The REAL reason you can't divide by zero

This video will walk you through the reasons why we avoid dividing by zero in maths.

Tags: #maths #learning #study #students #math #mathematics #puzzles #problemsolving #gcse

[kylebantsi]

Our lecturer said dividing by zero is a criminal offense

[Slammy]

I think it goes back to the basics of counting. If you have 5 items and you want to divide them into groups of size 0 you would be able to create an infinite number of groups with nil population. It's a logical absurdity under the assumptions of division.

[BrandonGrantSplash]

Math is hard you make it simple many thanks good Sir.

[SorakaOTP]

You can divide by 0, but you'll never get the answer because you'll get tired of writing infinitely long

[jiminverness]

If 1 ÷ 0 = infinity and 2 ÷ 0 = infinity, this does *not* mean that 1 = 2.
Remember, infinity is not a number, is not finite, and does not have a specific value.

[WojtekXD-bxjb]

By looking at lim (1/x) x->-∞ and lim (1/x) x->∞ you can see how when the number on the negative side increase in value, the y decreases, which shoots downwards at around 1. Same goes for positive numbers. As they decrease in value the y increases and shoots upwards at around 1. The thing is that 0 is both positive and negative. The values grow infinitely large and negatively infinitely large. If zero is part of both sides then anything divided by 0 is literally both positively and negatively infinite at once, which can be written as for example {-∞;∞} (this also disallows y=1/x from being a function, so dividing by zero in functions breaks everything). The thing is that such number is beyond anything else in math, even complex numbers aren't as bs as this. You cannot even use this value because even reversing it doesn't work: ∞*0!=1. 0/0 is the closest anything over 0 comes to making sense, as in that situation you simply get 2 different answers depending on how you see fractions: it's either 1 or {-∞;∞}

[omghealme]

Nice, I didn't think of it like this before! You've earned yourself a new subscriber!

[jl_MindfulMoves]

This is great, thank you for explaining

[Ak-]

Very interesting. This is a great way to think about it!

[summerjee]

Let's define 1/0 as the multiplicative inverse of 0. and then we can write 2/0 = 2 * (1/0) and so on. so x/0 = x * (1/0) = x * ∞ = ± ∞.

[KW-gbcd]

A lot of people are divided by zero; some say it's a number, and some say it isn't.

[glerbus]

simple, if its a positive divided by zero make it positive infinity, if a negative by zero, negative infinity, zero divided by zero, simple, 1.

[Jacobconnor]

before watching, I came up with a 'proof'. Which step is wrong?
Step 1: 1/♾=
Step 2: 2/♾=
Step 3: 2/♾=
Step 4: 1/♾= 0
Step 5: 2/♾= 0
Step 6: 0=1=2=3=4=5...=♾
Step 7: a/b is always equal to c
basically, 5/9 = 2 now???

[prabbit]

There's a very simple way to prove it has no value. If you have x/y=z, that can be re-arranged as x=y*z. If y=0, then the ONLY way that would work is if x and z are also 0 as y*z would always be 0 for any value of Z..

[persel_hd]

I think Zero is a state as well just as Infinity.
In this case infinity would be the maximum negative and positive amount while zero would be the minimal.
It's like the binary system just instead of 1 u use infinity.
If look at a graph the most logical x in "divided by 0" would be negative or positive infinity.
Furthermore if you calculate the average of both results (∞ and -∞) you get what? Exactly either 0 or a number that is both negative and positive (like 0).
so divided by 0 would either end in in infinity or zero, i personally like zero (is more realistic in common use).
I think you could also say with that, that
∞ + (-)∞ = 0

[drog]

All numbers multiplied by 0 equal 0, but that doesn't mean that all numbers are equal to each other. From this, it is a reasonable claim to make that 0 is an exception, and that any number divided by 0 equals infinity.

[Low_cops]

1:05 the fallacy there isnt that they are equal, but you are assuming that the two infinities are the same infinity. one of them (if your conjecture was true) would be larger. therefore, you cannot set them equal ti each other. if you accounted for this with some more conjecture, your equation would work out and all would work.

[mubashirulmoula]

Isn't there an argument that just like 0, infinity is neither positive nor negative?

[_mishki_]

You actualy candevide by 0. When i learned devision the teacher told us that the 3rd number (for example the 3 in 12:4=3) when its multiplyed by the 4 it should give 12. if you try to deivde 1:0=, thenew number is going to firs off be 1. you multiply 1 by 0 and you get 0. 1-0 is 1 and you add an extra 0 so it becomes 10. you then add a 9 so that its now 1.9. 9 multiplyed by 0 is 0 and 10-0 is 10 and you add an extra 0 so it is 100. 1:0 is when it is rounded the answer is 1:0=2 wich doesnt mach with the laws of deviding bc if you devide for example 12 with a 4 you will gett a smaller number (3). It breakes the law of deviding so it just says that it canot be devided by 0 if you try to devide something with a 0.

[sxkb]

Why can we not say the following?:
0:0=ℵ₀
1:0=ℵ₁
2:0=ℵ₂
3:0=ℵ₃
etc.