# Why can't you divide by zero? - TED-Ed

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**Published: 23 April 2018**- Check out our Patreon page: https://www.patreon.com/teded

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In the world of math, many strange results are possible when we change the rules. But there’s one rule that most of us have been warned not to break: don’t divide by zero. How can the simple combination of an everyday number and a basic operation cause such problems?

Lesson by TED-Ed, animation by Nick Hilditch.

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TED-Ed I just want to ask,when I tried 0 divided 0 in calculator,the result is ERROR. Why?

The voice is super annoying

Why do they use anti matter for i its till has postive mass if it was negative we would have no matter on contacted of each other

At minute 1:56 the video shows a triple equality that isn't true. I know what you wanted to say, but you have to be careful with notation.

When God divided O, boobs were created.

1 does equal 2.

We have two variables, a and b. As long as they're the same and not zero, it's fine.

They could be both 3, both 7, or both 1371742, but they can't be both zero.

1. a = b

2. a^2 = a*b(multiply by a)

3. a^2 - b^2 = a*b - b^2(subtract b^2)

4. (a+b)*(a-b) = b*(a-b)(factor left side as a difference of squares: a^2 - b^2 = (a+b)*(a-b) and right side as a distributive property, a*b - b*c = b*(a-c))

5. a+b = b(divide by a-b)

6. b+b = b(since a = b, you can substitute a for b in an equation, and vice versa)

7. 2b = b(for every a, 2a = a + a)

8. 2 = 1(divide by b)

B is not zero, defined by the given a and b are not zero.

Now that we have that 2 = 1, we can create an infinite list of axioms, each inferred from the last one:

1. 2 = 1

2. 1 = 0(subtract 1)

3. 2 = 0(combine 1 and 2: if a = b and b = c, a = c)

4. 3 = 1(add 1)

5. 3 = 0(combine 4 and 2)

6. 4 = 1(add 1)

7. 4 = 0(combine 6 and 2)

... .... .....

z. m = 1(add 1)

z+1. m = 0(combine z and 2)

z+2. m+1 = 1(add 1)

z+3. m+1 = 0(combine z+2 and 2)

... and so on.

Now we have an infinite list of things, if we continue this on infinitely.

Extract line 1 from the list, and all of the even numbered lines that are after 3(4, 6, 8... )

Now we have the list:

2. 1 = 0

3. 2 = 0

5. 3 = 0

7. 4 = 0

9. 5 = 0

... and so on.

Now renumber the lines.

1. 1 = 0

2. 2 = 0

3. 3 = 0

... and so on.

Now we have an infinite list saying that every positive integer = 0. Let's call this list l, and the items in it 1, 2, 3, 4...

By the rule if a = b, -a = -b(multiplying both sides by -1), since -0 = 0, we can create another list, called l'(l prime):

1'. -1 = 0

2'. -2 = 0

3'. -3 = 0

... and so on.

Now we have an infinite list saying that every negative integer = 0.

Also, if we have a fraction, we can substitute the top for zero, making that every fraction is zero too, call this l''(l double-prime):

1''. 1/2 = 0

2''. 1/3 = 0

3''. 2/3 = 0

... and so on, continuing with 1/4, 2/4, 3/4, 1/5, 2/5, 3/5... and so on...

This list, l''(l double prime) says that every fraction of two positive integers inbetween 0 and 1 is equal to zero too.

If you add 0 to 0 you get 0 also, and so if we make all of the mixed numbers = 0, in a list l'''(l triple prime).

Let's call infinity "t" for short:

1'''. 1 1/2 = 0

2'''. 2 1/2 = 0

... ... ...

t'''. t 1/2 = 0

t + 1'''. 1 1/3 = 0

... ... ... and so on... ... ...

And therefore, every fraction is equal to zero. Again, we have l quadruple prime(l'''') and l quintuple prime (l''''') saying that every negative fraction is also equal to zero:

1''''. -1/2 = 0

2''''. -1/3 = 0

3''''. -2/3 = 0

... ... ... and so on... ... ...

1'''''. -1 1/2 = 0

2'''''. -2 1/2 = 0

... ... ... and so on... ... ...

l'''' is just a negative of l'', and l''''' is a negative of l'''.

Since every fraction above 1 is just a mixed number, all of the fractions above 1 = 0 list is the same as l''', and the fractions below -1 are in l'''''.

Now we can merge all of these l lists together, in a superlist called q.

We have a list saying that every integer and fraction, positive and negative, is equal to zero now. Now that, since if a = b and b = c, a = c, every integer and fraction, positive and negative, is equal to eachother too!

Since therefore the numbers picked as a and b are zero too, therefore this could never exist since then a and b would violate the zero-rule. But then this could never have been proved, and therefore the rules of math are back to regular. Therefore the numbers picked as a and b would not be zero anymore, this could be proved.

So this could be proved, which means that a and b are zero, which means this could not be proved, which means that a and b are no longer zero, which means this could be proved again. It's a paradox.

Because your teacher keeps telling you so, it's simple

What is 0÷0

Any number that is devided by zero is zero

Example 10/0= zero not infinity

if a / 0 = 0, 0 * 0 = a

So what you're saying is that the product of 0 and 0 is any number, therefore the square root of any number is 0?

Is this not just advanced algebra and what they try to find out

I broke a math rule, but failed the exam.

Maybe current mathematics can't divide by zero but surely future mathematics will

0 is amazing by the way 🤔😁😜

After watching this ,I clicked Like but and app said "Removed from liked videos".

I was like wt!!! I already watched that many times ago and literally forgot.😅

You have a 20 cm ruler

You divided it by 3 doesn't mean you cut the ruler into 3 pieces of ruler that each piece is 20:3 cm long.

It means you cut the ruler into 3 pieces of ruler and you can just keep 1 piece.

So a 20cm ruler divide by 3 =a 20:3cm ruler

Not = 3 20:3 rulers

So when your mum tells you to divide a bread by 3, you cut the bread into 3 pieces and throw 2 pieces away.

infinity ÷ 0 is less than or equal to infinity.

Please add Hindi language in captions

As an English education major this finally put me to sleep. Thanks math!

Infinity divided by 0

Thanos:DID YOU SAY INFINITY?

1:56 This notation can be quite misleading

Remember infinity is a SYMBOL for a number we can't count to/it's an infinite amount of zeros. So it doesn't =infinity (saying infinity is a number)it is infinity

3:30

there's the fallacy

you have said "let the symbol infty be a number so that infty *0 =1" and you also said "assuming we know nothing about infinity"

then why should 2 infty =infty?

that is a preconceived notion of how infinity works

there are other ways to show this method isn't valid, just that this one in particular was not it

for example, let y so that 0y=1

1+1=2

0y+0y=2

2 0 y = 2

(2 0) y = 2

0 y = 2

but 0y =1

however note, this disproved EITHER associativity OR the existence of y, not necessarily the latter.

John has four apples, he distributes them fairly with Mike, how many apples do they each have? Two.

John has zero apples, he distributes them fairly with Mike, how many apples do they each have? Zero because there are no apples to distribute.

there are four apples on the table, they are not divided because there are zero people to distribute them, how many apples does everyone have? zero because there are zero people to divide them. 4 ÷ 0 = 0.

SOLVED

(Google calculator says that 4 ÷ 0 equals infinity)

my head.....

They is an answer to any ÷0. That is an infinity. And if it's 1÷0 it's infinity because it's not how much 0 is in 1. It's just the opposite of times. Look it's hard to explain but it's still infinity. Because reasons

Easy answer to the title question without watching the video is because you can’t turn nothing into something.

You can't divide 0 by 0 because that's just like saying I have 0 dollars and I divide it by 0 people. Check on our calculator

actually

once i asked my math teacher in fifth grade: What is 1 divided by 0? (said it before that became a math dilemma)

the next day he told me this:

"Any number times 0 would be 1"

Edit: acctually happened

Its equal to 0 dude

1:30 . 10÷2 means if you divide ten twice, how much is a single piece's value. Not how many times 2 can be subtracted from 10. I know, I'm being a snob. But there's a difference.

*number comparaison*

1 one

10 ten

100 hundred

10^3 thousand

10^6 million

10^100 googol

10^10^100 googolplex

g:64 graham number

aleph 0 infinity

aleph 1 infinity of infinity

*1 divided by 0*

3:30 ∞ + ∞ =2∞ so 0x2∞ =2

Why is 2∞=∞

Roni Shaheen, true, but 2∞ = ∞

How about 5 ÷ 0 =

$5 ÷ 0 friends = $0

$0 given to your friends XD

but somehow you must explain that the 5 dollar suddenly stop existing

If you cant divide by 0

Why can we answer multiplication

5 × 0 = 0

But how about this way

0 ÷ 0 = 5

Bry Bry, you are right, 0/0 can be 5. But also...

1 * 0 = 0

0/0 = 1

It can be 1, too. In fact, it can give any number in existence. Since it can be any number, and we don’t know which one, we call it indeterminate. We need more information to find its limit.

10 divided by 2 means that 10 items are divided into 2 groups of 5 of these things. This would indicate that 10 divided by 0 means there are 0 groups, thus dividing by 0 equals 0?

i thought the answer was always ERROR

my math teacher make me divide by zero im not confused

Anything to the power of zero is one.

But something cannot come of nothing.

So my question is...

What is zero to the power of zero?

_ShadowShot _, 0^0 is indeterminate/undefined. By itself it has no definable value.

Disappointed to see you break the rule of equals. 2x3=6x0.5=3 isn't correct; not all of them are the same.

Poor form Ted talks, poor form

Infinity times infinity is infinity squared 3:20

Austin Liu, but infinity to the power of any positive number is infinity.

Divide $10by 0 u still got $10 You don't have more money also divide 10 $ by 0.00001 it can not be logically more than $10

That's... that's not how division works.

3:28 Wouldn't ∞ plus ∞ equal 2∞?

@Gnome Ann I understand that you mean that ∞ + ∞ would still algebraically equal ∞. But 2∞ doesn't only mean that its value is ∞. It more importantly denotes that ∞ can be written twice, like ∞ + ∞ which actually does matter in this case because it would then set the equation true, and 0 + 2∞ would = 2.

Mr. Anonymous, it does, but writing out 2∞ is unnecessary, since infinity times any number except zero is equal to infinity, so:

∞ + ∞ = ∞(1 + 1) = 2∞ = ∞

(Note that it is not really formal math to do operations on infinity like this, if we wanted to be more technical, we would use aleph-0 or limits).

Excellent explanation. Thank you.

I've wondered about this so many times. Here's what I think:

Where do we use division in basic day to day life?? Like dividing things between people. If you have 10 candies and want to divide it equally to 2 people, you will divide 10 by 2, so you will give 5 to each. If you have 3 apple and want to give equal pieces to 2 people, you will give 1 each (3/2, Quotient= 1 reminder=1), 1 will be reminder but if you choose to absolute you further divide that remaining apple into 2 and give half each (3/2=1.5, 2*1.5 = 3), so the answer will be 1 and half each . So if you are having 20 KG mango, you give equal kg of fruits to 0 people, how will you divide 20kg with 0 people? You don't divide because there is no one to give it to, reminder is 20kg.(20/0=?) So what must be multiplied to 0 to get reminder 20 itself. Answer is 0. But 0*0 is not equal to 20. ughhhhh.

0 discovered in India and explored with Einstein in 20th century, breaking rules of Newton.

So breaking rules will continue in future also..

Alot better explained.. The rules applies in limit and calculas

Yes, fun worlds to explore, while completly pointless by any means, apart from the fun about nonsense.

Really?!

Mathematicians hate to be unemployed ... that might be TRUE!

0:0=1?

well all i knew is that MITOCHONDRION is the powerhouse of the cell.

3:40 looks like heavy quantum stuff... Is it possible to divide by zero in a quantum world?

10 ÷ 0 = 0

There is no multiplication

0 × 0 = 0

So 0 equals nothing and if 10 × 0 would be 0 because there would be nothing there

Just a theory