I Finally Found Out What 0/0 Should Be

[@BriTheMathGuy]

🎓Become a Math Master With My Intro To Proofs Course! (FREE ON KZbin) kzbin.info/www/bejne/aZTdmJl-irGNedU

[@mainhandle101]

Wait 3 days ago? This was seconds ago when this was uploaded

[@arjuns.3752]

How is your comment 3 days ago??😶

[@p_square]

@@arjuns.3752 I think it was uploaded early for channel members so it was originally uploaded for members but made public for subscribers today

[@mainhandle101]

@@p_square oh cool

[@reda29100]

This is the type of guy that doesn't take (0/0, or no) as an answer! Also, if we take (0+0)/0 instead (0-0)/0 = 0/0 = x-x= 0 but 0/0 is also x. So 0/0=x=0. So we reach a contradiction: the *only* solution for 0/0 is 0, but also based on the sol presented in the vid, 0 *AND* infinity.

[@hendmatar211]

If you don't have a pizza, and you don't slice it, you will end up with no pizza. infinity pizza doesn't exist, 0 pizza also doesn't exist. so infinity pizza = no pizza. I need pizza.

[@doi9956]

That mean my stomach is empty :(

[@austinlincoln3414]

lol wtf

[@flatouttroll5932]

hold on isn’t this just 0/1

[@tenoshrebello]

@@flatouttroll5932 yeah I think it's 0/1

[@parlor3115]

Infinite Pizza is UNACCEPTABLE!!!

[@Jtwoe]

Maybe 0/0 is the friends we made along the way…

[@supe4701]

But what are the friends we made along the way

[@lemonaski7311]

@@supe4701 the quadratic formula

[@443MoneyTrees]

Which is 0 LmAO

[@buycraft911miner2]

@@443MoneyTrees why did u have to call me out like that

[@akshat_shukla00]

My first friend that I made in college Was due to literally debating over 0/0 So yea..

[@PunmasterSTP]

I still feel like there is no definitive answer, but I really appreciate all of the topics and perspectives you brought up in your video. Thank you so much for sharing it!

[@santo8813]

0/0 might be kinda far fetched to be infinity, but anything else divided by 0 just makes perfect sense. How many 0s can fit into 1 (1/0), infinity. As after an infinite amount of nothing is crammed into something, it will fill up. Zero is so unimaginably small, and infinity is so unimaginably big, so it just makes sense idk

[@PunmasterSTP]

@@santo8813 Ah I see! So I suppose that an infinite amount of zeros could fit into zero as well...

[@axywrll6015]

if you keep dividing 0 it goes up. rounding is up so zero is neither negative or positive. but when you start going up ALOT, infinity has value and 0 will start to be the same number as infinity. that's as simple as I can say it.

[@PunmasterSTP]

@@idigulay1274 Sorry I'm not quite sure I understand, and google translate couldn't help me out either. What do you mean?

[@idigulay1274]

@@PunmasterSTP I'm sorry, my phone in my pocket pressed random keys

[@nuclearurpi1571]

0/0 is the "+ c" constant from integrations.

[@BadMathGavin]

But 0/0 = 1 and we don't add "+1" to the end. Maybe +c(0)/0 so it cancels to c lol

[@mistahmatrix]

@@BadMathGavinno cause when determining limits of functions that simplify to 0/0 it can equal any number, but only one is true for that case. Just like + C

[@AleksaBarjaktarevic]

Great idea.

[@rabih.1975]

0/0 is when you divide your friends on your math marks

[@adudeontheinterweb6571]

0 sometimes acts as a number and sometimes acts like an identity

[@banuelostorresdaniel982]

You can create an extension field defining 1/0 = ∞ and 0/0 = * is special element. Getting something analogous to projective geometry

[@angelmendez-rivera351]

Indeed. This is wheel theory in a nutshell.

[@jacobhatfield764]

Wait, in set theory, 0 is just the cardinality of null. So, dividing null by null would be undefined as it is an empty set. For instance, you can say that the difference of Set A-B would be A, but when would {}-{} make any sense?

[@findystonerush9339]

Wow! you almost got it! 0/0=(1/0)*0 and 1/0=infinity.And infinity*0=1 so 0/0=1!😄

[@maxv7323]

@@findystonerush9339 It doesn't appear justified that 0/0 = (1/0)*0 or that 1/0 = infinity, or that infinity * 0 = 1, nor have you even defined what you mean by infinity as a number.

[@Ewr42]

@@maxv7323 first two are trivial from examples from the video. third one idk in what context he got it to be 1, but we need to define more stuff to tackle these questions, current maths lack the transformations from logics and abstractions, we haven't defined what they mean and how they work, we don't understand this field because our axioms don't apply to it. It's an entirely new type of protomathematics that's only useful in highly specific cases and we can't figure out how to prove anything in it in a way everyone can interpret the same thing, because it touches on complex abstractions which need a ton of context, without any, anyone interpret what they want to interpret, it's a rabbit hole, but I do think there's a light in the end of the tunnel and it's like a wormhole to the answer, once someone flips the final switch and figures out how to properly map and how the rules work in this field

[@khoi34145]

3:26 Please note that in this step, you cannot convert the coefficient before 1/1, which is 1, to 0/0 to reduce to common denominator and get this because 0/0 still has an unknown value at this time so you don't know whether 0/0 is equal to 1 or not

[@Bassam-qc6wl]

He didn't claim 0/0 = 1 at all anywhere in this video

[@ShignBright]

I always said that 0/0 is equal to infinity! My understanding of division at the time was "How many times does the numerator go into the denominator?" and zero goes into zero infinite times, because zero doesn't add anything!

[@DemoniteBL]

Yeah, but then it could also be negative infinity.

[@puddingsyrup]

yeah but it doesn't only go infinite times. it also goes 1 and 2 and 3 and 4 times and literally every number of times since 0x always equals 0. no matter what the x is it is always equal to zero whether it's 73517390 or infinity or any other number. so that's why it isn't exactly equal to infinity and is undefined.

[@faytachiMPS]

0/0 being equal to infinity (or 0) is semantically and mathematically impossible as A) infinity isn't a number per se: infinity is not a value. Its a name given to a "boundless limit". Nothing ever equals infinity, things can only approach infinity as you change a variable. For example, x/y approaches infinity for x>0 as y tends to zero from the right. Whenever you hear a mathematician say something equals infinity it's shorthand for a limit of some kind. B) let's use expression x/0 x/0 isnt infinity as the rules of algebra say that, if x/0 = infinity, then infinity times zero equals x, for any x you choose. IF x/0 = ∞, THEN ∞ * 0 = x However, this is obviously wrong as any number multiplied by zero is zero. And infinity is not a number, it's an idea. C) assuming the expression x/0 and x is 10 apples, you can't add an infinite amount of zero groups together and end up with say 10 apples also you can rationalise 0/0 much simpler using the idea that division is the inverse of multiplication: 0/0 = 0 is absurd and incorrect because it would allow for the proving of 1=2 (which obviously is absurd) 0x1 = 0 0x2 = 0 lets say we allow the division of 0: 0x1/0 = 0x2/0 (both divided by 0, so equivalent to previous lines) (0x1/0) x 1 = (0x2/0) x 2 (both times by 1, so equivalent to previous lines) cancel out the zero on both sides and you get: (0/0) x 1 = (0/0) x 2 cancel out the expression 0/0 on both sides and you are left with 1 = 2, which is obviously incorrect meaning division by 0 is impossible

[@terminusadquem6981]

I've always liked to investigate areas of glitches in mathematics. It's like gateways to a whole new other dimension. The elements there behave strangely and don't seem to conform to the known laws of mathematics. We must investigate these like scientists and see what we might uncover, maybe the underlying structure or mechanism of mathematics and maybe reality to which this new mathematics will be telling.

[@terminusadquem6981]

@Lady Mercy [seemingly] glitches. Sorry, if I was not clear. Of course, I wouldn't know if it's a real glitch or not unless I have investigated it, but if you did, good for you. Math, though how practically powerful it is, still is incomplete. I guess you'd know that by Kurt Godel's theorem.

[@lelouch6457]

@Lady Mercy i don't really like thinking that infinity + 1 is still equal to infinity it's a long story but I suggest checking out a video made by veritasium on infinity but it basically goes like this you have a row from 1 to infinity each number serving as an index number and then you have a column with A and B in an going to infinity in any order corresponding to the index so it would like like 1-AABABBABABABAA(so on till infinity) 2-ABABABABABABAA(so on till infinity) 3-ABAABABABABABB(so on till infinity) (so on till infinity) so we would have every possible sequence of string of infinite A's and B's since there are an infinite number of real numbers and each number is acting as an index for the string of A's and B's for the infinite sequence of A's and B's but if we move diagonally in AB column and change the letter (if it's A change it to B vice versa) then we will have a string of A's and B's present nowhere in the infinte sequence of A's and B's since the new string will be different from the first letter of the first row by 1 letter (so A turns B) from the 2nd letter of the second row(B turns A) and so on till infinity proving that an infinite sequence of A's and B's in an infinte combinations is greater than the infinte real numbers hence some infinity's are greater than others we could also write the the A's and B's as infinity² since it's infinte in both rows and columns while the real numbers are infinte only in rows btw I still think 0/0 = infinity since let's say 25 divided by 5 is a representation of how many times I can subtract 5 from 25 until it's 0 or I am left with a number smaller than 5 which will become the remainder incase of 25 by 5 I can subtract 5 five times from 25 so 25/5= 5 therefore incase of 0/0 since you can subtract 0 and infinte amount of times from 0 it can be said that 0/0= infinity I hope someone finds it and takes the patience to read this if you do please like it so I know my time was not wasted writing this huge essay thing

[@ingenuity23]

@@lelouch6457 this is actually very similar to the proof that there are more real numbers between 0 and 1 than there are natural numbers. It also goes that way, generating real random numbers of infinite length and then generating a new number by taking the digits along the diagonals of each number, thus generating a new number not yet present on the list.

[@ingenuity23]

@@lelouch6457 the time clearly wasn't wasted and i feel this perfectly encapsulates the idea of "infinity" as a concept, rather than another arithmetic number. my previous comments also shows how some infinities are bigger than other infinities. I suggest seeing veritasium's video on Gödel's incompleteness theorem, which highlights this proof given by cantor

[@ingenuity23]

@@lelouch6457 kzbin.info/www/bejne/fpa0iWV-n9CWhNE a link to the video

[@siquod]

Meanwhile, at the IEEE: Yeah, we thought long and hard about what algebraic properties are least likely to cause problems, and so we decided 0/0 should be unequal to itself.

[@franchufranchu119]

Meanwhile at ECMA: Yeah so make a 1^100 equal 1^100+1. It's faster that way

[@Crazylom]

Are they tripping on ecluidicin?

[@Rudxain]

@@franchufranchu119 I know it's a joke, but almost every programming language uses the IEEE 754 "binary64" floating point standard format. This format (like every other fixed-precision floating-point formats) has precision limits which render some calculations into no-ops (they do nothing, even though data has actually been processed). Each format has its own specific limit, both for large absolute values and tiny abs values. "binary64" reaches its limit when the abs value reaches 2^53, because the mantissa has 52 real bits and 1 "ghost" (implicit) bit. Every other number after that limit must be an integer with 1 or more binary trailing zeros (mathematically, but not in memory) to preserve the magnitude (exponent) of the number

[@mikehenry9672]

@@Rudxain I wish I could understand what any of this means 🤣

[@Rudxain]

@@mikehenry9672 IEEE 754 is just a weird codename. "binary64" is almost never used as name because it's VERY ambiguous (anything can be a 64bit binary value). Floating-point is the opposite of Fixed-point, it means the "decimal" (actually binary) point can be moved freely left or right, you can represent a wide range of magnitudes (like the size of a solar system measured in centimeters, or the size of an atom measured in meters, although not with 100% accuracy). Fixed-precision means the memory use is constant, never grows, never shrinks, so there's a limit to both the magnitude (exponent) and mantissa (significant digits). It's just scientific notation but with specific (non-arbitrary) constant limits. The "ghost bit" is a bit whose value is always "1", so it doesn't need to be written in memory, therefore making it implicit, and squeezing more precision out of the limited memory. Trailing zeros are the zeros to the right, big numbers require them to preserve the magnitude if the mantissa is filled to the brim, these zeroes are also "ghosts" but in a different way, since their existence is purely mathematical (not in memory). The exponent is also responsible for "adding" these trailing zeros

[@markrothenbuhler6232]

It cannot be said enough: infinity is not a number! So I like that 0/0 can only be encompassed by infinity.

[@BriTheMathGuy]

Right?!

[@Bodyknock]

It’s true that Infinity isn’t a Real Number, but it is a number in other number systems like the Hyperreals. (Although even in the Hyperreals 0/0 is left undefined.)

[@sumdumbmick]

infinity is quite a few different numbers, actually. 0/0 is not encompassed by infinity, because infinity is valid mathematics, 0/0 is not. Bri got it wrong by assuming that 0/0 obeys mathematical principles, and thus concluded that it should be infinity according to that. but 0/0 lies outside of the scope of mathematics, so that assumption is wrong, and thus the conclusion that 0/0 has a relation to infinity is also wrong. it's trivial in fact to get division of any number at all by zero to appear to be any number. for instance, you can drop a hole into y=x at absolutely any point by simply multiplying both sides by 1, as shown below: - for any n != 0, n/n = 1 - y*1 = y, x*1 = 1, thus y = x is identical to y = x*1 - given both of the above y = x * n/n - to get division by zero at x-value m set n = x - m - now at x = m, y = x * (x-m)/(x-m) is identical to y = x * 0/0 - since x * 0 = 0, this means that we have y = 0/0 - if we take the limit here we will get that y = x, and thus at x = m it is necessarily true that 0/0 = x - since we can set m to absolutely any value we want 0/0 is thus also equal to absolutely anything and everything simultaneously if we look at other functions, like tangent, we can see that division by zero also shows up where solutions are impossible, like for tan(pi/2), where the limit from the left is positive infinity and the limit from the right is negative infinity. it's not possible to have two values more different from each other, yet division by zero yields both simultaneously an infinite number of times with just this one function.

[@angelmendez-rivera351]

@@Bodyknock *It's true that infinity isn't a Real Number, but it is a number in other number systems like the Hyperreals.* No, this is false. "Infinity" is not a number in the hyperreal numbers. There are many numbers in the hyperreal numbers that satisfy the property of infinity, because that is what infinity is: a property of sets, not a number. There is no number in the hyperreal number system called "infinity", so to say that there is such a number is a lie.

[@angelmendez-rivera351]

@@sumdumbmick *infinity is quite a few different numbers, actually.* No, it is not. This is a nonsensical statement. Infinity is a property of sets. Definitionally, we say that a set S is infinite if and only there exists an injection from the set N of natural numbers to the set S. Every number system is a set, as is every object in mathematics, and some number systems have infinite elements, and those elements are numbers that are infinite. There is no number called "infinity", though, because "infinity" is a property of sets, not a number. *0/0 is not encompassed by infinity, because infinity is valid mathematics, 0/0 is not.* This much is true, though I get the impression we will strongly disagree as to _why_ this is true. *it's trivial in fact to get division of any number at all by zero to be any number.* This is a bold claim, and I take this to be the thesis of your comment, so I will be deconstructing the rest of your comment in context of this thesis. *now at x = m, y = x·(x - m)/(x - m) is identical to y = x·0/0. Since x·0 = 0, this means that we have y = 0/0.* Not so fast there. In order to conclude that x·0/0 = 0/0, you must necessarily assume associativity of ·, which is not at all warranted here. *if we take the limit here we will get that y = x,...* No, this is a nonsensical claim. In the equation y = 0/0, there is nothing to take the limit with respect to, we just have two constants. Also, limits are irrelevant to questions of evaluating arithmetic expressions. *if we look at other functions, like tangent, we can see that division by zero also shows up where solutions are impossible, like for tan(π/2), where the limit from the left is +♾ and the limit from the right is -♾.* Yes, it is true that lim sin(x)/cos(x) (x < π/2, x -> π/2) = +♾, and lim sin(x)/cos(x) (x > π/2, x -> π/2) = -♾. However, this has nothing to do with the topic of division by 0, since the denominator is never equal to 0 in these expressions. What you have proven is that lim tan(x) (x -> π/2) does not exist, which does not itself prove tan(π/2) is undefined. In fact, I have an easy counter-example to your claim. Let f : R -> R with f(x) = 0 if x = π/2 + n·π, where n is an integer, f(x) = tan(x) otherwise. Then here we have lim f(x) (x -> π/2) does not exist, yet f(π/2) = 0. This disproves your claim that lim f(x) (x -> π/2) not existing proves f(π/2) is undefined.

[@fabroloscevola]

I think we could create a new set of numbers with the properties mentioned in this video, and call it "null numbers" or "abstract numbers" or something like that. This set would have its unity called "null unity" or "nonentity" and put it the symbol of "Ω"

[@rich1051414]

As a programmer, I like the idea of 'null entity'. I understand how it can be hard to differentiate from 'zero' for everyone else, but 'undefined' is a different concept to 'zero'. If you have zero apples, you know how many apples you have. If you have 'undefined' apples, you don't know if you have zero, or a hundred, 0.25 apples, or infinite apples. But you still know they are apples.

[@Miscio94]

@@rich1051414 "undefined" is not a number, so it doesn't answer the question "how many X are there". What is undefined is not the amount, but the calculation. So it just means maths stops working for a while and you just have to ask the question again. In other words, 0 / 0 = makes no sense

[@cubicinfinity]

I'm supportive of this. You can make as many alternate systems as you want without threatening the originals.

[@ganges6569]

Nothing divide nothing is still nothing

[@md-sl1io]

no because the nothing was divided out of it so u get left with 1

[@sebastiendaigle7214]

@@md-sl1io so how do you divide nothing ? its just nothing. You can't devide nothing by nothing, the answer is nothing.

[@youtubecanthandleshit]

​@@md-sl1iowhere did the 1 come from

[@blazyegamer]

Nah it's null

[@Ghost_9960]

So 0/0=0?

[@robertfrydell6894]

So you're saying that nothing over nothing is very large. Ok man. Ok.

[@firstkraken]

My belief is that dividing by zero gives you the list of every number ever and will be.

[@cubicinfinity]

Changing a scalar to an infinite set is quite an interesting property.

[@djpeacannon8461]

I still think undefined is the best way to go about this and my main reason is through physics. Mass is equal to force divided by acceleration. However, if an object has no resultant force applied to it and is not accelerating, then it's mass could be calculated by 0/0. We know this mass could be anything, meaning the mass is undefined by this equation. This doesn't make the object have infinite mass or every object that wasn't accelerating would become a black hole of infinite density and destroy anything around it, which isn't the case. This isn't a solution derived from actual mathematical approaches so there are probably a lot of counter examples to this point but I felt this could be an interesting talking point.

[@oneno9635]

Hmmmm wt about sayin that 0/0=0 but the pnt is definding this will always make the anser hve no sense and i was like thiss one 0/0is acctualy can be evry number but this wrong i think and i dnt like to say undefined bcz it just like i avoid to anser so uhm 0/0=0 is good for math or just sayin is equal infiniti . But well u have good pnt and now is 23:43 and m tooooo slmy so i tink that all dat i say is wrong and to many wrinting fault so uhm heh i home u see this and anser

[@lalaommprakashray8499]

Bud Hear me out We all know that 0/anything= 0 So acc to rules of algebra 0/0= anything So 0/3=0 so 0/0= 3

[@deusexmaximum8930]

​@@lalaommprakashray8499that's the weird part, though. 3 isn't "anything", it's something. It's like having infinite potential but never being able to use it. It's like having a wish but never being able to ask the genie to grant it.

[@navsha2]

I agree because it says mathematically you cannot divide by zero in the form of a fraction

[@deusexmaximum8930]

@@navsha2 "it's impossible because the rules say so" absolutely braindead take

[@thomaskaldahl196]

When I was little I tried to devise a system where 0/0 = 1. I Said 1/0 is some constant called Omega, and 0 times Omega is 1. To resolve the issue where 0 + 0 = 0 implies 2 = 1, I asserted 0 + 0 > 0 instead. I let 0 be defined as 1 - 1. Therefore 2 - 2 > 1 - 1. This also means for example 3 - 2 > 1. Zero squared is 0 - 0. 0^2 - 0^2 = 0^3, etc. I constructed an infinite sum k = 1 + 0 + 0^2 + 0^3 etc, and noticed that 1 - k behaves like the new "zero," breaking division and such. To resolve the new issue of division by 1 - k, I devised a system where (1-k)/(1-k) = 1, and 1/(1-k) = Omega_1, wherein a new constant k_1 such that (1 - k_1) caused new division problems until the creation of the new constant Omega_2, etc.

[@nikkiofthevalley]

"When I was little" So you knew advanced mathematics when you were "little"? (Whatever age that is)

[@thomaskaldahl196]

@@nikkiofthevalley "Little" in this case means like 14 years old

[@parallax256]

your system succs

[@parallax256]

that's not advanced math, that's just LOGIC at the time of this reply, I'm 12, and I've literally found a better way to approximate the area under a curve (using right triangles) I don't really know advanced math I just play around with numbers a lot I USE LOGIC

[@Anonymous-df8it]

Can you define k_1 and prove that 1/(1-k_1) can't be defined as Omega_1?

[@cesarecorrea94]

-♾️ satisfies your equations too. It's better to stay as undefined. Maybe it could be contextual, like 0/0=6 for f(x)=(x^2-9)/(x-3) to keep the continuity of the function, rather than marking it as discontinuous because of the undefinition.

[@LorenzoF06]

how much is -♾️+1 though?

[@cesarecorrea94]

@@LorenzoF06 It's -♾️. -♾️+x=-♾️, for any real number x.

[@solsystem1342]

@@LorenzoF06 similarly: -inf * a = -inf (assuming a is a positive real number).

[@TKZprod]

@@solsystem1342 even -inf * -1 ?

[@orisphera]

3:26 This formula can be thought of as multiplying both the numerator and denominator of the first fraction by the denominator of the second fraction and vice versa and then adding them. In this case, you can just say that the rule that you can multiply both the numerator and the denominator by the same number and get the same result doesn't apply to multiplying by zero

[@sekwatigiven2772]

What if 0/0 definition can make us time travel

[@victorscarpes]

I like to think that the derivative is 0/0 with context. For that to make sense, 0/0 must be context sensitive. I know that limits are involved with derivatives, but i find this line of thinking kinda neat.

[@angelmendez-rivera351]

Your line of thinking is not only not neat, but also wrong, since there is no division by 0 involved in the evaluation of a derivative.

[@victorscarpes]

@@angelmendez-rivera351 I'm fully aware that there isn't any division of 0/0. It's a limit, dy and dx aren't zero. But, this limiting process was created to make such computations possible. For example, if we want the velocity of an object, we divide the distance traveled Δx by the time Δt it took. When we want the instantaneous velocity, we would, using the above procedure, we would end up with 0/0. The derivative is computing 0/0 without actually having to compute 0/0. That's what it was created for.

[@angelmendez-rivera351]

@@victorscarpes *I'm fully aware that there isn't any division of 0/0. It's a limit, dy and dx aren't zero.* dy and dx are also not quantities in themselves, even though the notation unfortunately suggests otherwise. *But, this limiting process was created to make such computations possible. For example, if we want the velocity of an object, we divide the distance traveled Δx by the time Δt of travel. When we want the instantaneous velocity, we would, using the above procedure, we would end up with 0/0. The derivative is computing without actually having to compute 0/0. That's what it was created for.* No, this is false. Historically, when calculus was rediscovered by Newton and Leibniz (I say rediscovered, because it is now well-known at this point that techniques of calculus has been used millennia before), they formulated it by appealing to infinitesimal quantities, and they called it infinitesimal calculus. The concepts of the derivative, the integral, and the method of exhaustion, were then understood as special applications of this infinitesimal calculus. The primary notion in this infinitesimal calculus was that there existed infinitesimal nonzero quantities ε that were taken to have the property that ε^2 = 0. This method, though, was extremely nonrigorous and very heavily criticized, it being widely seen as apparently inconsistent and leaving too much ambiguity. This created problems for calculus as a mathematical application. Later, when real analysis was invented, calculus was reformulated in terms of topological ideas and ε-δ arguments from real analysis. What this allowed was for a consistently rigorous mathematical theory that allowed us to do everything that calculus was invented to do, all without ever needing to appeal to infinitesimal quantities at all, instead, relying solely on the properties of the real numbers. Limits were invented not to allow calculations that involved division by 0. They were invented to set calculus on a foundation that did not rely on ill-defined infinitesimal quantities, but instead only on the properties of the already known system of the real numbers.

[@victorscarpes]

@@angelmendez-rivera351 I must admit i mixed up a bit about the limit. Do infinitesimals create a bunch of weirdness and inconsistencies? Absolutely. Is analysis the mathematical rigorous way of defining this stuff? Absolutely. But, altough i love mathematics, i'm an engineer. Thinking of dx and dy as actual quantities of infinitly small size is pretty useful.

[@angelmendez-rivera351]

@@victorscarpes *Do infinitesimals create a bunch of weirdness and inconsistencies? Absolutely.* They _used_ to. This is why they were replaced by limits. However, infinitesimals did not stay defeated, and they have made a comeback. In the mid 20th century, a mathematician by the name of Abraham Robinson develop a rigorous system for dealing with infinitesimal quantities and infinite quantities, a system that was dubbed "hyperreal numbers". These numbers are the basis for nonstandard analysis, which can serve as an alternative foundation for reformulating calculus in a simpler way. In this reformulation, limits are replaced by the standard part function. The standard part function is a function that gves you the real number closest to the finite hyperreal number you input. So for example, if I have a hyperreal number 7 + ε^2, where ε is infinitesimal, then st(7 + ε^2) = 7. If I have -3 - ε, then st(-3 - ε) = -3. When defining the derivative, you can simply define it as st([f:(x + ε) - f(x)]/ε), where f: denotes the natural extension of f to the hyperreal numbers. However, since this system is recent, relative to the history of mathematics, not many textbooks have been written implementing this system for educational purposes and it is not yet part of curricula in most countries. It is likely it will become common in the future, though.

[@Jacobconnor525]

i think its everything at once if it’s not undefined. 1/0=inf. 2/0 = inf. So 0/0 is every fraction existing. also 0=0x anything

[@jyotishekhar8086]

Hi can you make more videos on integration? I am having a hard time keeping up with it. As always the video was great!!

[@BriTheMathGuy]

I will try!

[@Grassmpl]

Make sure to formally define and use Riemann integrability. Better yet compare it to Lebesgue integrals.

[@dankastik6477]

@@BriTheMathGuy differentiation too 😵

[@timm1328]

since the real numbers form a field and which implies that arithmetic operations always yield a real number, then your definition leads directly to contradiction since you define 0/0 to be infinity, but infinity is NOT a real number. best to leave 0/0 undefined... at least within the real numbers. maybe an extension of the real numbers, like the hyperreals.

[@angelmendez-rivera351]

How did you miss the point of the video this badly? Obviously, he knows division by 0 is not possible within the real numbers. He is not trying to go against the mathematical consensus. He is exploring a new idea. He even said this in the video.

[@mformathamatrices9801]

0/0 = φ Where φ = 0/0 😎 Mathematician can't even do that

[@p_square]

only the "official" yt account of Euclid could do that

[@mformathamatrices9801]

@@p_square it's just for rising star math KZbinr challenge of Blackpenredpen , but people are liking it🤣

[@FaizThe-kc6dk]

φ is golden ratio

[@asparkdeity8717]

This is what Bri was referring to about his last video if anyone is wondering: One workaround to this is to define any such indeterminate forms to equal the nullity, ⊥ . It’s essentially an absorbing element that is more “powerful” than 0 or ∞, so we define results like: 0/0 = ⊥ 10/0 = ⊥ etc… Same goes with indeterminate forms involving infinity. ‘⊥’ has the properties: x + ⊥ = ⊥ ⊥ + ⊥ = ⊥ x ⊥ = ⊥ x / ⊥ = ⊥ ⊥ - ⊥ = ⊥ etc… for any x, including x = ⊥ The only exception to our standard maths rules are the properties 0*x = 0 and x / x = 1 for any non-zero number x, and also x - x = 0; Since ⊥/⊥ = ⊥ and 0*⊥ = ⊥ etc… So basically rather than just infinity, we create a new concept ‘⊥’ which we can treat like a number. Again this is only a theoretical work-around to the problem, it is not official.

[@Sabagegah]

Zero doesn’t even feel like a real word now.

[@XBGamerX20]

0/0 is actually 0x = 0 which can be any real number so it means infinite solutions. therefore 0/0 can technically equal 0, 1 and infinity, but it stays undefined because basic expressions don't allow more than one solution and thus it's wrong to write one out of the infinite solutions. again it's only solvable when it comes to equations with one or more variable

[@thewierdragonbaby4843]

This might sound dumb but why should basic expressions have to just have one solution? There are multiple expressions which don't just have one answer, for example √25 = ±5, meaning √25 = 5 and -5 at the same time because they both work for x²=25. In a similar way all square roots are equal to two numbers at once, all cube roots equal to 3 numbers, all fourth roots equal to 4 numbers etc. So, I don't see why 0/0 can't be infinitely many numbers at once just because it's a division

[@XBGamerX20]

@@thewierdragonbaby4843 expressions mean you have different types of math operations, like 3x + 2. thats an algebraic expression and it means that there's no equal sign to something specific. you just simplify. also square root is considered to give one solution depending on the sign for example sqrt(9) = 3 etc. you just don't write ±3 if you see the root only. same applies for logs, exponents, absolute values etc. and x² = 9 is different, you basically get 2 solutions because you in fact square root both sides and get |x| = 3 if you simplify it. and you get x = ±3 I mean you can get cases where in expressions you'd have more than 1 solution like using the quadratic formula for x > 0 or having x inside absolute value bars

[@thewierdragonbaby4843]

@@XBGamerX20 oh okay, I guess that kinda makes sense, but why would you only have 1 answer for roots? also on a completely unrelated note wouldn't |x| = 3 have infinite solutions if you consider the complex plane?

[@faytachiMPS]

0/0 = 0 is absurd and incorrect because it would allow for the proving of 1=2 (which obviously is absurd) 0x1 = 0 0x2 = 0 lets say we allow the division of 0: 0x1/0 = 0x2/0 (both divided by 0, so equivalent to previous lines) (0x1/0) x 1 = (0x2/0) x 2 (both times by 1, so equivalent to previous lines) cancel out the zero on both sides and you get: (0/0) x 1 = (0/0) x 2 cancel out the expression 0/0 on both sides and you are left with 1 = 2, which is obviously incorrect meaning division by 0 is impossible

[@DeJay7]

I actually agree 0/0 should equal 0 So the only thing that changes is 0/x=0 for all real values of x, *including 0* . x/x=1 must remain for all real values of x except for 0, 'cause that would break the whole fabric of maths, and x/0 should of course stay undefined/not accepted.

[@GrndAdmiralThrawn]

I hate theoretical mathematics. I like practical mathematics. If you have 0 pizza and you decide to cut it into 0 pieces, you still have 0 pizza. AFAIC, a numerator of 0 negates anything that could possibly be in the denominator. Even 0.

[@beatlesetchansonplus]

@@GrndAdmiralThrawn What you're saying makes no sense. Obviously, if you slice 0 pizza in any number of pieces, even 0, you still have 0 pizza. But, what you did is not division : If you have 1 pizza, and slice it in 2 pieces, how many pizzas do you have ? Well, still 1 pizza. What you have however are 2 pizza halves, hence 1 divided by 2 equals a half. So, using pizza slicing as a definition for division (which is perfectly fine), we arrive at : given A pizzas, and B pieces, we call the size of the pieces A/B Exemple : 15/3 is 15 pizzas "sliced" into 3 pieces of 5 pizzas each. 15/3=5 So, what would be 0/0 ? 0 pizzas sliced into 0 pieces of pizza. What size is my no piece of pizza ? Well, I have 0 piece of 50000 pizzas, so should 0/0=50000 ? No, since any piece size would work here, by practical maths, there just can't be any answer to question. And that's fine, since in practice, there are many questions where we don't have an answer to.

[@mhmd-mc113]

But then 0 = 3*0 0/0 = 3 0 = 3

[@DeJay7]

@@mhmd-mc113 So here you're assuming 0/0 = 1 which is incorrect and you got 0/0 = 3, and I don't even know why that concludes to 0 = 3

[@mhmd-mc113]

@@DeJay7 i wasn't proofing it I wad showing the other guy that not always algebra rules apply Sometimes you simply cannot move stuff or devide or subtract infinity for example Cause if you do youll get results like 0=1 And 0/0=3 And 1+2+3...=-1/12

[@salahshinigamiamv9814]

Logically it's impossible 0 represents the absence of things/numbers "There's 0 pens on the table = no pen on the table" In division...when we try to devide nothing it will always give us nothing "0" Therefor We cannot devide nothingness by nothingness Nothing happened/happens/will happen we do so, therefore it's Mathematically Invalid to try to find a solutions to an nonexistent problem That's my take on it, what do you guys think?

[@salahshinigamiamv9814]

@Lady Mercy 0/0 and 0=0 are two different things 4/4 is 1...but 0/0 doesn't give us 1 because of the reasons I've stated before.

[@martinho5474]

Theorically (for pure maths) maybe you could give a meaning for 0/0 but when you put it on practice no one discovered yet a way to use 0/0 with aplicativable value (it's useless for physics and engeeniers) but It doesn't mean it will be impossible

[@MrIndianKnight]

I knew how to do it so for it lets take an example that you have to distribute 0 slices of pizza among your 0 friends so it means that you don't have any friends or any pizza to eat

[@Nikku4211]

So this is why anything / 0 = complex infinity.

[@doge_69]

@@rahulkhatwani548 no bro try it 1/0 is the same as 0/0

[@GodisgudAQW]

I think it should be 0 because infinitely expanding nothing should give you nothing. In more detail, in the expression a/b for a != 0, the limit of a/b as b approaches 0 is infinity or negative infinity (depending on which side you start from. That is, dividing by 0 is like infinitely expanding (in one way or another). Basically, when you divide a number by a value between 0 and 1, the smaller the denominator, the larger absolute value the resulting expression gets. So I see dividing by 0 as the ultimate expansion operator. Great, so if you infinitely expand anything other than 0, the result is infinite. But I think things should be different with 0. If you infinitely expand 0, you still get 0. If you have nothing and then infinitely zoom into it, you will still see nothing! But if we accept that 0/0 should be infinite, then we are saying that 0 is indeed something that can be expanded, which to me contradicts the very notion of 0, which is pure nothingness. So, infinitely expanding 0 should still be 0 from a philosophical point of view.

[@FrogworfKnight]

Except it often isn't. The whole idea of Calculus is actually based on taking the difference quotient formula (essentially a modified slope formula for curves) and applying what happens when you make the change in x and make it zero. This in turn makes the change in y also zero. With the exception of whole numbers (like an equation of y=7), the result is not zero, but instead a whole other function that describes the slope of the line tangent to the original equation.

[@lordnoodle2146]

I get what you are saying but when you look at in a particle sense. If you got a bucket of nothing and keep trying to fill it with nothing then you can constantly keep filling it and infinite amount of times thus inversely. You take as much nothing out as you wish. It is why personally I avoid the question by denouncing zero as a number in the first place and more of a concept

[@faytachiMPS]

0/0 = 0 is absurd and incorrect because it would allow for the proving of 1=2 (which obviously is absurd) 0x1 = 0 0x2 = 0 lets say we allow the division of 0: 0x1/0 = 0x2/0 (both divided by 0, so equivalent to previous lines) (0x1/0) x 1 = (0x2/0) x 2 (both times by 1, so equivalent to previous lines) cancel out the zero on both sides and you get: (0/0) x 1 = (0/0) x 2 cancel out the expression 0/0 on both sides and you are left with 1 = 2, which is obviously incorrect meaning division by 0 is impossible as for the first part, say we have 20 oranges and want to distribute them amongst a table. if i wanted to divide them into 2 groups, the expression would be 20/2 meaning each person receives 10 oranges. if i wanted to divide it into 1 group, it'd be 20/1 --> each person receives 20 oranges for dividing by zero, however, what is the number of oranges that each person receives when 20 cookies are evenly distributed among 0 people at a table? There is no way to distribute 20 oranges to nobody, so the resulting answer is undefined, not zero, because the parameters defining how the oranges are to be distributed are zero

[@andrewrichesson8627]

0/0 is equal to the set of all numbers since if 0 = 0x, then x can be any number.

[@derblaue]

which works quiet well with the infinit different limits you can get with 0/0. Like yx/x will always be y so we get any limit for 0/0. If we add 1/x to it we also get ±∞ and thus the extended real numbers. It will work with complex numbers aswell. Possibly for quarternions as well. So our current rules for any field will lead to limits of 0/0 sitations to be anything. Which is also a good reason to leave 0/0 undefined.

[@angelmendez-rivera351]

No, because 0/0 is not defined to be the solution multiset of 0 = 0·x, it is merely defined as an arithmetic function.

[@cubicinfinity]

@@angelmendez-rivera351 0/0 is not undefined; it's indeterminate. There is a difference.

[@angelmendez-rivera351]

@@cubicinfinity No. It is not indeterminate. I have explained this elsewhere more than once, but there is no such a thing as indeterminate.

[@cubicinfinity]

@@angelmendez-rivera351 This is the definition I am talking about: en.wikipedia.org/wiki/Indeterminate_form How can I learn about what you are referring to?

[@rayandeshpande6423]

2x = x , we could substitute x as 0 then 2•0= 0 which is indeed true , yes but x+1 = x is not possible hence we can say 0/0 could definitely be 0 satisfying first equation or prove it to be a fluid term with multiple values Adding to it , we can use laws of exponents to prove the same , however i know that in the laws of exponents the condition says (x≠0)

[@Maanjiro_g]

If you divide nothing to nothing they will get nothing which is also be written as 0/0=0

[@arttukettunen5757]

When you login to a new game and your K/D ratio is 0/0 and showed as 0, then you get 1 kill so it's 1/0 and it will show your K/D as 1. *Problem solved, diving by 0 outputs the same thing you would get from dividing by 1*

[@mrsharpie7899]

Ah, so it's like a factorial! Also, I know you're joking, but this probably causes way more problems than most other definitions

[@mudspud]

gamer

[@farfa2937]

@@mrsharpie7899 TBH tho I'd rather salvage the indetermination in the context of the problem I'm solving. Since you can make the case for 0/0 = anything, giving it any one value would make it pretty inconvenient for many applications.

[@martianman8948]

Let's appreciate this guy for solving problems which are beyond math rules.

[@law26504]

Congrats on getting a sponsor bro! You totally deserve it.

[@BriTheMathGuy]

Thanks a ton!

[@AmritGrewal31]

@@BriTheMathGuy at first glance, I read it as "thanks son" I was like: well, that can't be right

[@okuu_utsuho]

“Imagine that you have zero cookies and you split them evenly among zero friends. How many cookies does each person get? See? It doesn't make sense. And Cookie Monster is sad that there are no cookies, and you are sad that you have no friends." - Siri’s response to 0/0

[@SJ-mf2ci]

Imagine if you had an infinite number of cookies and an infinite number of friends eating them. If any number multiplied by 0 = 0 (0x = 0), then it makes sense that 0 divided 0 = any number (0/0 = x) it works in every case without a contradiction. 0x = 0, 0/0 = x, 0x/x = 0/x, 0x/0 = 0/0.

[@studentjohn]

I would instinctively say that things like 0/0, infinity - infinity, 1/0 etc don't need defining as anything other than themselves - but it is useful to examine them and define what properties they have. Then, if two or more turn out to share properties, you can advance the thesis that they are the same mathematical entity, or related to each other by a mathematical entity that is somehow involved with each of them.

[@baralike8206]

Last year I had an exam with a question asking to simplify an expression as much as possible. I simplified it down to something like "x + x/x", and when I got there, I thought that if I would replace "x/x" with "1", they would no longer be the same expressions since "x + x/x" isn't defined for x=0 (0/0) while "x + 1" is. Unfortunately, I lost a mark for this but never really understood why I was wrong. Do you agree with me or was I wrong?

[@h-a-y-k4149]

Maybe you can deduce from the initial statement that x ≠ 0. Otherwise you can just say x + 1 (x ≠ 0)

[@baralike8206]

@@h-a-y-k4149 Yeah I agree that "x + 1 (x ≠ 0)" should've been the correct answer, but stupid me thought that that was the same thing as "x + x/x". However, the correct answer was "x + 1", which is what's bothering me, especially because the teachers couldn't explain to me why.

[@methatis3013]

@@baralike8206 depends on the beginning problem. If you could just substitute in 0 for the initial x and the whole thing works out properly, then 0 is a part of solution as well. So even if you somehow got x/x, solution still might be x = 0, depending on the initial conditions

[@MrRenanwill]

You must look equation as finding a solution set. If zero is possible, you should take care of this case accordingly during the process of calculations. If zero is not possible, you should prove that It must be the case. For example, If (x^2-1)/(x+1)=-2, then x must be different of -1, because It would say that we are deviding by zero which is not possible, hence, for x not equal to -1, we have ((x+1)(x-1))/(x+1)=-2 hence x-1=-2, hence x=-1. Which is a contradition with the hypothesis. This means that there is no solution for this problem. Usually, contradiction comes from this type of equation. The basic tip is to redo the calculations with care when some contradiction comes to appear. Logically thinking, this is because we have left behing some piece of information during the calculation that would show the problem in the computations. Can you imagine what would happen if I hadn't realized that x=-1 is not a solution? A simple substituition of x=-1 would solve that problem and let we know that x=-1 can't be a solution, but in exams It is not easy to predict what would happen.

[@h-a-y-k4149]

@@baralike8206 imo the main reason is that generally the answer must be as simple as possible. For example, if the answer is just 1, saying 8/8 (which is still 1) is still a correct result but the teachers may consider it wrong. Also leaving it like x + x/x still doesn't mean that x can't be 0 (see the answer of @Me That is). You need to explicitly say that x ≠ 0. One can easily deduce this condition, though, but it's just a formality in my opinion and not crucial (especially if the problem has already stated that x≠0)

[@dreadnaught3x390]

I've always thought about multiplication and division as an organization of groups; for example X multiplied by Y is the same thing as X groups of Y. Similarly, X divided by Y is the same as turning X into a number of groups equal to Y. Explaining all of that probably seems redundant because most people might have already concluded all of that on their own, but most of the reason I'm doing it is just put things into words rather than symbols for the purposes of creating a more mentally tangible situation. Anyways, apply this to what 0 represents: nothing. If you take nothing and put it into no groups, that means there are no groups of nothing. By definition, having no groups of nothing would mean you have no groups in which nothing resides, as in, every group has something in it. Thus you effectively have everything. I think one reason why all of this might be an issue on a computational level is because you can only describe the answer by what the input is not. Hopefully all of that was understandable and logically sound.

[@gachabloxgirl3958]

Yeah I think what you said makes most sense. I see a lot of people saying having no groups of nothing, for example someone commented that cutting 0 slices out of a non-existent pizza means there's no pizza hence 0/0 = 0, but that doesn't really make sense because no groups of nothing should mean that all groups have something.

[@DepFromDiscord]

We could set it as an imaginary thing, like sqrt(-1) = i

[@angelmendez-rivera351]

That does not work.

[@kiwenmanisuno]

You can't "really" (pun intended) say that, since that number would have to be equal to any number, it would practically be useless

[@davidjames1684]

10^-100 / 10^-100 = 1. If we make the exponent -1000, then -10,000, then -100,000, we still get 1. So someone can argue that as the expressions become close to 0, we basically have 0/0 = 1. They could have said that division by 0 is undefined, unless the numerator is also 0, with the justification that a "super tiny" numerator over the same "super tiny" denominator IS defined as 1. "Super tiny" in this context meaning VERY close to 0.

[@IceFlamesYT]

im tired of people saying 0/0 is undefined. division is defined as “in a/b, how many times do you have to subtract ‘b’ from ‘a’ to get 0?” since the numerator is already 0, the division is complete and therefore the answer is 0!

[@Grassmpl]

If we define division of two real numbers to be subsets of R, then we get 0/0=R, x/0=empty set for x not 0, and x/y to be the singleton set containing the number defined by usual division if y is not 0.

[@angelmendez-rivera351]

You could do this, but definitions of arithmetic operations as being subset-values instead of being real valued are useless.

[@Grassmpl]

@@angelmendez-rivera351 no they are useful. Consider the topological space Spec k[x] where k is an algebraically closed field. The points are the elements of k corresponding to the ideals generated by linear polynomials, together with a generic point, corresponding to the 0 ideal. Each non generic point forms a closed subset by itself. If you localize a ring by a prime ideal, you will see that the 0/0 resembles the concept of the generic point.

[@angelmendez-rivera351]

@@Grassmpl I think you missed the part where I specified "arithmetic" operations. I didn't say anything about topology.

[@perodactyl490]

EDIT: This is one of the comments I randomly leave behind without thinking and then later regret it. Please disregard it. I think that 0/0 is NaN, because when programming, languages like javascript say that NaN != NaN and any operation used returns NaN Another thing I would like to note: In JS, Infinity - Infinity = NaN because it's impossible for it to say whether one is greater than the other.

[@individual1st648]

isnt it only nan because its not defined? and that languages are programmed to, well, treat 0/0 as undefined

[@ninetysixvoid]

NaN stands for Not a Number

[@somenerd8139]

You can’t actually have infinity in programming. Computers can’t store infinite digits, so that is a completely invalid point. And as the commenter above me already stated, NaN stands for Not a Number, which is the same thing as undefined.

[@jonasharestad7664]

NaN! = NaN factorial = NaN*(NaN-1)*....*(NaN-∞) = NaN*NaN*...*NaN = NaN^∞. And by the definition of a factorial (ln(n!)=n*ln(n)-n+1), you have that n!= e^(n*ln(n)-n+1) = n^n*e^(1-n). By setting n=NaN ==> NaN!= NaN^NaN*e(1-NaN)

[@nomenomeha30anosatras33]

NaN means "Not a Number", so it's the same thing as saying "undefined".

[@roiitzkovich4545]

So I guess the best answer is to define 0/0 as an axiom for "F*CK THAT I'M OUTTA HERE".

[@wolfiegames1572]

What about this: 1^x = 1 x is equivalent to an infinite range of numbers AND x = log1(1) x= log(1)/log(1) x=0/0 0/0 is an infinite range of numbers.

[@kofidwirahsclass4662]

Thank you, you are helping us all.It’s always easier when you have the good teacher

[@GEMSofGOD_com]

Using set powers, cardinalities, os, Os and alephs is useful

[@angelmendez-rivera351]

Yes, but no, not really. It is true that infinity is in the realm of set theory, as you describe, but the topic of division by 0 is not a set-theoretic topic, it is a group-theoretic topic.

[@GEMSofGOD_com]

@@angelmendez-rivera351 you are correct

[@pushpashukla5086]

One more idea 💡 0/0 = 100 - 100 /100 - 100 Using a^2 -b^2 = (a+b) . (a-b) in numerator Hence , 10^2-10^2=(10+10)(.10-10) And taking ten common in denominator Hence = (10+10)(10-10)/10(10-10) (10-10) gets cancelled Hence , = 10+10/10 =20/10 2 So 0/0 is 2 😂

[@gaetanbouthors]

you cancelled 10-10 which is basically dividing by 0. by that logic: 0*5=0*7, simplify the 0's and 5=7

[@bitrr3482]

@@gaetanbouthors 0/0 is really really broken

[@jancermak1988]

It's easy. 0/0 is undefined and it's all. Why should be 0/0 defined if it's totaly useless?

[@kepler6873]

We don’t know if it’s totally useless yet. If defined, it could become the way to evaluate x/0 which, at minimum that I can think of, would let us figure out what happens at the middle of a black hole where the volume is 0 but the mass is a number, creating x/0 density. I’m 99% sure it will never work though, since you can cause a bunch of shenanigans by defining x/0. One example is the 1=2 proofs

[@jancermak1988]

@@kepler6873 No. I wrote that 0/0 is useless. This does not mean that X /0 is also useless. But X/0 is undefined because it's nonsense. Nothing can be divided into zero parts. Therefore, division by zero is not defined. And the black hole has not zero volume. It has a volume that is equal to an infinitely small number, so this is a limit approaching zero. So even here there is no need to divide by zero to find that the density of a black hole is infinite.

[@herbie_the_hillbillie_goat]

@@kepler6873 It's undefinable. You can't just give it whatever definition you want. That's not what UNDEFINED means in the mathematics.

[@kepler6873]

@@herbie_the_hillbillie_goat I made the comment at like 3AM, I know yeah. Sorry for blanking out on it at the time.

[@angelmendez-rivera351]

@@jancermak1988 Your understanding of division is not very good if you are thinking of division as "breaking into parts". Try dividing π by -e using that method, and you will quickly see why that is not a definition of division. Anyway, you are wrong. Having a value for 0/0 and x/0 is useful, and this is why wheel theory and the theory of involution monoids in general was developed in the first place.

[@itsaya_aya]

I always thought of it as of dividing nothing on nothing. Logically, it will give you nothing. But then, dividing nothing on anything is nothing, and diving anything on nothing is impossible, so dividing nothing on nothing may give you an infinity...

[@BEGOBLOX2]

you have literal air and try to divide it no times, to start that just means you arent even dividing, so take that complicated mess out then its just 0, nothing

[@Firefly256]

4:11 negative infinity also works?

[@m7mad182]

It's both negative/positive infinity Like you just said 0/0 = x is the same as x*0 = 0 so yeah anything times zero is zero ☺

[@angelmendez-rivera351]

This would make 1/0 = ♾, not 0/0 = ♾.

[@findystonerush9339]

Well Noooo but it's both negative 1 and positive 1! because -0/0=-1 0/0=+1 -1+1=0 0--1=1 so 0/0=1

[@findystonerush9339]

@@angelmendez-rivera351 correct! 1/0=infinity and that means 0/0=1 because 0*1=0 so the answer is 0 times bigger! and infinity*0=1 so 0/0=1!

[@angelmendez-rivera351]

@@findystonerush9339 No, that is ridiculous. 0·♾ is not 1. This could not possibly make sense.

[@marcodesantis3610]

When I was little somebody at school told me that fractions are like a cake, so i assume if we take 0 "pieces" from a pool of 0 pieces we still end up with 0 pieces. Based on this 0/0=0, no matter what math we do. We are struggling on finding abstract solutions but maybe the answer could be that simple, just like a childhood thing. What do you think about it?

[@derblaue]

I don't think this analogy works since taking pieces from a pool of pieces doesn't represent division since we usually associate division with taking fractions of a whole pice, not multiple indivisable pieces. So it becomes quiet difficult: If we have a whole "non" piece (a piece that is nothing as a place holder for 0) and try to take a "non" piece of it are we left with an infinit amount since we take nothing away. On the other hand we can't take anything from nothing so we get nothing.

[@marcodesantis3610]

@@derblaue yes you are right but isn't "we get nothing" the same as 0? I mean, of course you cannot take x (x ≠ 0) "non piece" because you cannot take something that does not exist but doing 0/0 is like taking nothing of nothing, so we get nothing. I'm just trying to think more like a philosopher that a scientist.

[@marcodesantis3610]

@@derblaue of course whit this way of thinking we cannot do even the simplest fractions like 4/2 because we cannot take 4 slices of a cake if the slices are 2 but to solve an unsolved problem we can try to think in a non conventional way.

[@berylliosis5250]

This is math, which is basically about coming up with systems and understanding their properties. If 0/0 = 0, you can come up with several different systems based on how you allow that change to propagate, but none of them are particularly interesting (the new operators lose important properties, such as division and multiplication being inverses). There's nothing preventing you from defining it that way, but it doesn't lead to interesting new systems

[@itisALWAYSR.A.]

I think you're equally asking "how many people can take 0 pieces from a pool of 0 pieces until the final condition is satisfied." Here, the answer basically becomes Yes.

[@gamingwithgavin9145]

I honestly think zero divided by zero is zero

[@deleted-22222]

i think it can be any number. as stated in the video: if a/b = c then b * c = a so if 0/0 = c then 0 * c = 0 and 0 times any number is equal to 0.

[@가시]

응

[@aleksszukovskis2074]

hah lol

[@skpcboy]

eung moment

[@user-goohanbeom]

%

[@tali64squared]

At the end, you can simply substitute 2x for x in x + 1 = x to get x + 1 = 2x; we can then subtract x from both sides to get x = 1.

[@Gabriel-doodle]

0 is nothing. Dividing any number with 0 is saying it’s split into “nothing” parts. However, 0/0 is splitting nothing with “nothing”, and because 0 is nothing, that means 0/0 = 0

[@azimmeme9994]

If you had 0 cookies and 0 friends, there are 0 cookies left over since you never had any to begin with

[@daviddavidsson6243]

I think zero divided by zero is a good way to write every number at the same time. ”Proof”: a/b=c where a=b=0 Then a=b*c which is 0=0*(any number) means that c=every number at the same time

[@legonlavia]

0/0=error, but it can be simplified to e*o*r^3, where e is the Euler's number, r is the radius of our universe, and o is the "little-o" notation

[@johnyshinde129]

Instead of considering 0/0 a number we can consider it as a set. Because Every possible number can fullfill this condition.

[@happygood18]

2 words. It's Undefined.

[@paulopaulopaulopaulopaulo0]

if you have 0 candy and give it to 0 people, the result is 0

[@GabriTell]

Secondary School: _"You cannot divide by zero"_ Baccalaureate: *YOU FOOL 😎* **Proceeds with Functions Limits**

[@HyperFocusMarshmallow]

Start with a set(or several if necessary). Define your operation. Prove properties. Use them. Or if we’re just playing around start with an existing such structure, extend the domain by a new element, insist rules of the previous structure should keep holding until you get confused. Patch up the result with glue.

[@auztenz]

In my opinion i feel like 0/0 should be a new number like how they defined √-1 ( i ) So lets define 0/0 to be Π Π+1=Π Π²= Π Π×i= Π 2Π=Π

[@ScienceSpider-sigma]

I think 0/0 has an answer of everything, which makes sense, because if you take the set of all real numbers and multiply it by 2 (basically stretching a line around its centre) you get the same line (numbers) likewise if you add 1 to every number the set if numbers will still have the same numbers because it’s just shifting an infinite line 1 to the right, infinite plane if you include complex numbers, and this is also why you conceptualised this nullity element with all those specific properties because it really meant everything

[@monkelettuce1799]

Man I became a huge fan of you and your channel. Keep up the good the work pal But i would love it more, if you made your videos a bit longer Cheers

[@BriTheMathGuy]

Thanks so much!

[@barakeel]

0/0 should be the set of real numbers R (very similar to the idea presented in the video). Then, I would need to define what adding,substracting, multiplying and dividing sets means. A+B = {x+y | x in A and y in B} A+y ={x+y | x in A} x+B ={x+y | y in B} So 1 + 0/0 = 1 + R = R. 2*0/0 = 2*R = R

[@wheelpool]

0/0 = ♾ because any a*0 = 0. On the other hand, there is no definite answer for infinity (it is endless), therefore 0/0 must be undefined.

[@DylanSnider]

Yeah 0 has infinite solutions when plugging in a.

[@babyboy5553]

You can consider multiplication as a way of ssimplifying successive aditions, 3x2= 2+2+2 (or 3+3). So, when it comes to division you can consider it as a way of simplifying successive subtractions (only with natural numbers), 10÷3=10-3-3-3=1 (means you can subtract the number 3 three times and the rest will be 1- natural numbers of course). So, having that in consideration, x÷0= x-0-0-0-0-0.....=x, which means you can subtract the number 0 infinite times and the rest will be the x. The same way 10/3=3 and rest 1, x/0= infinity and rest x.

[@TheStrings-83639]

I like how some people still say the rules of mathematics are made up when there are things you simply CANNOT do in it.

[@GamerB3n]

If you have 0 cakes, and you split it into 0 slices, you end up with 0 cake

[@Dvir226]

-∞ upholds everything you said about ∞, so what will 0/0 be, ∞ or -∞? Also, what will 0/0 will be in Zp, for example? It's underined and it's better to keep it that way

[@surajv1986]

You can by the same reasoning state that 0/0 =0, since x = 0 also satisfies the equation 2x = x. So we end up with potential contradictory solutions, i.e. 0/0 = infinity or 0/0 = 0. So, I'd go by the standard definition and state that 0/0 = undefined

[@TwiNightWasTaken]

Theory: 0/0 is 0. If I have no cookies, and I divide none of those cookies by nothing, I still dont have any cookies. The universe wont give me infinite cookies by doing this. I know this has no mathematical reasoning at all, but it's just a thought.

[@shahalkalady7440]

This question haunted me for a while. Thanks

[@icepl831]

zero stands for lack of value therefore nothing devided by nothing is still nothing

[@Ethan13371]

I say 0/0 , like infinity times zero or infinity divided by infinity, should be the set of all finite numbers, like how a square root can give multiple answers (positive or negative). That explains the x+x=x solution (-2 does not equal 2 either, but square root of four is fine, so I invoke that fine-ness here) For the x+1=x problem, we assign this special number (Infinity times zero, or 0/0 in this video) a special name and define it as a constant with its own unique rules, just like 0 and infinity); This also lines up with limits, because depending on the rules of the limits 0/0 could approach any finite number of that sign, so really we get positive nullity (for lack of a better term) when we divide positive zero by zero, and negative nullity when we divide negative zero by zero (remember that this is posited as the same as infinity times zero and negative infinity times zero)

[@davidchedester8181]

If x/x = 1 when x≠0, x/x should still equal 1 when x IS 0 because any number divided by itself is technically 1 (excluding infinity). But we could also say 0/0 is 0 because of real world equations like "You have 0 pawns for 0 chess boards." Each chess board will have 0 pawns because there were no pawns to begin with.

[@bartangel4867]

It has been ages since I was in school and was not a good student. (well since I was 13 anyway) one of the things they always thought is that you don't divide by zero. I once thought about what about 0/0 first answer I got is simply you don't devide by 0. which is not a satisfactory answer because it isn't an imaginary number (at least the way I understand imaginary numbers like I said I'm not a good student) unlike if you divided any other number than zero by zero. because if you use multiplication as reverse of division you do arrive at correct numerator unlike it is in the case if you divide any other number by 0. I do agree that zero over zero is undefined if undefined simply means it has no single answer. but I do believe that it being every number that multiplied by 0 gives you zero a correct answer its just not a singular answer but multiple of answers. as far as 0/0+1= 0/0 being impossible because x+1 is not x in this case if x=1 then 1+1=2 and 2 is not equal to 1. however 0/0 can just as easily be 1 as it can be 2 because every number that we know of multiplied by 0 gives you 0 therefore a correct numerator. and if you take 0/0 as equal to 1 it is just one of the answers and its just as true that 0/0 is 2 or 3 or -1 or -2 or whatever. and 1+1=2 and I see no real reason why not to say that 0/0+1 is equal to 0/0. I know i would be burned at the stake if any mathematician would have their way (and to be honest I'm pleasantly surprised that a mathematician such as yourself chosen to actually consider this question rather than say it is nonsense)for suggesting it but I really don't see anything wrong with it at this point. especially considering that there is for example particle wave duality so one thing can be in two states at once. furthermore I wouldn't necessarily say that negative number to infinite power is an imaginary number at least not the way I understand what imaginary number is. It is definitely undefined even more so than 0/0 but i don't see it as imaginary (although I know it is not a number at all but rather a concept) if we would treat infinity same way we treat numbers then the concept resulting from it might not be same type of concept as imaginary number such as square root of negative number. (of course once again in this case I might be completely wrong like I said I was a bad student and what I'm suggesting is sacrilege) because no number multiplied by itself gives negative number but if you multiply negative number by infinity by taking only odd numbers you don't come up with a real number but with real concept and if you do the same with even numbers you also get a real concept. and yes if you apply the infinity containing both odd and even numbers you are not able to define if the number is positive or negative and this number would not only be undefined but also not on the number line as we know it. but that doesn't necessarily mean that it is like even root of negative number because in this case you have the answer already given and you are supposed to find the number that fits the answer number that not only doesn't exist on a number line but multiplied by itself is supposed to give you an answer that does exist on number line also it doesn't seem to make any sense as far as we know. now I'm the type of guy who would never say never but square root of negative number simply seems not to make any sense. while negative number to infinite power has some chance of being a real concept (even if not a real number) now the last thing for which I will probably be called insane or worse I'm not even sure if infinite root of negative infinity is a fully imaginary number or at least a concept. because if you take infinity of odd numbers the concept makes sense (even if it isn't a number) and yes if you take infinity of even numbers it is an imaginary concept. but if you take them both you are not able to determine if the concept is real or imaginary and it has a real part. I don't know what possible use any of this would have but we do have uses for one hundred percent imaginary numbers so maybe at some point we will have uses for all or at least some of what I talked about. and if there was something tangible that had something to measure where 0/0 for example applies then this thing would be not one position or size or dimension or whatever but many many of them at the same time and understanding this system would give us information about something unusual and who knows what kind of applications something like that would have. some scientist put 0/0 in the equations relating to black holes. now we don't know for sure if this equation applies also the denominator for this equation is 1-0/0 which can add up to any number including 1 and 1-1 is 0 . and since the numerator is sometimes non zero number it doesn't seem to make sense. but there are things in universe that appears not to make sense until we understand them.

[@Not-CrypTic]

if you have nothing, and u share it with no one, you end up with nothing, so 0/0 is 0 i just solved a mathmatical mystery with how i learned division when i was like 5

[@FrostyLive]

Back in the first or second grade when I was first learning math the way my teachers taught us about division was "splitting x into y groups" so if you were to do 6/2 it would be splitting 6 into 2 groups, so in each group there is 3. By this logic you would be splitting 0 into 0 groups, in each group there is 0 0/0=0 (This also goes for any number, 1/0, 2/0, 589/0, they all equal 0)

[@williamwilting]

This is a problem indeed, in my opinion, because if you perform operations on any other pair of numbers, even if the pair of numbers is identical, then you can calculate an equation and then inverse it to get the starting number as the result, as long as the operations themselves are equal in the order of operations (addition is equal to subtraction, multiplication is equal to division, and exponentiation is equal to calculating roots). For example: 2•4=8 and 4•2=8, so, the 'inverse multiplication', or in another word, division will give us 8÷4=2 and 8÷4=2. In both cases we end up with the starting number when we divide a number by the same number we multiplied it with. 2•4÷4=2, 4•2÷2=4, 8÷4•4=8 and 8÷2•2=8, all according to the order of operations, because multiplication is equal to division, as long as these equations are properly made from left to right as they should be. However, this obvious reasoning falls apart when division by 0 is involved, because in such equations as the ones above, I can multiply number like, let's say, 3 by 0, but then going 'backwards' by dividing it by 0 doesn't work, because you can't divide by 0. It can even create problems with variables if at least one of the variables is equal to 0. For example: If x÷y=z, and any number can take the place of one of the three variables, then any combination of values should result in a definable answer, right? Well, if division by 0 is undefined, and y=0, z is no longer a definable answer. So how can an equation like that actually exist if you don't add the declaration that y≠0 (or in other words 'can be anything but 0')? That declaration is not given, so you 'may' assume that the equation should still mean that z can be a definable answer. And then my question would be: Is it even allowed to say that 'undefined' can be a number by itself and is equal to z in this case? I never heard that 'undefined' could be considered a number, so if y=0, z can no longer be part of an equation, because its value is no longer equal to something that can be called a number. You may think that I'm taking this too far, but that is how my way of thinking works with this particular subject. However, I wasn't able to advance beyond high school in terms of education. But this kind of subject creates very interesting conversations about mathematical issues.

[@only4use929]

0/0 can only be defined when 4th-dimesion is possible Means the space exist in 0 having infinite space in 0

[@BloxxingDinosaurus]

I KNEW it. I KNEW that dividing by 0 would have to equal Infinity.

[@CosmicStar3]

"imagine you have 0 cookies, and you divide them between 0 friends. See, it doesn't make sense, and cookie monster is sad that there are no cookies, and you are sad that you have no friends"

[@ImmacHn]

Before watching, my first thought was "Illegal".

[@weifuufuu]

First I was like in school you can't define 0/0 because you can't devide with 0. Now I question myself.

[@pelasgeuspelasgeus4634]

Division is by definition a repeated subtraction. So, a/b means "how many times can you subtract b from a?". If you place a=b=0 the answer should be infinity and not undefined.