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@abdealijuzer8852

Жыл бұрын

0*♾= 0 + 0 + 0...= 0

@angelmendez-rivera351

Жыл бұрын

@@abdealijuzer8852 Multiplication is not repeated addition. There is a nearly 200-replies long thread in the comments section, and you may want to check it out. I have explained there why saying multiplication is repeated addition is incorrect.

@anonymous_4276

Жыл бұрын

@@angelmendez-rivera351 hey I have had this one question bugging me for a long time. It's as follows: A line segment consists of only points, right. A point has no length. So how do we get a finite non-zero length by stacking an infinite number of points beside each other? Maybe this sounds a bit dumb but I just can't figure it out.

@angelmendez-rivera351

Жыл бұрын

@@anonymous_4276 This is a genuinely good question. To answer this question, I need you to understand that there are two different types of infinite sets. Some infinite sets are called countable, or enumerable, and those infinite sets which are not countable called uncountable. Uncountable sets and countable sets are both families of infinite sets, but uncountable sets are actually bigger in size than countable sets, they literally have more elements. This may seem strange, but what it all comes down to is that not all infinite numbers are equal. The infinite number that we use to describe countable sets is Aleph(0). If a set is countably infinite, then we say that the set has Aleph(0) elements. Aleph(0) is infinite, and is thus larger than every natural number. However, there are other infinite numbers greater than Aleph(0). There is an entire hierarchy of these: Aleph(1), Aleph(2), etc. 2^Aleph(0) is also greater than Aleph(0). Aleph(0) is the smallest infinite counting number, we call it the smallest infinite cardinal. If a set has *more than* Aleph(0) elements, then it is called uncountable. A set that has Aleph(1) elements, or 2^Aleph(1) elements, or Aleph(2) elements etc., is thus an uncountable set. Why is this distinction between countable and uncountable sets important? Because, this distinction is the key concept to answering your question. As you are aware, a line is a set of points. In fact, a line is an *infinite* set of points. But, it is not merely an infinite set of points. It is actually an uncountable set of points. Meanwhile, lengths are only countably additive. What does that mean? Suppose you have a countable set of sets. This countable set of sets has a length, and this length is equal to the "sum" of lengths of the infinitely many sets it contains. However, if we replace this countable set of sets with an uncountable set of sets, it is *no longer true* that the length of this uncountable set has to be the sum of the lengths of the sets that it contains. It could be much larger, something completely unrelated. This is just a property of how lengths work. A line is an uncountable set of points, so while the individual points have length 0, it is not at all required that the line have length 0 like the sum of the lengths of its parts. The sum of the line could actually be anything. It could be 0 (e.g., the Cantor set) or it could be infinite. The reason this is unintuitive is that we tend to think that lengths must *always* add, which is not true. Lengths only add when dealing with a countable set of lengths. Why do we end up mistakenly believing that lengths always add? Who knows? Maybe because humans suck at mathematics, so we can only learn how to do mathematics by shattering those preconceptions. If you want to understand the theory of lengths, then you need to check out measure theory. All of the concepts are formalized in measure theory, which provides you with the rigor to properly talk about length without vagueness or weird ambiguities. A measure μ is a special type of function, which takes as inputs sets E from a special family of sets, and it outputs μ(E), which, roughly speaking, is the "length," is some sense, of the set E. Not all measures represent length in the geometric sense, though. This is why checking out measure theory is properly. Once you have this well-defined concept, you can say things like μ(U{A, B}) = μ(A) + μ(B), which is just a symbolic way of saying that the "measures" or "lengths" of A and B combined together into one set is the sum of the lengths of A and B individually. However, if E[α] is an uncountable family of sets, where α is, say, a real number for example, then the length of the union of all the E[α], say, μ(U{E[α]}), is NOT the sum of the lengths of each individual μ(Ε[α]).

@anonymous_4276

Жыл бұрын

@@angelmendez-rivera351 thanks a lot for this detailed and elaborate answer!! Now I'm pretty interested in studying Measure Theory.

Isn't it just 0? Like, no matter how many times you add 0, your answer will never become bigger. And if your start value is 0, that means it will be 0.

@blueghost.

Жыл бұрын

Just what i thought, if you have nothing of everything doesn’t that mean you have nothing?

@deadpool20065

Жыл бұрын

I also think that but 0× infinity is a undefined form in limits So there is really a SUS theory behind this

@guydror7297

Жыл бұрын

Lol

@diomgis

Жыл бұрын

Usually in calculus what is meant by 0 is not a pure zero, more like infinitely small value, so you can’t really tell

@OmerA282

Жыл бұрын

No, it doesn’t work like that. You need to calculate it by limits. It’s not the zero you know it as

In measure theory 0*infinity is defined to be 0 because it's useful in this context.

@mmeister8582

Жыл бұрын

Im surprised he didn’t talk about that

@pierreabbat6157

Жыл бұрын

Is the infinity countable?

@angelmendez-rivera351

Жыл бұрын

@@pierreabbat6157 ∞ is not a cardinal number, so that question makes no sense.

@mdrizwanansari7573

Жыл бұрын

@@pierreabbat6157 what is a countable number? Can you define it?

@ilovecairns5181

Жыл бұрын

@@angelmendez-rivera351 :| you act so smart but don’t know what the guy was talking about

"Infinity times anything is infinity" Negative and complex numbers have left the chat Edit: Either I'm just blind or it was added in recently somehow, but there's a note saying it only applies for positive numbers. Please stop nuking my notifications.

@superhero25e

Жыл бұрын

Lmao yea

@vanshpandey6793

Жыл бұрын

Math moment🌚

@superhero25e

Жыл бұрын

I just realised: they didn't leave the chat, an impostor killed them 😱

@goosehonk6715

Жыл бұрын

@@superhero25e shush

@upsidedown-pug1974

Жыл бұрын

0:07 there is note that it's only with positives

For most people that think 0*inf = 0, the answer is: it honestly depends on which set of predefined notion are you basing it off of.

@roneitback

Жыл бұрын

If we really wanna beat that inf to a zero, lets just say 0*inf*0

@user-hs7hw6hq7w

8 ай бұрын

​@@roneitbackbut then, if 0*∞ = ∞, then it will be same in ∞*0, or, ∞

@jobie_robloxia

8 ай бұрын

0xinfinity will always be 0, and infinity times 0 is always 0. Let's start with 0, if you keep adding itself, it's still zero. Now let's go with Infinity, if 3x0 = 0 and 5x0= 0, then infinity times 0 should be 0 because we should count it 0 times to get the product(term for multiplication equation answer)

@victorkao1472

8 ай бұрын

@@jobie_robloxia but you are assuming is that infinity is the concept of limit that x is approaching as x grows bigger. But what if you think about it from the other point of view? Infinity * 1000 is infinity. Infinity * 100 = infinity. Infinity * 10 = infinity. Infinity * 1 = Infinity. Infinity * 0.1 = infinity. Infinity * 0.01 = infinity. Infinity * 0.001 = Infinity. And so on and so forth. Until the other number infinitely approaches 0. In fact, there are countless different answers depending on how you approach the problem So again, the answer varies depends on the predefined notion you are basing it off of

@hack5960

8 ай бұрын

0x ∞ =1.

I kept expecting you would mention how in complex analysis and measure theory (more generally the extended reals) it's common to define 0 times infinity as 0

Maybe the real infinity was the friends we made along the way...

@Tristan-ol6te

Жыл бұрын

No

@evanhanchett893

3 ай бұрын

@@Tristan-ol6te yuh huh

Its "not an exact 0" times ∞ that's indeterminate. It's what we call indeterminate when something **approaches** to zero. An approaching zero and an absolute zero are different! Also note that infinity always means something that "approaches" it, it's an idea not a number. Otherwise, an exact 0 times ∞ (approaching ofc) is 0

My calculator says its zero

In my opinion, 0 * ∞ = 0, 'cause multiplication of numbers is simply adding a number given times. Let's imagine a number line. Adding two numbers is like taking two line segments of length of those numbers, laying them from 0 along the number line, one after another, and reading number from the point where the chain of line segments' ends. F. ex. let's add 3 and 4. We get two segments: of length 3 and of length 4. We lay them along the number line and the end point is 7 - product of addition;. If we have addition sorted out, we can look closer at multiplication then. Multiplication is repeated addition and that's simply it. E.g. 4 * 3 means we have three line segments, each of length 4. We lay them along number line and get result of 12. Now, we can consider 0 * ∞. Let's assume that 0 is represented as a point instead of segment, since in this case segment should have length of 0, which is the same thing as point. We start by laying those points one after another, for infinite amount of times, but there's the catch: since points have no length, we stay in the same place for eternity, no matter what we do. We can take another approach. Let's rewrite it as ∞ * 0. This equation tells us we have one ray (ray is infinite, but has a starting point) and we lay it on the number line 0 times, which means we don't actually place there anything, 'cause we were ordered to do it no times - never do it! So we end up in the spot where we started - 0 on number line, therefore 0 * ∞ = 0! And that's the answer! At least for me

@xyz.ijk.

Жыл бұрын

Careful … 0! = 1. 😁😁

@enderfun2852

Жыл бұрын

@@xyz.ijk. If I remember there are gamma and pi functions that sort it out so don't worry

@xyz.ijk.

Жыл бұрын

@@enderfun2852 love the power of the gamma function

@hughcaldwell1034

Жыл бұрын

I think the problem with this method is it implies that the interval [0, 1] has length 0. The interval is made up of an infinite number of points, which have 0 length. So their total length, according to you, must be 0. This is a problem.

@xyz.ijk.

Жыл бұрын

@@hughcaldwell1034 I agree with you for this and similar reasons, but the issue is really what number system is one using. Which branch of mathematics is controlling I think is the issue. Are we approaching this from below Omega or above Alpha, etc.

I think it works the same way as 1^inf. If that "1" is a solid 1, it will stay as so. But if it is some kind of kind of calculation that doesn't give a solid 1, that (if I am not wrong) ends up being e (2.71828...) This case, if it's a solid 0, 0*inf should stay as 0.

@insertusernameherepls

Жыл бұрын

You're basically saying if the number is not 1 it isnt 1...?

@insertusernameherepls

Жыл бұрын

@@rafastyles1002 I kind of get what you're saying. It's like saying (x-1)/(x-1) is the same as 1/1 unless x=1 then it would be something else.

@rafastyles1002

Жыл бұрын

@@insertusernameherepls correct

one way i like to think of it is when you're adding together an infinite amount of 0's you get 0, but adding 0 amounts of infinity is what stumped me EDIT: please ignore my stupidity, this kind of stuff trips me up EDIT 2: don't reply to this original comment, instead read the thread

@saar4869

Жыл бұрын

but isn't 0 amounts of infinity also 0? because if there is no infinity then there's nothing and therefore zero. maybe i'm wrong i'm just thinking intuitively.

@NoOffenseAnimation

Жыл бұрын

@@saar4869 yeah that would make sense... but infinity is not a normal 'number' so there could be something we're missing out on

@Nofaz

Жыл бұрын

But with this idea, when we tried it on 1 times infinity it should get 1 because it just an infinite amount of 1 multiplying itself infinitely. Yet, we agreed that the answer should be infinity. Right?

@NoOffenseAnimation

Жыл бұрын

@@Nofaz i guess in that case it would depend on which way round it is, an infinite number of 1's or 1 amount of infinity... idk this is messing with me

@Nofaz

Жыл бұрын

@@NoOffenseAnimation I think we miss out the part that it should be addition of not multiplied of. 0•∞ should be 0+0+0+... or no infinity at all. Then 1•∞ should be 1+1+1+... or just a single ∞. In both cases for 1•∞ give us ∞ but for 0•∞ it seem both of the answer should be 0 too. Weird.

if 0 x infinity isn't 0, it means that you CAN go somewhere with 0+0+0+0..., and it would mean that (the number you found)/0 = infinity and that is undefined, and it would kinda become like x^0, which is undefined but determined

Why is it that hard to say 0*infinity=0? By def it means either 0+0+0+0+0+0...... So it equals 0 Or either you have 0 times infinity, so you have none of it, so 0. WHY is it that hard to admit? Like 1^infinity, 0^0, etc There are some I can understand since there are different sizes of infinity (number or reals>number of integer) like infinity-infinity or inf/inf, but the rest is easy to define. I don't understand why those are undefined.

@Deejaynerate

Жыл бұрын

1^infinity is actually well defined and equal to 1 if the 1 being raised to infinity is a fixed, non-limit one. Thing is that when that one is the result of an approach via limits, you tend to get very wonky results as it's not exactly 1, and exponents behave differently if they're larger or smaller than one, so you might get infinity if your limit approaches (slightly more than one)^infinity, zero if your limit approaches (slightly less than one)^infinity, or you might even get neither! [e is traditionally defined as a limit of (1+)^infinity]. Thus, 1^infinity is usually seen an indeterminate form, which are mentioned in this video. 0^0 is also an indeterminate form, but that one has less justification being undefined. We already have a handful of functions where it is necessary for 0^0 to be defined as 1 and most computers pretty much output 1 by default anyway. So algebraically, there is an intuitive reason to define 0^0 as 1, but once again in the context of limits, you can get different results out of it.

@Deejaynerate

Жыл бұрын

As for the first one, infinity is not a real number, more so the idea of a number defined to be larger than any real number, so trying to define it in terms of algebra gets very ugly very fast

@pierre8235

Жыл бұрын

@@Deejaynerate but I'm not talking about limits at all, I'm talking about these calculations

@vitowidjojo7038

Жыл бұрын

Because it involves limits, i guess? I am pretty sure limits are mentioned multiple times in video, so must be it. I personally think limits are not needed for this case. I would go with 0*(infinity)=0

@nonoliveleftgreen

Жыл бұрын

Because, a-a = 0. So 0 * infinity = a-a+a-a+... , and a-a+a-a+a... does not converge.

I read somewhere that "Inifinity is not a number, its a concept" and I no longer have doubts after that

@mat0c834

Жыл бұрын

i think of infinity as a group of numbers haha

@fisherfresh6708

Жыл бұрын

​@@mat0c834 I thought is a concept *uno reverse*

@1unar_eclipse

Жыл бұрын

"Infinity isn't a number, it's a concept. But we're not dealing with real numbers; this is floating point, baby!" ~ jan Misali

@asherkime5910

Жыл бұрын

Some of them are but in this context it’s not

@insertusernameherepls

Жыл бұрын

Infinity may be a concept, but so are negative numbers.

0:00 - 0:08 Talking about ∞•x or x•∞ is nonsensical, because ∞ is not a real number, and ∞ is not an element of any algebraic structure where • (multiplication) is well-defined. I will elaborate on this more later. 0:18 - 0:34 The question about 0•∞ is a question about algebraic concepts, and it has nothing to do with limits, ultimately, in the same way that the question about 2 + 3 and the question about 0^0 are both questions about algebra, not limits. If you want to ask a question about limits, you may want to ask "what is lim x•y (x -> 0, y -> ∞)?," not "what is 0•∞?" These are completely different questions, with possibly completely different answers. Just like how floor(0) and lim floor(x) (x -> 0) have completely different answers. We need to stop teaching students to conflate the two questions, when *the entire point of calculus is precisely to **_not_** do that.* I say this in the nicest and most respectful way possible. I need everyone to stop saying "we can use limits to compute arithmetic," because that is just not how limits work at all, nor is it why the concept was invented. Again, I say this with good intentions. 1:20 - 1:29 This is another thing I need instructors to stop doing completely, and this is one thing that I have seen students botch so many times. I realized later on that you actually acknowledged this in your video, but I am still going to make this point, because people need to hear it regardless. The function g is the product of two function j and k, where j(x) = 1/(1 + x^2), and k(x) = x. This is straightforward. Now, j approaches 0, and k approaches ∞. Yes, this is all true, but saying "g approaches 0•∞" is just incoherent, and it misleads and confuses students. And there is no mathematical justification for this. In fact, I understand that the idea here is that lim g (x -> ∞) = lim j•k (x -> ∞) = lim j (x -> ∞)•lim k (x -> ∞) = 0•∞, since lim j (x -> ∞) = 0 and lim k (x -> ∞) = ∞. But, as innocent as this idea looks, it is incorrect. You cannot break the limit of the product into the product of the limits, that is not mathematically valid. It is mathematically valid if and only if both limits exists *and are finite.* Since this condition does not hold here, it is not mathematically valid to do it. This is how you end up with crazy stuff like "0^0 and 0/0 are indeterminate forms," when it just makes no sense. 0/0 is undefined, period. 0^0 = 1. These are true for completely different reasons, none of which involve limits. If you want to talk about the product of two functions, where one approaches 0, and the other ∞, then that is fine, but you have to do it with the correct notation and language. 2:02 - 2:07 But you see, that is not what it is at all, though. This concept of indeterminate forms is one of the reason why every student I have met is bad at calculus. This is why I think the curriculum needs to be completely reformed, and the way we teach calculus has to change drastically. There are no "indeterminate forms." What is actually happening here is that you have expressions of the form lim f•g (x -> ∞), where we know that lim f (x -> ∞) = 0, and lim g (x -> ∞) = ∞. The problem is that this information is *not enough information* to actually compute lim f•g (x -> ∞). You need additional information about f and g: in particular, information about their derivatives. It is that information which helps you determine lim f•g (x -> ∞), be it in the form L'Hôpital's theorem, be it via algebraic simplification, or something else altogether, who knows. This all has absolutely nothing to do with 0•∞. You could say 0•∞ = π•e, for all I care, and it would have *exactly zero effect* on calculus, because these limit expressions do not require you to ever know what 0•∞ is, because that is just not what these expressions are about. The so-called indeterminacy has to do with the functions themselves, not with 0 and ∞. 2:07 - 2:16 Right! Exactly. And this is the problem with the "indeterminate form" nonsense. And this is why people need to stop bringing up limits like they are relevant to the discussion. It makes me glad to see you acknowledge this, because I personally believe this a huge problem with mathematics education. This is not something so trivial as a minor semantic technicality. No, this underlies the backbone of the entire conceptual understanding of what a limit is in all contexts, and it also underlies our fundamental understanding of arithmetic operations. Continued in the replies...

@angelmendez-rivera351

Жыл бұрын

2:37 - 2:45 I think it would be far more helpful to actually give precise definitions here. + is defined as some binary operation, which in this context, ought to satisfy the rules x + (y + z) = (x + y) + z and x + y = y + x, and 0 is defined by the rule that 0 + x = x + 0 = x. This concept is important. Operations are defined by rules, by axioms. Multiplication is defined as some binary operation that distributes over addition. This means that a•(x + y) = (a•x) + (a•y) and (x + y)•a = (x•a) + (y•a). 2:46 - 2:59 Oh, we can actually do so much better than this, and there is actually a precise definition that is intended for the symbol ∞ for most of mathematics. But this is a complicated definition that involves this highly-advanced idea called the Dedekind-McNeille completion of the real numbers. So, here is a bit of a quick review: as you know, one of the properties that defines the real numbers has to do with the fact that they are totally ordered (it always makes sense to talk about a 3:17 - 3:22 Well, ultimately, it all comes back to definitions. If you define Triangle and Circle in an appropriate fashion, then talking about their product is completely sensible. But, they keywords here are "in an appropriate fashion." The way ∞ is defined in such a way that is not defined in an appropriate fashion for the operations + and • to actually be applicable. And that is what it boils down to. Again, the actual "why is the definition not compatible with + and •?" is a question that requires some relatively advanced mathematics to answer, but the point is that the definition guarantees that these operations are not applicable. 3:22 - 3:36 It being "undefined" has nothing to do with creativity or lack thereof. It just has to do with theorems in group theory, ring theory, lattice theory, and so on. These are theorems that tell you about the fundamental relationships between different types of algebraic structures, and they tell you about what kinds of things are possible or impossible. The mathematics that tell you that the algebraic closure of the real numbers can exist (the complex numbers) are the exact same mathematics, ultimately, that tell you that there cannot exist an algebraic structure with a notion of division where one can divide by 0. It is a theorem, much in the same way that Fermat's Last Theorem is a theorem. There is nothing we can do about it. The result may be unsatisfying, but it is a truth about mathematical structures in general. 3:56 - 4:05 This is inaccurate. Wheels are actually a very complicated and unintuitive type of algebraic structure, unlike groups and rings, which have intuitive and natural axioms. And yes, Jesper Carlström, who has developed most of the theory of wheels, titled his doctoral dissertation "Wheels - On Division by 0," and yes, he does claim in his paper that his inspiration for defining wheels is to make division by 0 possible. However, while wheels are certainly a worthwhile structure to develop and study, saying that they define division by 0 is misleading. The symbol / has a completely different meaning in wheel theory, than that of division, and Dr. Carlström even provided multiple examples of wheels where, for example, 0/2 is not equal to 0, and 2/0 is not equal to /0. If you consider the free wheel over the empty set, you get a wheel where, yes, /0 and 0/0 and 2/0, 3/0, 4/0, etc., are all well-defined. However, in this structure, 1, 2/2, 3/3, 4/4, etc., are all different quantities, they are not equal. Also, 0, 0/2, 0/3, 0/4, 0/5, etc., are all different quantities as well. This is not true in all wheels, of course, but the point is that these are examples that demonstrate that the / operation in wheels is nothing like division, actually. Now, yes, it does generalize some theorems about division, and you could even make an argument that the / operation is more useful than division. But even so, it is different enough from division, that simply saying it is division is just outright inaccurate, and it will misinform people about how wheels work. I will admit, until recently, I was pretty ill-informed about wheels too, which is all the more why I care so much about this now. 4:05 - 4:21 One of the wheel theory axioms is that 0•/0 + x = 0•/0. From the other axioms, one can prove that x•0•/0 = 0•/0, so yes. But, again, I should make it clear, / does not denote division here. / denotes what Dr. Carlström called a monoid involution, which he explored very thoroughly in his paper. Also, the notation /0 = ∞ is mostly abuse of notation, and it is by no means a universal standard. And it is a notation that I would highly discourage. The typical definition of ∞, and /0, are completely different mathematical objects with essentially no actual relationship to one another whatsoever. That is all for the criticism. I know I probably sound overly critical and perhaps harsh, but again, I reiterate, I say all of this with the intent of improving the way we all think about mathematics, and for the sake of helping people realize that we have been doing a bad job at teaching mathematics, and that we can do a much better job. I am not doing this for the sake of hate, or for the sake of being a villain. Blunt as I am with some of my remarks, I do believe that pointing all of these things is important for people to have a better genuine understanding of the things being talked about. And regardless of the criticisms, I do respect the work this channel does in bringing these not-so talked about topics into the limelight.

@BriTheMathGuy

Жыл бұрын

@@angelmendez-rivera351 Thanks very much for taking the time to write this all out Angel. These are all great points and super good info for anyone willing to take the time to read. I always appreciate your comments! Hope you have a fantastic holiday season and a happy new year.

I think it’s 0. Oles Drow said that and I agree. Adding 0+0+0+0 and so on will always be 0. Actually, I don’t like the limits too much just because of how it approaches, on one a part may be big enough to overpower, so It really is just let’s say something like 0.001*1000000000. The opposite is also true. Correct me if I am wrong.

@lakshay-musicalscientist2144

Жыл бұрын

Well you could assume 0.999... + an infinitely small value equals one , because we know that something infinitely small is conventionally perfectly equal to zero while also having a meaning, multiplying the infinitely small unit with anything finite won't alter the answer as it's still infinitely small , but infinities can help us make it a finite or an infinite value , you could also consider 0 as 0- and get similar results. In the Cartesian system you have an infinite amount of points each being infinitely small , to get the immediate next point is simply not possible as you would simply end up getting the same number but you could imagine it as 1 + an infinitely small point to get the next point or +2 infinitely small points to get the next to next point , the thing in calculus is that these 3 points would be considered exactly equal on a finite scale but not in an infinite or a different scale , hope you understand a bit now.

@lakshay-musicalscientist2144

Жыл бұрын

If you agree that that 0.9999... =1(exactly equal) in the Cartesian plane then you kinda have to agree that something infinitely small is exactly equal to zero

@3dplanet100

Жыл бұрын

Makes sense! 0+0+0+0+0... is 0, no matter how many times you add 0. Same with 0×0×0×0 is 0, no matter how many times you multiply by 0. It will NEVER add any value. So infinity times 0 is 0. Could be Undefined or Undetermined or whatever but it will always be 0.

@adamosburn754

Жыл бұрын

Except multiplication is scaling, not repetitive adding, as is often taught. Repetitive adding gives a generic idea of multiplication, but it is really a scaling thing. So multiplying by zero is finding the place on another scale with the same value for that scale. Eg, 2*3 = 6, so the new scale is a 3x scale. If 1 was the increment of the first scale, then 3 is the first increment on the 3x scale, or 3 on our scale that counts by ones, is 1 on the scale that counts by threes (to the 1-scale). Might be confusing but, zero on the 1 scale should be smaller than zero on the three scale by a third, if zero were a number. But it's not, it's a scale, so when you multiply by zero you are putting it on the zero scale, which doesn't register on a 1-scale, so we call it nothing. And when you multiply by infinity it's scaling it by every number, making it many scales simultaneously. Since it is all scales simultaneously, it is infinite on an infinite number of scales, and zero on the zero scale. While zero gets scaled to nothing in any scale - even the infinite. So you end up with 0-scale times ∞-scale = 0, on the infinite scale (takes up so little of the scale it doesn't exist in any meaningful way) and with ∞, on the zero scale (takes up so much of the scale that no part exists in any meaningful way). So you end up with what you started with: 0*∞ - an infinite scale with a value so small you can't see it on the scale, but that small value is too large on a zero scale to see it on the scale.

@phantom-math

Жыл бұрын

@@adamosburn754 Definitely one way to see it. I just think 0 scaled up even infinitely can’t be increased. Thinking of it as the area of a polygon, an area of 0 would mean there is no polygon at all, or shape. No matter how much you scale up the size, you can’t increase it. It would be like creating something out of nothingness. Honestly this is why infinity is so confusing.

My intuition says 0 * inf = 1, but only as long as the 0 and the inf are represented as limits that change at the same rate, such as 1/x and x. The limit of 1/x is 0, and the limit of x is inf. Further, 1/x * x = x/x = 1. In the video examples using limits, the first had an inf component that changed faster than the 0 component, so it took over and drove the value to inf. Conversely, in the second example the 0 component changed faster than the inf component and took over, driving the value to 0. Using 0 and inf that change at the same rate would give a value of 0 * inf = 1. For fun, if you use functions for the 0 and inf components that intricately change their change rate, I suspect you could have the value approach even more fascinating things. Nothing I've confirmed, but it feels like you could have it oscillate between values, representing a simultaneous convergence on multiple values other than 1?

@PotassiumLover33

Жыл бұрын

bruh why 1

@utkarshanushka2577

Жыл бұрын

Yeah my teacher taught us 1/0=inf so inf×0=1 But I don't agree I think it really depends I think it's either 0 or better left undefined As a×b means a times b or vice versa similarly infinity times 0 means 0+0+0+..... which will still be zero (According to me) Or as I said it should better be left undefined

@quinton1661

Жыл бұрын

@@PotassiumLover33 Take reciprocals. (1/1 * 1/1 = 1), (1/10 * 10/1 = 1), (1/100 * 100/1 = 1) - if you take these to the limit: (1/∞ * ∞/1 = 1) -- which can be written as 0 * ∞ = 1 ta da

@0ans4ar-mu

Жыл бұрын

@@utkarshanushka2577 Just because you can easily represent multiplication as a series of additions that doesn't mean that's all multiplication is, and neither should it limit how we think of it.

@brandonklein1

Жыл бұрын

Yeah this is very related to L'Hospital's rule and most of the time "0*infty" (as being used as a shorthand for the limit of a product of two functions) ends up being something finite, at least when the functions are modeling something physical.

Isn’t this just an undetermined form like 0/0? I mean, it can be both 0 and infinity, it could be even any value I think, because let’s take an example : 10^-9* 10^18 = 10^9 Here we have one number approaching zero while the other one is really big (to satisfy : 0*infinity ) and we can see that the result is still a really big number as well. However, I can do the also the following : 10^-18 * 10^9 = 10^-9 Here’s the same situation, the result give a really small number. All this to explain that 0*infinity is just an undetermined form like 0/0 (that’s still just my point of view)

@asherkime5910

Жыл бұрын

Those are numbers, infinity isn’t

@evanrishel8513

Жыл бұрын

Well put

@aparnarai3708

Жыл бұрын

@@asherkime5910 then multiplication isn't possible in the first place

@asherkime5910

Жыл бұрын

@@aparnarai3708 that's why they're using limits and making a whole video about it

@ALisztf

Жыл бұрын

@@asherkime5910 infinity does play the same role of a big number

Zero always wins

I think 0 x ♾ is 1 if your using limits. The examples in the video with limits had the sides unbalanced, and they approached their goal at different rates. If we make a limit that has sides at the same rate you get 1 limit x -> ♾(1/x) * x (1/x) * x = x/x = 1 If you have nothing and everything at the same time it makes sense for it to be 1 If you aren't using limits I would define infinity as 1 + 2 + 3 + 4 + ... 0 * (1 + 2 + 3 + 4 + ...) If you use the distributive property it becomes (0 + 0 + 0 + ...) which is 0

What if you multiply two seperate limits together? For example: lim (x approaching infinity) of x * lim (x approaching 0) x . The solution in my head was just to leave it like that, as it cannot be simplified further, so 0*infinity just remains 0*infinity in this case (as in its its own seperate thing)

@user-pr6ed3ri2k

Жыл бұрын

keywords: in that case in that case, it's automatically undefined, unless they are both x-->n (n is constant), and ∞≠0. ∞0 would still be as useless as the thumbnail shows, so ye

@phiefer3

Жыл бұрын

There are laws for how to deal with limits, in this case the product rule and quotient rule apply. Specifically, the product rule is that the limit of a product of 2 functions is equal to the product of their limits, and since it is an equality we can go in reverse as well, merging the 2 separate limits into a single limit of the function. The quotient rule is similar, but it does have an extra condition that the function in the denominator cannot have a limit of 0 in order for this rule to hold (in which case you need to use other techniques for evaluating the limit). Both of these rules also carry the condition that the limiting condition of both limits is the same. However, one might notice in his examples of such functions in the video the parts that approached 0 actually approached 1/infinity, and so multiplying these two functions would probably end up looking more like infinity/infinity (or if you really wanted you could argue them to be 0/0). These are also indeterminate forms (it's actually possible to convert any indeterminate form into any other indeterminate form with a little bit of work). That being said, this doesn't simply leave our limit as undefined, as there are other techniques available for dealing with such limits. Such as L'Hopital's rule and other tools that allow us to evaluate these limits. These rules help to explain why in the 2 examples shown in the video one them the limit was infinity and in the other it was 0 (and in truth for other examples you can get literally any other value as the limit to such a function). In general indeterminate forms don't really mean that there is no solution, but rather that there is no single solution that applies in all scenarios. The solution to an indeterminate form is contextual, it depends on the specific problem being solved and the function(s) involved. Sometimes 0 x infinity is 0, sometimes it's infinity, sometimes it's 3, and sometimes there may really be no solution. So when just asking a generic question like "what is zero times infinity" where there is no context to build off of, then there simply is no solution (unless you define it such as the wheel algebra example, though one could argue that such a "nullity" element is the same as a non-existent value, the name even implies that).

@havenbastion

Жыл бұрын

The answer is the average of all existence!

@angelmendez-rivera351

Жыл бұрын

@@phiefer3 *Specifically, the product rule is that the limit of a product of 2 functions is equal to the product of their limits,...* No, this is inaccurate. You are close to being correct, but you are missing the condition that the limits must both be real numbers. This is not a minor detail, but rather, is the most important part of the actual theorem you are citing. This is why, if lim(f) = 0 and lim(g) = ∞, saying that lim(f•g) = lim(f)•lim(g) = 0•∞ is actually incorrect. In fact, if you are applying the limit theorems, then arriving at arithmetic expressions such as 0•∞ is impossible. *These are also indeterminate forms...* I need teachers to stop saying this. There is no such a thing as an "indeterminate form." As far as real analysis is concerned, this is complete nonsense, and I have explained the problems with teaching said nonsense in my post in the comments section, with more detail at that. 0/0, 0•∞, ∞/∞, are all undefined. Well, saying they are "undefined" really does not explain anything here. The mathematical fact is, you cannot divide by 0. Writing a symbol that denotes such a division is incoherent, since such a division is impossible. Performing arithmetic operations with ∞ is also impossible, so using symbols denoting such operations involving ∞ is also incoherent. That is the point. *That being said, this doesn't simply leave our limit as undefined,...* lim(f•g) is not undefined, no, and I am not claiming it is, and I do not see anyone claiming it is undefined. 0•∞, however, is undefined. There is no contradiction here, because I explained a few paragraphs above, lim(f•g) is _not_ equal to 0•∞. As far as real analysis is concerned, these two symbolic expressions have no actual relationship to each other. The question is not "what is lim(f•g)?" The question is "what is lim(f)•lim(g) = 0•∞?" These are different questions, and they have different answers. *...unless you define it such as the wheel algebra example...* I strongly recommend that you stay away from appealing to wheel algebra, because, to be completely honest, and I mean this in the most respectful way possible, I am not convinced you grasp the totality of the implications of wheel theory. In fact, I am not convinced Bri has such a grasp either, and to be honest, neither do I, but I at least know enough wheel theory to realize I understand very little of it. Anyhow, "nullity" within wheel algebra does not work at all in the way that Bri says it does. It is far more complicated a subject, and it is ultimately not actually relevant to the discussion.

@insertusernameherepls

Жыл бұрын

@@phiefer3 Very close

undefined?

If I add 0 to 0 forever, do I not simply get 0? Same question, if I raise 1 (not 1+ or 1-) to infinity, isn’t it simply 1 times 1 forever which is 1 forever?

@insertusernameherepls

Жыл бұрын

Yes but infinity is very weird.

@theimmux3034

Жыл бұрын

infinity probably isn't that easy but you're right about the limits

We should make a rule that the "power" of × 0 is greater than the "power" of × ∞, kind of like BODMAS

@theimmux3034

Жыл бұрын

math isn't what you think it is, it is a separate idea

"Like all great questions, the answer is, of course, it depends" 🤣🤣🤣

I can see your point but tehnically 0 times infinity should be 0. After all, multiplication is adding up a the same number, a number of Times equal to the number u multiply it with. But no matter how many times u add 0 with 0 u can write 0+0+0+0... An infinite amount of times and you still get 0

@asherkime5910

Жыл бұрын

Infinity isn’t a number

@insertusernameherepls

Жыл бұрын

Yes but infinity is weird

@theimmux3034

Жыл бұрын

for a finite x 0x = 0 but infinity isn't a number, it is a harder concept to grasp (i have no idea)

@Davidutul

Жыл бұрын

I mean there are many concept of infinity. Even the universe is said to be infinite but not bc it has an infinite size but bc it has a finite size that keeps growing towards infinity. If we can't multiply it with 0 bc it isn't a number we shouldn't be able to do anything with it bc it isn't a number. We shouldn't be able to add it with any positive or negative number or divide with it or stuff like that, yet we think we cam do all that so despite it is not considerated a number we give it the propriety of s number. The only diference is the proprietiee we give it. Similar to how 0*any number is 0, infinity plus, multiplied, dividend with any number is infinity. Just a "bigger infinity". So having the proprieties of a number to be able to be added, divivded, multiplied or be substracted, makes it a number wich means that you can multiply it with 0 and the result, by math logic that i said în the first coment, is 0

@asherkime5910

Жыл бұрын

@@Davidutul adding or multiplying or any of those operations result in the same size infinity. the universe's dimensions aren't known but we do have a definite answer for the size of the observable universe, which is the only one practically used. nobody says the universe is infinite, at least not anybody credible

The fact that there are so many ways to think of this is why we can't really answer it. My favorite answer, however, is 1: Take reciprocals. (1/1 * 1/1 = 1), (1/10 * 10/1 = 1), (1/100 * 100/1 = 1) - if you take these to the limit: (1/∞ * ∞/1 = 1) -- which can be written as 0 * ∞ = 1

@thelordz33

Жыл бұрын

If you multiply 1/infinity and infinity/1 you get infinity/infinity which has this equation saying infinity/infinity = 1, not 0 * infinity = 1. I get your assumption is 1/infinity = 0, but -1/infinity also equals 0 so 0 * infinity could also equal -1 but since 0 is neither positive or negative, both of these are wrong.

@quinton1661

Жыл бұрын

@@thelordz33 There's a reason why the answer is generally considered to be indeterminate, because we can argue until we're blue about what the "real" answer is. In this case though, you can simply follow the pattern to its logical conclusion: the larger the denominator, the smaller the result. If the denominator is infinitely large, then the result is infinitely small. In general, any number divided by ∞ is 0. I'm not saying you're wrong or right. There is no objectively correct answer, but it's fun to think of all the ways we can play with ∞ and 0

@insertusernameherepls

Жыл бұрын

@@thelordz33 What if you count 0 as +-0

at the start of the video you said ‘zero times any value is always zero’ infinity is a value and therefore zero times infinity is zero

*”We might as well say: what is triangle, times circle? - the question doesn’t really make sense.”* Archimedes: *”Am I a joke to you?”*

That triangle times circle example is unfortunate given that cartesian products exist.

@hughcaldwell1034

Жыл бұрын

I know, I's wondering if I'd find any objecting topologists...

@angelmendez-rivera351

Жыл бұрын

Well... but everyone pretty much understands what he meant.

@angelmendez-rivera351

Жыл бұрын

Also, Cartesian product is not multiplication. You are conflating concepts now.

According to me 0×∞=r, where r belongs to number, any number, doesn't matter whether it's real or complex. Its anything. This relation is a door to any number.

Whenever you treat infinity like a number, you're going to get the wrong, conflicting, indeterminate, etc, answers.

@kilian8250

Жыл бұрын

That’s not true, there are lots of contexts where we can work rigorously with infinite numbers. A few examples of contexts where we have infinite numbers are projective spaces, the hyperreal numbers and ordinal numbers.

@fahrenheit2101

Жыл бұрын

I mean didn't that get ruled out in this video alone - you can come up with systems that work consistently with infinity, you just have to do so at the expense of some nice quality of traditional arithmetic. And even traditional arithmetic has some arbitrary choices made.

@kilian8250

Жыл бұрын

@@fahrenheit2101 but the thing is that you don’t really, not when it comes to the hyperreals. Their arithmetic works exactly like the real numbers do. The hyperreal numbers form a field, this means that all operations (addition, subtraction, multiplication, division) work like they do for real numbers.

@pvanukoff

Жыл бұрын

The neat thing about the internet is there's no shortage of people willing to swoop in and point out how you're wrong in some way. "WELL, ACKCHUALLY...".

@fahrenheit2101

Жыл бұрын

@@kilian8250 Really? I guess I figured we'd be using the system which worked best without sacrificing nice operations and properties. I guess nobody really cares enough for us to use hyperreals.

The CDC mainframe I used in college had positive and negative infinity and positive and negative indefinite.

But we may take every number from 0 to ∞ and devide by infinity. In all cases we will get 0. For example: 0.00001 / ∞ = 0, 1 / ∞ = 0, 2 / ∞ = 0... 100 / ∞ = 0... (∞ -1) / ∞ = 0. Multipliying is reverse version of dividing. So, if we multiply 0 and ∞ we will get all results from 0 to ∞, but not including ∞ (because ∞ / ∞ is not equal 0). Main diference between multiplying 0 * ∞ and multiplying other numbers, that with other numbers after multiplying we will get only 1 number, but in case multiplying 0 and ∞ we will get not 1 number, but array of numbers. The same case is multiplying 0 and -∞. In this case we will get array of all negative numbers from 0 to -∞, but not including -∞.

1/0 = infinity .°. 1 = 0×infinity

@vitaminprotien679

Жыл бұрын

That's what I was saying...

@landy4497

Жыл бұрын

can't have a 0 in the denominator and do algebra with it

@pablosarrosanchez460

Жыл бұрын

1/0 ≠ infinity, it isn't defined

@friesgaming487

Жыл бұрын

1/0 = ±♾ just graph y = 1/x. as x approaches 0, y approaches negative and positive infinity at the same time

@lakshay-musicalscientist2144

Жыл бұрын

With that logic , 69/0 is infinitely so 0xinfinity = 69 , the correct answer is that it depends on the function, it is not a defined particular value .

Amazing video 👏. Could you make a video on Floating Point Arithmetic? The first development has some of these ideas within the system.

@PretzelBS

Жыл бұрын

kzread.info/dash/bejne/loWczJeLd9fHl5M.html if you haven’t seen this your welcome

Hello!! Me encanta el abordaje que hace este canal con ciertos planteos o preguntas que yo me he hecho también!! 0/0, 0⁰, 0*♾️, etc, involucrando a 0. Para mi 0*♾️ es 0, como dijeron en otros comentarios. Yo lo razono así (se que para cada persona, es algo intuitivo y filosófico a la vez, lo que le resulte más armónico, con cierto criterio): 0*♾️ es "infinitas sumas 0+0+0....=0" Además ♾️*0 sería "ninguna vez el ♾️ en forma de sumando" (0 sumandos ♾️=0). Se que habrá diversos puntos de vista, personalmente me agrada este Sdos y gracias ✌️

It's simple. 0 × ∞ means that the 0 has ∞ amount. 0×0×0×0×0×0×0×0.......and so on until infinity =0 And if we change it to ∞ × 0, the result is still the same; the ∞ has 0 amount. =0 Therefore, 0 × ∞ = 0 But the problem is if 0 × ∞ = 0, then ∞ = 0/0 Every number that is divided to the number itself, = 1. So, does ∞ = 1? And this applies to every positive number, not just ∞. For example 0 × 2 = 0 2 = 0/0 = 1 So, does every positive number = 1?

I also thought of limits, but in a simpler way. The limit of 1/x is the basic case I came up with. The limit as x goes to infinity is 0. But also the limit as x approaches 0 is infinity. So does that mean we can multiply both sides and get 0x♾=1? Not so fast: 1 is just a finite constant. We could've used any, like 42,069 or 6^6^6 muahahaha... So do all constants equal each other? Is 1=2? Is every number a solution? What's going on here? Furthermore... 1/x approaches positive infinity from the right as x approaches 0... but it approaches NEGATIVE infinity as x goes to the left. Is negative infinity equal to positive infinity? Are they both two separate solutions? I know these seem like silly questions to ask, but thinking about as many things as you can and playing around with them is what mathematical curiosity is about.

@Osirion16

Жыл бұрын

You're wrong assuming the limit as x goes to infinity is 0, in reality the limit does not exist as from 0- you get -infinity and from 0+ you get infinity. That also reveals there's a vertical asymptote at x=0. I believe this answers your question about "does positive infinity = negative infinity or are they both two separate solution" There are indeed 2 solutions and this is why division by 0 is undefined, it is because it can go both ways. I don't know if you've learn the concept of limits at school, but you still seem to be grasping the matter you'd just need more thorough explanations ( like when a limit doesn't give you the same value when you approach from left and right, it means the limit doesn't exist etc )

In floating point, 0*∞ is NaN (not a number), which acts much like bottom in wheel arithmetic.

@gasun1274

Жыл бұрын

and what would be the top? 😜

@insertusernameherepls

Жыл бұрын

Its not *a* number

@IsomerSoma

Жыл бұрын

In mathematics it isn't a number either.

@AlbertTheGamer-gk7sn

6 ай бұрын

Aaaah, good ol' sodium nitrogen, enough to splash a bit of chemistry with math.

I would disagree with this I think 0*infinity has an infinite number of solutions between 0 and infinity (exclusive of 0 and infinity) (here x is any non 0, non infinity number) x/0 = infinity (there are a couple formulas which can sort of prove this- for example in the formula for number of reflections, if theta = 0, that is, mirrors are parallel, you get infinite images as the ans) now rearranging the above equation, we get: infinity * 0 = x

@insertusernameherepls

Жыл бұрын

*yes*

Multiplication is just fast addition so 0+0+0+0+0+0+0+0+0+0 for infinity is just 0 so 0*infinity is 0.

I was thinking of 1 since x approaches to infinity as 1/x approaches 0,might have been a nice way to put it though it still feels weird

Or is 0 EQUAL TO Infinity?

@wackyanimations3326

Жыл бұрын

at that point it’s childish. that would legitimately be a statement I’d make in 4th grade trying to be smart.

the answer is 0. Because logically nothing could come out from nothing, so no matter how many ♾times you try to make something to come out from nothing, there's still nothing to be multiplied in the first place, just repeated the idea of nothingness

In measure and integration theory a function whose constant value is ∞ on a set of measure 0 has integral 0, and a function whose ocnstant value is 0 on a set of measure infinity has integral 0. Thus in this ocntenxt it is reasonable to define 0 ∞ = 0.

0 × ∞ 1. 0 + 0 + 0... 2. Infinitys added 0 times?!

If I have absolute 0, and not something approaching to 0 times infinity, is it 0? Because that's what I said in my HW in calc. The question was find the limit of x*[1/x]. [1/x] is the floor function of 1/x

@dylanboji2817

Жыл бұрын

p

@foopfoop4323

Жыл бұрын

@@dylanboji2817 ??

0⋅∞=undefined

Dude it common definition that repetitive addition of same number in itself is multiplication so we easily say that adding infinite 0 to 0 =0

if infinity is (any number)/0 and if we multiply it with 0, we get (any number)

Consider 1/0 = inf and 1/inf = 0. 0*inf is just 1*inf/inf = inf/inf by replacing the 0, or 0*inf = 0*1/0 = 0/0 by replacing the inf. Both cases are indeterminate, thus why 0*inf is also indeterminate

Indeterminate doesent mean 'doesent exist in any way' it means 'the value you want'

but 0 infinities or infinite zeros is 0 please someone correct me if im wrong

a number that is base10 all 3s, like: "...3333333333" is an "infinite" number. A string of 4s "...4444444" is also an infinite number. \infty isn't a specific value. A = 3 + 10*A = 3 + 30 + 300 + 3000 + .... // "....3333" B = 4 + 10*B = 4 + 40 + 400 + 4000 + ... // ".....44444" solve them for values: (1-10)*A = 3 A = 3/(-9) = -1/3 (1-10)B = 4 B = 4/(-9) = -4/9

Let's consider this function f(x) = 1/x The limit of this function as x approaches 0 would be either +∞ (if approaching from the right) or -∞ (if approaching from the left). So for the sake of simplicity we can say that 1 ÷ 0 = +∞ or 1 ÷ 0 = -∞. Now algebra tells us that if a/b = c then a = b × c or b = a/c. Taking this principle to the function f(x) we get *1 = 0 × +∞* or *1 = 0 × -∞* But this implies that +∞ = -∞ which is false as far as algebra is concerned. Now replace 1 with any positive integer _k_ so we get f(x) = k/x. The limit of f(x) as x→0 will still be either +∞ or -∞, but now we get this situation where this becomes *k = 0 × +∞* or *k = 0 × -∞* So 0 × ±∞ can mean 2, 3, 4, 5..... And that's why 0 × ∞ is indeterminate

@insertusernameherepls

Жыл бұрын

T-T so close

couldn't you do an induction on 0 * n = 0 to show 0 * infinity = 0? i think infinity * x = infinity for all x =/= 0.

@edsangha3724

Жыл бұрын

but having the exception for x*infinity = infinity unless x=0 contradicts x*0=0 so there would have to be an exception for ifinity as x

@brandonklein1

Жыл бұрын

Because infinity isn't a real number.

Define a as a different number of 0 0 × ∞ = 0 (a+a+a+a+a...) = 0×a + 0×a + 0×a + 0×a... = 0

0 x ∞ should be equal to 0, when we multiply a with b what we are doing is adding b times a, eg: 2x3= 2 + 2 + 2, so by this logic 0 x ∞ will be 0 + 0 + 0 + 0 + 0 + 0 + ..... which in the end is equal to 0

it makes sense that its limits would tend to either 0 or infinity, because that's kinda the range of answers you could get with 0 * ∞ looking at it from the idea that n / ∞ always tends to 0, multiplying both sides by ∞ leads to n = 0 * ∞ regardless of the horrendous mathematical rules i probably broke, this uncertainty is kinda by nature. when we say 0 * ∞ is indeterminate or undefined, this is because it could be whatever you want to define it as

@kilian8250

Жыл бұрын

It could also tend to anything else. For example the function x*(5/x), as x->0 x->0 but 5/x->∞, but x*(5/x)->5.

This is a little different from what everyone is saying, but I've always thought it was -1. We know that the x and y axis on a coordinate plane are perpendicular, and we know that if two lines are perpendicular, the product of the slopes is -1. The slope of the x-axis is 0 and the slope of the y-axis is infinity. This is because we are dividing by zero, so we end up with infinity. So 0*infinity = -1.

infinity * 0 = 0 + 0 + 0 + 0 .... so it's zero 0 * infinity: what if we take infinity and but 0 of them in a box? we get 0 so 0(infinity) has to be 0

⅒ = 0.1 ¹⁄₁₀₀ = 0.01 ¹⁄₁₀₀₀ = 0.001 ¹⁄₁₀₀₀₀ = 0.0001 As the denominator gets larger the answer gets smaller. So if the denominator gets larger to the highest point, the answer should get to the smallest point possible. ¹/ ͚ = 0 ∞ × 0 can be equal to 1. But this can be true to any numenator between -∞ and ∞. Imo -∞ ∞ So I think this can be any real number. If the above explaination is not clear. Imagine this. It takes you 1 minute to eat a slice if pizza. 🍕 It does not matter how large the size of it is. It can be ½, ⅓, ⅒ or anything but it takes exactly 1 minute for you to eat each of these slices. Now how much time will it take if you eat ½ of the pizza at a time? 2 minutes. If you eat ⅒ of the pizza at a time you will have to eat 10 slices of pizzas and it will take you 10 minutes to end the pizza 🍕 Now if you eat ¹/₀ At a time, that means you eating nothing out of pizza at a time. How long it will take you to end the pizza. As you are not literally eating it, it will take you ∞ amount of minutes to end it. So ¹/₀ = ∞ ∞•0 = 1. Again Numerator can be any number. You can have any amount of pizza 🍕🍕 🍕 So ∞•0 can be any real *_number_*

@mistershaf9648

3 ай бұрын

Kinda like 0/0. Anything*0=0, so 0/0=anything.

Its 0 because when you are multiplying things like 3x2 it is 3+3 3x3 is 3+3+3 3x4 is 3+3+3+3 so 0 x infinity is 0+0+0+0+0+0+0+0+0..... and so on which equals 0

I think it is as follows: 0•∞= 0↓1+0↓2+0↓n = 0 where n=∞ and ↓ means subscript. As 0 is the additive identity. ∞•0= _ = 0. As multiplication is repeated addition, a number added to itself 0 times is nothing and nothing=0. Therefore: 0•∞ = ∞•0 = 0.

Any infinity is unreachable and we'd go to some other dimension in reality where the thing will get observed, because if it won't, then the beginning of calculation wasn't even there in the first place. So here's non-zero aligned with non-infinity. Choose one to beat the other, this is that extra dimension. If you choose infinity, then it's, well, what infinitely produces this smth else. If you choose zero, then, well, here we are producing this smth else from this very beginning. In other words, the derivative is the opposite of the boundary.

Anything times zero is zero as well

Oh I really feel only 4 options are there: 1) 1 2) 0 3) infinity 4) every number

you can reword things like "1*2" as 1 2 times, which is 1+1, so 2 0*inf = 0 inf times, which is 0+0+0... = 0. inf 0 times = _ = 0

Taking the natural log of (0 x infty), I get -infty + infty, which may or may not add up to zero. I learned long ago that infty cannot be treated as a number, so I guess the product really is undefined.

I believe 0 times infinity is undefined, actually, i could think these things: 1. We have an infinite amount of numbers that could turn it into a valid result, as anything finite over infinity is equal 0. Take a look on some examples: 1/infinity = 0 4/infinity = 0 296/infinity = 0 10183552/infinity = 0 (2^82589933)/infinity = 0 As we have this set, then 0 times infinity is undefined as to be defined, we need only 1 kind of correct result, but we have an endless amount of results that makes 0 times infinity have a result. So as my exit, 0 * infinity = undefined (This is just my opinion, as it can be agreed of disagreed)

0 * infinity is 0, because infinite 0s is just 0. Like, if you add 0 by 0, it is 0. Like, take this math problem for example. No matter what, it will never be infinite. Let’s see. TU 00 + 00 --- 00 + 00 --- 00 Exactly. In that case, it would also be: TU 00 x inf --- 00

inf as representing a number, 0*inf=0 as a a concept of 'infinite'.... well 0 * inf you have an infinite number of zeros. if this is important, this is as simple as the equasion gets without some form of infinity notation for the zeros...

It is -1 Adjacent slopes multiply each other to -1 Take the lines y=2x and y=-0.5x This lines are adjacent because their slopes multiply each other to -1 (2*(-0.5)=-1). If the slope of the x axis is 0 and the slope of the y axis is infinity, and we know that their adjacent to each other than by that logic 0* infinity = -1

For those who think it is 0; in order to terminate the multiplication, you need two or more ''limited'' inputs or else it is an endless computation that won't give any product. Similar loops can be observed in coding as well. If you don't close the loop with a predetermined value, it won't end. You cannot tell the result of a calculation which is not complete to begin with. By that logic we could say ''all humans are dead right now since they will die eventually anyway''. Does it make any sense? Of course not. The process is still running which is the reason why the end result can only be ''predicted'' until it actually ends. Because this is all theoretical domain, people use the most convenient interpretation for practical purposes so that the task at hand can be approached reasonably.

I think if we talk about limits, the two different outcome is because x aproach infinity "slower" than x squared. But we can't get any closer than that

if you use infinity as a number, you can say that 0 * infinity = x meaning that 2 * (0 * infinity) = 2x which can also be wrote as (2 * 0) * infinity = 2x making 0 * infinity = 2x proving that x = 2x in normal algebra, the only number that works for this is 0, so the answer is 0

@coolvideoskhatamovs4264

Жыл бұрын

infinity works here too

Why can't we just make infinity calculatable by giving it stages like ∞¹ ∞²... (not infinity over 1 or 2 but rather infinity stage 1, stage 2.)? This means stage 2 infinity is half much as stage 4 infinity even though they're both infinite. What i mean is, The amount of infinite numbers Between 0 and 2, must be greater (exactly 2x bigger.) than the ammount of infinite numbers between 0 and 1. So the infinity between 0 and 1 is ∞¹ And the infinity between 0 and 2 is ∞². (Infinity between 0 and 258 is ∞²⁵⁸, between 0 and 9642 is ∞⁹⁶⁴²...) This way you could calculate with infinity ( ∞³ + ∞⁶ = ∞⁹ or ∞⁵ × 5 = ∞²⁵). You could also prove that 0.9999999... isn't 1, but rather 1 - (1 × 10^[-∞]) as it's supposed to be. The original formula for proving that 0.999 is 1: e = 0.999... e × 10 = 10E = 9.999... 10e - 1 e = 9e = 9 9e ÷ 9 = 1e = 1 e = 1 The same formula with calculatable infinity: e = 0.999... e × 10 = 10e = 0.999...¹⁰ 10e - 1e = 9e = 0.999...⁹ 9e ÷ 9 = 1e = 0.999...¹ e = 0.999

@Fifasher2K

Жыл бұрын

But what is your answer?

@Mrg_0

Жыл бұрын

​​​@@Fifasher2K on the 0 × ∞? İts 0 × ∞ as in no (zero) infinites. So ∞⁰ or just 0. However since infinity isn't a number, I think it would be more logical to see 0 × ∞ as in infinite ammount of zero's (∞ × 0). So there is an infinity in the answer, but its also 0 at the same time. The answer is infinite long, but not infinitely big. So my answer is ∞⁰ or rather 0,000...

5:20 ooh ooh Triforce

What happens when an unstoppable force meets an immovable object?

0+0+0+0+... = 0 inf plus itself 0 times would presumably equal zero because there are no actually infinities. Therefore 0 * inf = 0 Or if you want to nitpick about whether inf is a number, just use omega.

I think zero times infinity is zero but infinity times zero is infinity.

@YouTube_username_not_found

9 ай бұрын

I like 😃your answer because it ignores the principles we already know 😎. We are familiar with multiplication being commutative for real numbers but nothing guarantees it would be the case when ∞ gets added (as an example, matrix multiplication is not commutative). This does not mean your answer is correct😐. In order to find the correct answer we need to do a lot of steps. It is not that easy (which I have no grasp about😅). Nevertheless you bring a very crucial point 😃 to this question that can help to solve it.

it's 0 because if you have none of anything, you don't have that thing. no infinity.

I think, all number that multiply with 0 equal 0. So 0 × ∞ = 0.

Elon Musk gave me infinite bucks exactly zero times, does this mean I’m not broke anymore??!

In ordinal and cardinal numbers, as set as set theory, 0*infinity is just 0. This is because the Cartesian product between the empty set and any set is the empty set.

I think it's 0 based on the definition of multiplication x*y = (x + x + ... + x) y times 0 * infinity = (0 + 0 + 0...) infinite times, which would equal 0

There's another element at play here. If we define infinite like this ∑[i=0, n→∞](x+1/x)i and we define zero with this: x+1−∑[i=0, n→∞] (x/x+1)i X is the same on both sides, so the answer would be 1

0 * Infinity = 1. It’s as simple as cos*tan = sin cos(x) * tan(x) = sin(x) is a true statement. Since tan(90) = Infinity, we’ll use x = 90 to get cos(90) = 0 and sin(90) = 1. Since cos(x) * tan(x) = sin(x), 0 * Infinity = 1.

Nothing multiplied by infinity is still nothing, it’s just an infinite amount of nothing. 0 x 3 is nothing, but larger. A bigger amount of nothing. Since it’s still nothing, it still equals 0.

Zero times infinity is 0+0+0+...+0 which is 0. And infinity time zero is just zero because you add zero infinities together. 1/x will never be an actual 0, no matter how big x is, so when you multiply it by something like x², you won't get 0. Instead of finding the limit of these functions, find the limit of y = 0 × x.

0 * infinity is just 0 added to itself an infinite number of times and if looked at the other perspective, infinity is just being added to itself 0 times so we can conclude 0 * infinity = 0

@insertusernameherepls

Жыл бұрын

Ye but infinity is not your average number

Circle * Triangle = 362-gon

it equals a positive number with limited value a / 0 (where a is positive) approaches infinity a / infinity (where a is positive) approaches zero therefore infinity * zero = a

2:49 The idea that infinity is somehow different because "it's an idea, not a number" overlooks the fact that numbers themselves are just ideas! Everyone tries to struggle with the *essence* of mathematical objects, but mathematical objects have no essence. What is important is *structure* . Once you understand this, you understand why questions such as "What is infinity?", or "Is infinity a number?" are questions mathematicians don't think are very useful.

@Killua2001

Жыл бұрын

On that note, hasn't there been some recent movement on the Continuum Hypothesis suggesting "it's not all that useful a question in its most popular form"? I remember reading a Quanta Magazine article on it a while back.

@DarinBrownSJDCMath

Жыл бұрын

@@Killua2001 CH is really only important in a few very esoteric areas of math. For example, I think I remember it mentioned maybe twice in classes outside of set theory during my entire graduate career. I once asked a prof about it, and he said something like, "If you find out your problem depends on CH, find another problem to work on." I think the attitude is starting to shift in the way it did for non-Euclidean geometries 200 years ago. No one is unsettled by hyperbolic or elliptic geometry today. And no one is asking "Is the parallel postulate true or false?" The difference of course is that mathematicians have built their entire edifice on set theory (ZFC or NBG), but the same could have been said of geometry well into the 18th century. Only time will tell.

As an accountant I can answer: What ever you want it to be. 😉

What the point of using calculus if you're using it wrong. You don't need to take some function that limits to zero. For the case of 0 * f(x) where lim f(x) = Inf, limit will be 0 no matter what. And when using different equations to get 0 * Inf. That's indeterminate form, you don't just take it and use it to prove some point, but use L’Hopital rule and there is no longer limit of 0 * Inf.

I tried using two limits at the same time, one with x -> 0 and other with y -> ♾ to compute x * y, but with the switch of order of which limit is evaluated first I got a different answer... For example lim x -> 0 { lim y-> ♾ (x * y) } can be evaluated as lim x -> 0 { ♾ }, as ♾*x = ♾. But by doing this we eliminate the 'x' from the question thus no matter what x approaches, the answer should be ♾. In contradiction, if I apply lim y -> ♾ { lim x -> 0 (x * y) }, it's pretty obvious that x * y -> 0 as x -> 0. Thus the expression reduces to lim x -> ♾ { 0 }. And yet again, by eliminating y no matter what y approaches, the answer should be 0. Also, lim x -> 0 {1/x) = ♾ and lim x -> ♾ {1/x} = 0 so using limits, 0 * ♾ should be lim x -> 0 { x * 1/x} or lim x -> ♾ {x * 1/x} which both equal 1. That's weird how we use limits to define ♾ (1/x) but now using limits to solve 0 * ♾ makes it a mysterious question with no answer... Also, I agree with people in the comments mentioning 0 * ♾ as 0 groups of ♾ or ♾ groups of 0 which is 0...

When working with stuff like this I think it should be stated whether we want just the simple straight-up value or the limit, since in calculus 0 isn't really zero but a very small value

@theimmux3034

Жыл бұрын

calc 0 is a 0. The limit as x approaches any value or infinity of 0*f(x) is 0 for all f(x)