also a valid way to prove that 0/0 is indeterminate? • (31 votes) David 10 years agoPosted 10 years ago. Direct link to David's post “I'm just stating what Sal...” I'm just stating what Sal said in the video, but some people say that 0/0 is obviously 0, since 0/4, for example, is zero. They say zero divided by anything is zero. However, some say anything divided by zero is undefined, since 4/0 and 5/0 are and so on. Others say that 0/0 is obviously one because anything divided by itself, just like 20/20 is 1. All of these points of view are logical and reasonable, yet they contradict each other. These statements are impossible and don't work, since a mathematical expression consisting of only constants (numbers like 1, not variables like x and y) can only have one value. These thoughts can not merge, as 0 is not 1 or undefined, and vice versa. So 0/0 must be undefined. Also, if you think about it more closely, (Sal also says this in the next video.) division must be able to be undone by multiplication. For example, 6 divided by 2 is 3, and it can be undone by multiplying 2 by 3 to get 6. If 0/0 is 1, then 1 times 0 is , so it is correct. If 0/0 is 0, then 0 times 0 is 0, so it is also correct. If 0/0 is undefined, then you can't multiply back. The first two can not be proved false using this method, nor can the latter, since it is not exactly defined as division anyway. (16 votes) Christine Moreda 7 years agoPosted 7 years ago. Direct link to Christine Moreda's post “If we have something and ...” If we have something and we divide it by 2, then don't we separate it into two pieces? (Now, to look at what we mean by "divide" or if we actually mean more than one thing.) So with two divided by zero, we could continue adding zero to itself forever, but still not get to two. 1/3 says you have 1 number of thirds. Since dividing by zero (i.e. having a "zeroth" as a denominator), I think, is impossible, then there is no such thing as a zeroth of a pie. On a similar note, if you say you have zero halves (0/2), Divide (per some online definition) also means calculate how many times one number goes into another. (So, to restate my main point...) Each side is multiplied by 0 in order to prepare to cancel out the zeros, like this: The problem with this is that a/0 is impossible, so when the zeros are "cancelled," what's really getting cancelled (on the left side) (along with the zero we added) is a part of an impossible number. If the number is impossible, then who are we to take a part of it out (the zero), and assume the remaining part is valid? So, if a/0 = b, and a/0 is impossible, then it seems that b is impossible too. I've yet to finish a review of imaginary numbers and how they are used, while keeping the above in mind. I'm curious how this applies to the study of more advanced math, science, and astronomy. 4/10/17 I corrected this post and would love to hear/read anyone's thoughts on it! • (17 votes) Jubjub Bird 7 years agoPosted 7 years ago. Direct link to Jubjub Bird's post “1. Separating into n piec...” 1. Separating into n pieces means that you need n new pieces to get the original piece. If you separate into 0 pieces means that you need 0 of the new piece/s to get to the original 1. In other words, you're trying to find- meaning define- a number that when multiplied by zero you get 1. Which is impossible. 2. (No 2, because in the question it's just a definition) 3. When you say "forever", it means that you would have to add an infinite amount of 0's to get to 2. But doing that would only give you 0, meaning you'll need to add a few more zeros- another infinite amount- and you'll stay at zero. And you keep going, and staying at zero. So yeah, it is impossible- impossible to define it's answer. 4-5. Interesting way of looking at it. But that doesn't prove that it's not undefined. 6. 0/p is 0, just like you say. 7. 2 does go into 0, just like it goes into 1 and into 0.3. in fact, it goes into 0 better than into them! Into zero it goes exactly 0 times (a whole number), but into 1 it goes only a half time and into 0.3 it goes only 0.15 times (both are fractions). 8-11. The flaw in your logic is that you aren't allowed to multiply by 0 when solving equations. 12. I don't know what to say about this, because I don't know anything about imaginary numbers. 13. I also don't know much about how this relates to more advanced math, science, and astronomy. 4/26/17 I re-answered to the corrected post, and I still say the following: (2 votes) mk 4 years agoPosted 4 years ago. Direct link to mk's post “Imagine having 0 cookies ...” Imagine having 0 cookies to give among 0 friends. How many cookies would each person get? See, it doesn`t make sense. And the cookie monster is sad that you have 0 cookies, and you are sad that you have 0 friends. • (11 votes) phineartsacademy a year agoPosted a year ago. Direct link to phineartsacademy's post “I'm just thinking about w...” I'm just thinking about why x/x=1. Division is repeated subtraction. 10/5=2 cause 10-2-2-2-2-2=0. You subtract 2 five times from ten to get zero. You subtract ten one time from ten to get zero. You subtract zero zero times from zero to get zero. Therefore, 0/0=0. And then it works in reverse. 0*0=0. And the rule x/0=0 isn't broken. x/x=1 is ignored, but I already explained why. Also, it makes sense because zero isn't a number. Zero is a symbol that represents nothing. And nothing is undefined. • (6 votes) Venkata a year agoPosted a year ago. Direct link to Venkata's post “Zero isn't a symbol. It i...” Zero isn't a symbol. It is a number just how 1 or 45 is. Just how every number tells us the existence of something, zero tells us the existence of nothing. As for 0/0, you can't define it as 0 because a lot of problems arise, some of which are far beyond the current scope here, and will be dealt with in a really interesting branch of Mathematics called Calculus. And to add on, there's a reason why your logic doesn't work. So, okay, suppose we say 0/0 is 0. What is 0/1? That's also 0. What about 0/2? That's also zero. 0/1 = 0 says "I subtract 0 from 0 one time to get 0". 0/2 = 0 says "I subtract 0 from 0 twice to get 0". These are fair statements to make. But, subtracting 0 from 0, 0 times is a bit absurd, as that's similar to not doing anything at all. So, the idea of division being repeated subtraction breaks down. Finally, I'll leave you with this. 0/0 has a special name in the context of limits. It's called an indeterminate form, and it pops up a lot in advanced Math, along with other indeterminate forms like infinity/infinity. Just know that 0/0 can be any number you want it to be. Think of it like this. Let 0/0 = x. So, we have x * 0 = 0. Now, what value of x satisfies this equation? Well, any number does! That's why 0/0 can be any number, but in the future, you'll learn methods to narrow down what number it is, as you'll need it to solve problems! (10 votes) Redapple8787 7 years agoPosted 7 years ago. Direct link to Redapple8787's post “From what I understand, w...” From what I understand, whenever mathematicians can't find a good answer for something, they leave it undefined. Do they leave things undefined quickly? How many undefined things are there in the world? Can undefined cases even exist? • (6 votes) David Severin 7 years agoPosted 7 years ago. Direct link to David Severin's post “In real life, there is no...” In real life, there is no reason to divide something by nothing, as it is undefined in math, it has no real applications in the real world. But in theory, it can be undefined. Similarly, infinity is also just a concept in math, it cannot have a real application either, even if you ask how many atoms are in the universe, it is a certain number even though it might be a very large number. There are not a lot of undefined things in math, but all of Geometry is based on three undefined terms, a point, line and plane none of which can exist in the real world, but without the theory of these, real world applications would be more difficult. You act like having something undefined is just an arbitrary thing mathematicians do, it is not at all. (8 votes) doo*shbag a year agoPosted a year ago. Direct link to doo*shbag's post “i think 0/0 is 0 bcs if u...” i think 0/0 is 0 bcs if u have zero friends and zero cookies how many cookies will each friend get? • (5 votes) Kim Seidel a year agoPosted a year ago. Direct link to Kim Seidel's post “The Multiplication Proper...” The Multiplication Property of 0 tells us that any number times 0 = 0. If you turn that into an equation, you have: (8 votes) Brian Trzepacz 5 years agoPosted 5 years ago. Direct link to Brian Trzepacz's post “If 0 x 5 = 0 then I divid...” If 0 x 5 = 0 then I divide both sides by 0, 0/0 = 5. So, • (4 votes) Kim Seidel 5 years agoPosted 5 years ago. Direct link to Kim Seidel's post “Essentially, yes. This i...” Essentially, yes. This is why 0/0 is considered indeterminate - there is no single agreed upon solution. (5 votes) T.J.King2002 8 years agoPosted 8 years ago. Direct link to T.J.King2002's post “Could 0/0 be equal to ale...” Could 0/0 be equal to aleph-null? • (6 votes) Journey to TĐN 2022 2 years agoPosted 2 years ago. Direct link to Journey to TĐN 2022's post “No, it can be anything. B...” No, it can be anything. Btw aleph null is undefined as it is an infinity(∞) (1 vote) Harpreet Chandi 6 years agoPosted 6 years ago. Direct link to Harpreet Chandi's post “What? At 2:21 wouldn't 0/...” What? At • (3 votes) Idhikash Jaishankar 6 years agoPosted 6 years ago. Direct link to Idhikash Jaishankar's post “"What? At 2:21 wouldn't 0...” "What? At (5 votes)Want to join the conversation?
Following the principles of division and multiplication, we can re-arrange the equation like this:
0x = 0
From here it becomes obvious that this equation is true for any x, because 0 multiplied by anything is still equal to 0:
0 * 0 = 0; 0/0 = 0
0 * 1 = 0; 0/0 = 1
0 * 2 = 0; 0/0 = 2
... and so on
And if we have something and divide it by 1, then don't we "separate" it into one piece?
So if we have something and divide it by 0, wouldn't that be like making it disappear?
Wouldn't that be impossible, rather than undefined?
To take a thing and turn into nothing?
(So, my first hypothesis is that dividing by zero is not undefined, but is defined as impossible.)
Divide (per somewhere online, I read), means to calculate how many times we could add one number to itself to get another number.
(For example, 10/5 = 2. We add 5 to itself 2 times to get 10.)
Doesn't that make 2/0 impossible, not undefined?
So with 3/0, would you have 3 number of "0ths"...
I've never heard of a "0th" and I don't think they exist.
0 (zero) of a pie is 0.
1/3 of a pie is 1/3.
1/2 of a pie is 1/2.
1/1 of a pie is a whole.
1/0 of a pie?
Or you say you have zero thirds (0/3)
Then you have zero of those things.
But you could also read those as zero divided by two (0/2)
Or zero divided by three (0/3)
With 10/5, 5 goes into 10 two times. So 10/5 = 2.
But with 0/2, how does 2 go into 0?
(So, now it seems that 0/2 is undefined!) (Though, using a different meaning of division, we know we can have zero halves and that that simply equals 0!)
(So that is part of the reason why it seems to me that we are not being consistent in our meaning and usage of division, and that is affecting how we think about dividing by zero.)
I think that dividing by zero, regardless of what you mean by "divide," is impossible.
So next would be why this classic example meant to show that we can't divide by zero is actually flawed:
a/0 = b
(a/0) x 0 = b x 0
It is the entire number a/0 that is impossible, not just the 0 at the bottom.
But I wonder if this is normal practice -- to pick and choose which parts of impossible things we use and which we don't. It seems that would really mess up our math.
Any thoughts on dividing by zero, or any of this?
Note that I didn't call p/0 impossible. I called it impossible to define, which is why it's undefined.
Thoughts. Mathematicians are really comfortable with it being undefined, and they really don't have any motivation to change that.
ZERO!
x*0 = 0, where "x" is any number.
Solve the equation and your got x = 0/0. So, 0/0 can be made to equal any number. Since there is no single agreed upon solution, we say that 0/0 is indeterminate.
0 x y = 0, y = 0/0, so nothing divided by nothing can be anything?
2:21 2:21
FAQs
The problem with dividing zero by zero (video) | Khan Academy? ›
One can argue that 0/0 is 0, because 0 divided by anything is 0. Another one can argue that 0/0 is 1, because anything divided by itself is 1. And that's exactly the problem! Whatever we say 0/0 equals to, we contradict one crucial property of numbers or another.
What is the contradiction of dividing by zero? ›These notes discuss why we cannot divide by 0. The short answer is that 0 has no multiplicative inverse, and any attempt to define a real number as the multiplicative inverse of 0 would result in the contradiction 0 = 1.
What is one of the many consequences of dividing by zero? ›Depending on the context and the type of number involved, dividing by zero may evaluate to positive or negative infinity, a special not-a-number value, zero, generate an exception, display an error message, or crash or hang the program.
Why is 0 factorial 1 khan academy? ›"It's the product of all integers greater than or equal to 1 and less than or equal to 0. But there are no such integers. Therefore, we define 0! to equal the identity for multiplication, which is 1." Answer Button navigates to signup page • 3 comments.
What is the error divided by zero? ›Answer: If a number is divided by zero gives the answer “equal to infinity.” Unfortunately, no data structure in the world of programming can store an infinite amount of data. Hence, if any number is divided by zero, we get the arithmetic exception .
Why is it wrong to divide by zero? ›As much as we would like to have an answer for "what's 1 divided by 0?" it's sadly impossible to have an answer. The reason, in short, is that whatever we may answer, we will then have to agree that that answer times 0 equals to 1, and that cannot be true, because anything times 0 is 0.
What is the error in the divide by zero formula? ›To correct the error, do any of the following: Make sure the divisor in the function or formula isn't zero or a blank cell. Change the cell reference in the formula to another cell that doesn't have a zero (0) or blank value.
What is the fault of divide by zero? ›Divide-by-zero faults occur when a program attempts to divide a number by zero, which is mathematically undefined. This can happen due to programmer errors, user input errors, or data corruption. For example, a program may try to calculate the average of a list of numbers, but the list is empty or contains only zeros.
Is it illegal to divide by zero? ›A division by 0 still cannot be defined. That is why the true answer is actually undefined. Undefined does not mean infinity, but rather there is no consistent answer.
What happens if you divide 0 by 0? ›In ordinary arithmetic, the expression has no meaning, as there is no number which, multiplied by 0, gives a (assuming a≠0), and so division by zero is undefined. Since any number multiplied by zero is zero, the expression 0/0 is also undefined; when it is the form of a limit, it is an indeterminate form. Q.
Why do we get infinity when divided by zero? ›
If you divide by a very small negative number, you'll get a very large negative number. There is no “division by zero” and there is no “answer” of infinity. You are thinking of a limit. Division of a number by x, as x tends to 0, is “infinity” but this is the answer to a limit, not a calculation.
Why is division by zero not defined? ›You can understand why if you think about how division and multiplication are related. 12 divided by 6 is 2 because 6 times 2 is 12 12 divided by 0 is x would mean that 0 times x = 12 But no value would work for x because 0 times any number is 0. So division by zero doesn't work.
Who invented zero? ›Aryabhata, a great astronomer of the classic age of India was the one who invented the digit “0” (zero) for which he became immortal but later on is given to Brahmagupta who lived around a century later 22, another ancient Indian mathematician.
Is dividing by 0 a logical error? ›Detailed Solution. "Divide by zero" is NOT a logical error it is runtime error. Runtime errors: These occur when the program is running and something goes wrong.
How do you ignore divide by zero error? ›Arguably the cleanest (mathematically) method to avoid divide by zero errors is to multiply quantities, rather than dividing one by the other. This method, while adding no overheads to the simulation, would require the reformulation of some equations to be adequately implemented.
Is 0 0 is infinity? ›Uh, 0/0 doesn't equal infinity, it's UNDEFINED because if 0/0 = x, then x times 0 = 0, but that's true with every number.
What is the rule for dividing by zero? ›Dividing 0 by any number will give us a zero. Zero will never change when you multiply or divide any number by it. For example, a person has zero toffees which are to be divided among 7 ( let's say) children.
Is it possible to divide 0 by 127? ›Yes, it is possible to divide 0 by 127. The quotient would be 0. When you divide 0 by any nonzero number, the result is always 0. This is because 0 divided by any number is an example of zero property which states that any number multiplied by 0 is always 0.
What is it called when you can't divide by zero? ›Because what happens is that if we can say that zero, 5, or basically any number, then that means that that "c" is not unique. So, in this scenario the first part doesn't work. So, that means that this is going to be undefined. So zero divided by zero is undefined.