Why dividing by zero is undefined | Functions and their graphs | Algebra II | Khan Academy

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[uzairhussain]

The problem is at school level we are not taught the detailed historical devolopment of Real number system and arithmetics.... So its really hard to intuitively understand the essence of Maths in early classes.

[ReyhanMehta]

To be honest, I really think that zero should be treated as the absence of a number rather than a number itself (especially in cases like these)

[jakeseo]

Sal: Dividing by zero is undefined and impossible.


*Riemann Sphere has entered the chat*

[riversonthemoon]

I'm cancelling one of the terms, which is a step that is often used in a proof.
Consider this more explicit example from Wolfram MathWorld:
1. Let a = b
2. ab = a^2
3. ab - b^2 = a^2 - b^2 Factorize to get
4. b(a-b) = (a+b)(a-b) Cancel the (a-b) to get
5. b = a+b Since a = b you can write this as
6. b = 2b Cancel the b and you prove that
7. 1 = 2

Where did it go wrong? It went wrong at step 4. Since a=b, we've divided by 0 which has brought us to a contradiction.

[stjimmy]

something divided by zero being 42 actually makes a lot of sense :)

[marr]

Everyone should think about it this way:

1÷0.001=1000, because there are 1000 0.001's in 1. Just like how 10000÷10= 1000 because 10 goes into 10000 1000 times.

So therefore 1÷0 is the same thing as saying: "How many zeros are in 1?" - The answer?

[addieroxrev]

wow..now the concept is so much more clearer !! ..this my friends is TEACHING !

[FollowerofDuck]

its an interesting concept! especially its connection to black holes

[janehuskmann]

Here's my bitcoin about this:
To divide by zero is, basically, to multiply by infinity. Many programs tried to divide by zero, only to keep multiplying the number being divided until it crashes. I know he mentioned the first part of that in there, but still...

[ptripathy]

42. I get the reference from "A Hitchhikers Guide To the Galaxy" ;)

[RandomBitzzz]

42!!! I love it. That is the answer to life, the universe, and everything

[Turtlegamer]

I think that anything divided by 0 is undefined because the answer to x/0 must = x when multiplied by 0. Well the only way that could work is if x = 0 because anything times 0 is 0. I think this explains this well but doesn't explain why 0/0 doesn't = 0.

[nyfanta]

I am learning in the middle of the summer! how interesting!

[Spootmeister]

This may have already been stated elsewhere, but an even better reason for division by zero to be undefined is that division can be defined in terms of multiplication, as follows: a/b is the *unique* number c such that cb=a. Let b=0. Then for non-zero values of a, cb=a is false for every value of c. If a=0, then cb=a is true for *every* value of c, meaning that a/b does not yield a unique answer. So in one case, no number c satisfies the definition of a/b. In the other case, every value does.

[BoutinMathieu]

What a great explanation! Thanks a lot, I really liked the way you presented it.

[lsmk]

it works exactly as the video says!
try to plot the graphic of 1/x at wolframalpha. as it approaches to 0 from left, it goes down and down. analogically, it goes up and up as it comes from the right. therefore, it is not possible to define a value for it, as it:
a- never stops growing (or getting smaller)
b- has different values in each case
hope it helps a little!

[masvindu]

Think of it like this. 1/1/n = n(1)/1 = n/1 = n

Clearly, As n approaches infinity, 1/1/n approaches infinity. Since infinitesimal can be defined as 1/infinity (Read about hyperreal and surreal concepts if need be), 1/1/infinity = infinity is just a simple rearrangement, no operations are actually carried out, that would be another story.

Though my comment was not meant to be looked at in the sense of calculating those numbers, it was purely meant for intuitive conception.

[ThePeterDislikeShow]

I wish we had Khanacademy when I was in 8th grade

[Pinewoodpaladin]

GOOD SHOW! Bravo my good man, Bravo! Thanks for explaining this topic to it's current date and definition.

[Pinewoodpaladin]

GOOD SHOW! BRAVO! Thanks for the explanation.