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

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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[TEDEd]

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[echo.]

“1=2”

*years of academy training wasted*

[KevinTyler]

Math is quite interesting when you're not studying it for the test.

[shipweck]

Another interesting method is to use limits. If you look at a graph of 1/x, you’ll notice that the graph skyrockets up when approaching zero from the right, and plummets down when approaching zero from the left. This is because if we begin to approach zero from the right (or positive) side (by starting a 1 and then to 0.1 and then 0.01...), the answer approaches infinity. But when we approach zero from the left (or negative) side (from -1 to -0.1 to -0.01...) the answer approaches negative infinity. This means that if we were to assign a value to the graph when it reaches zero (yes I know you cannot do this), it would have to equal both positive and negative.

[cubicalgamer]

I tried something similar to this. Just as sqrt(-1) = i, I defined 1/0 as o. Then, I went as far as I could trying to figure out all the properties of this new number that I could. I had to bend quite a few rules and I still ran into a bunch of contradictions. I hope that someday, as my math knowledge grows, I can make o a number.

[wukennylee]

Wait, so "MATH ERROR" isn't a number ?

[cruithne_]

My maths teacher has a shorter answer: "trust me, just don't"

[nuzayerov]

This can also very nicely be explained by using a y = 1/x graph. Where x approaching from positive x-axis to 0 gives us an Infinitely large positive number. While x approaching from negative x-axis to 0 gives us an infinitely large negative number. And 1/0 cannot be both positive and negative infinity at the same time.

[mitragh]

Math teacher here! Beautifully explained. Thank you for the great work 🙏

[gd]

"Congratulations! You've earned 2nd place!"

Me: "Let me tell you how 2=1."

[LegendOfMario]

2:41
"Why can't we take the square root of negative numbers, John?"
"Because you just can't, Emmy."
"What if I would call it "i"?"
"Wait, how would that even make se-"
*A WHOLE NEW WORLD OF MATH OPENS UP*

[Kaldrin]

I really liked the comparison with complex numbers and the multiplication by infinity, was very cool and clear, I never looked at this angle

[Damaris_Lane]

Didn’t know I could enjoy maths. This was wholesome. Thanks Ted-Ed.

[imnotsus]

*Everyone gangsta till they realize the only number in the whole world that has no value is the most complicated to understand*

[billyk]

Yes, and the mitochondria is the powerhouse of the cell

[ZeroKung]

I enjoy watching this alot more than learning at school for exam

[fuberlin]

Finally! I can now in piece acceppt that this is not possible! Great explanation! Thank you!

[runonline]

♾ next generation mathematicians breaking rule:
The inverse of infinity is 8

[ThePinkRubber]

Other animal : *eat, sleep, reproduce. Try to survive.
Humans : "what if i divide 10 with 0"

[pallavij]

I worked on the math work on division, multiplication and addition. 1:41 The thing is a example:12/2=6*2=12