🎓Become a Math Master With My Intro To Proofs Course! www.udemy.com/course/prove-it-like-a-mathematician/?referralCode=D4A14680C629BCC9D84C

@MemeAnt

8 ай бұрын

First (I am part of the problem)

@Elijah629

8 ай бұрын

second second days

@BeansBem

8 ай бұрын

uh... nooooooo....

@brianlam4101

8 ай бұрын

Just leave it to undefined for god sake

@MemeAnt

8 ай бұрын

@@brianlam4101 that’s not funny though

dont divide by zero at home kids

@BriTheMathGuy

3 жыл бұрын

*Adult supervision required*

@electronichaircut8801

3 жыл бұрын

Do it outside

@aaronrashid2075

3 жыл бұрын

Batteries not included

@Sovic91

3 жыл бұрын

@@electronichaircut8801 And make sure to safely contain the resulting black hole

@potato8910

3 жыл бұрын

@@Sovic91 is that what Happens when I divide 0?

As James Tanton likes to say: We can do anything in math. We just have to live with the consequences.

@BriTheMathGuy

3 жыл бұрын

I like it!

@angelmendez-rivera351

3 жыл бұрын

Pretty accurate, frankly

@customan10

3 жыл бұрын

Member tanton?

@johnjordan3552

3 жыл бұрын

Pros: Innovation in engineering and sciences Cons: Harder exams Conclusion: Isn't worth it

@mathnerd97

3 жыл бұрын

But if we can do anything, doesn't that include avoiding the consequences?

I had a math professor who was careful to say, "For the purposes of THIS CLASS," ... such and so would not or could not be done. That left the door open for me to really appreciate this!

The "nullity" reminds me of NaN ("not-a-number") in programming. According to standard floating point arithmetic, the result of any operation where NaN is one of the operands is always NaN. The difference there though is that 0 / 0 = NaN, but 1 / 0 = Infinity

@reignellwalker9755

8 ай бұрын

God bless you all and Jesus loves you so much, that is why he died for you. By putting your faith in him as lord and saviour you will be saved.

@wifegrant

8 ай бұрын

That's kinda built into the code package you use. With quantum computing I suspect this to become way more complicated. Pretty sure with MATHLAB you will have different outcomes more robust than a simple Java math class.

@yosefmacgruber1920

6 ай бұрын

NA and ERR have a way of propagating through spreadsheets.

@billiboi122

5 ай бұрын

@@reignellwalker9755as much as people who preach their religion annoy me, i must admit that someone with a roblox pfp praising someone for talking about coding for seemingly no reason gives off a powerful aura

@12carbon

4 ай бұрын

​@@reignellwalker9755Saved from what?

"One divided by 0 is undefined." Me, a blissfully innocent middle schooler: "Why don't we just define it?"

@jpase

3 жыл бұрын

(1:0)

@tonylee1667

3 жыл бұрын

We can define it but then it would make ZFC inconsistent and every statement is true

@God-gi9iu

3 жыл бұрын

Eo

@God-gi9iu

3 жыл бұрын

Oo

@coolbeans5992

3 жыл бұрын

Ikr. I’m also a middle schooler

So basically, if you allow for division on zero, you have to give up some basic algebra rules

@BriTheMathGuy

3 жыл бұрын

True!

@TheLethalDomain

3 жыл бұрын

I feel like the rules remain, except the nullification factor, well... nullifies whatever it's a part of. You only "lose" rules in the sense that those rules do not apply to this special operator with a specific definition. The rules "lost" are the rules that exist being submitted to nullification. It's literally no different than saying 1 + 1 = 3 nul 1 instead of just 2. That's a logically factual statement with the additional statement without taking away from the rules. To me, it doesn't take away from anything, but rather adds a special case where the rules are bent only for that function while still applying anywhere else in the equation not attached to the nullification. To me it's no different than saying the square root of negative one equalling i breaks math. Yet after time it seems less and less of a strong argument against it.

@angelmendez-rivera351

3 жыл бұрын

Calling them "basic algebra rules" is misleading. Algebraic structures are defined by the axioms that we impose on them. On the real numbers, we impose the field axioms. With a wheel, we modify those field axioms slightly, making them more general, to accomodate for the intoduction of /0 and 0/0 as elements of the wheel. As such, the field axioms are special cases of the wheel axioms.

@TheLethalDomain

3 жыл бұрын

@@angelmendez-rivera351 Honestly, your comment gets to the point faster and in a way that's different given I am not familiar with wheel algebra. Very well said.

@angelmendez-rivera351

3 жыл бұрын

@@TheLethalDomain Well, you can also read the Wikipedia article on wheel theory. The Wikipedia article does a really decent job at explaining how does this all work, keeping it simple, but rigorous.

0:15 Wow, I didn't know Ant is such a strong word in math

So you mean we can't create a black hole dividing by zero. Fine, I'll go back to the blackboard.

Me in Algebra One: I like your funny words magic man

@cerulean22b69

3 жыл бұрын

And there's me in precalc thinking the same thing.

@goldenwarrior1186

3 жыл бұрын

@@cerulean22b69 same

@nicolastorres147

3 жыл бұрын

Me finishing my 3rd year as a math major: Interesting

@thewatermelonkid1337

3 жыл бұрын

i like your profile picture!!

@teamcons993

3 жыл бұрын

@@thewatermelonkid1337 Thank you!

I can’t tell being this is April 1st if this is a joke or not😂👏🏻

@BriTheMathGuy

3 жыл бұрын

Well yes but actually no

@SaiyaraLBS

3 жыл бұрын

@@BriTheMathGuy LMAOOOO

@angel-ig

3 жыл бұрын

@@randylejeune Conway's *

@Invictus___me

3 жыл бұрын

@@angel-ig I think that was a prank as well

@o_poky9359

3 жыл бұрын

@@BriTheMathGuy yesn't

This reminds me of stuff I learned in engineering. One was the delta function which is defined as infinity at a single point and 0 everywhere else. If you integrate over it you get 1. I mentally imagine it as a rectangle with 0 width and infinite height and area of 1. And you could multiple delta by constants to get other areas. We used it for theoretically perfect spikes. Calculus classes hated this. I remember another where when a function went to infinity, it could “wrap around the plane” to negative infinity or even to positive infinity. I think it had to do with finding stable points by wrapping them or something. It’s been so long that I don’t remember clearly anymore. But it sounds similar to mapping the plane to a sphere to make all infinite points touch. (And thanks reminding people infinity is a ranging concept and not an actual number.)

@cstockman3461

10 ай бұрын

The delta function does actually have a rigorous definition in terms of the concept known as distributions, or continuous linear functionals on the space of smooth functions with compact support.

@qcubic

8 ай бұрын

As a calculus student, I'm actually really intrigued

@reignellwalker9755

8 ай бұрын

God bless you all and Jesus loves you so much, that is why he died for you. By putting your faith in him as lord and saviour you will be saved.

@_kopcsi_

8 ай бұрын

that’s called abstraction. a*b=1, while a->0 and b->inf. but actually this is the essence of calculus/analysis: when we say that a continuous interval van be decomposed to infinitely many infinitesimal (0-like) intervals.

@MemesMcDreams

7 ай бұрын

Isn't a rectangle with 0 width and infinite height a line?

I always wanted to learn abstract algebra. Maybe this is a good excuse to order an abstract algebra book with my nullity dollars in my wallet.

@KRYMauL

3 жыл бұрын

First you need to understand Linear Algebra and that’s complicate af.

@anshumanagrawal346

3 жыл бұрын

You do realise that now you can use as much as money as you want and you'll still be left with what you have right noe

@kennyb3325

3 жыл бұрын

Eh, I cannot think of a reason you would *need* linear algebra in order to understand abstract algebra. Rings, groups, and fields should all make just about as much (or as little) sense either way. Speaking of fields, the problem with defining 1/0 is that you are probably going to lose your nice field properties by doing that...

@9WEAVER9

3 жыл бұрын

@@kennyb3325 Vector spaces and Vector Subspaces can be quite abstract Concepts that should be introduced in a course on linear algebra before one Endeavors into abstract algebra, at least in my experience

@kennyb3325

3 жыл бұрын

@@9WEAVER9 A first course in abstract algebra need not cover those things. Rings, fields, and groups are more familiar (since we can think of good examples like the integers, rational, or real numbers) and can serve as the entry point to abstract mathematical structures, perhaps better than vector spaces. Of course, one would want to be introduced to vector spaces before encountering modules.

I now realize just how mathematically accurate NaN actually is in the floating point standard. NaN for life!

@BriTheMathGuy

3 жыл бұрын

True! Thanks for watching!

@revimfadli4666

3 жыл бұрын

A professor of mine said that it was mostly designed by mathematicians instead of electronics engineers. He complained that it could've been faster to compute had it used twos complement instead

@fariesz6786

3 жыл бұрын

IEEE engineer 1: do you have an idea how to handle 0/0? IEEE engineer 2: NaN to speak of

@angelmendez-rivera351

3 жыл бұрын

But NaN does not actually work anything like 1/0 and 0/0 do in wheel theory.

@kazedcat

3 жыл бұрын

Angel Mendez-Rivera Floating point have two zero. +0 and -0 and they have a set of subnormals and NaN is also a set.

Funny, a few years ago, I pretty much had the same idea of defining 1/0 and I called it zeta. I just thought, well, we defined sqrt(-1) = i, what if we define 1/0=zeta. After playing around with it, I noticed 1/0=zeta -> 1/zeta=0 by algebra. I concluded I just made a complex sphere. Also x*zeta=zeta just like x*0=0. I came with the phrase "Zeta, the other zero on the other side" for a clickbait title if I ever gonna talk about this lol. Then I got stumped when I ask what about 0*zeta, which you also discussed. Interesting stuff. I didn't think of the nullity number though.

@andrewjacquot

Ай бұрын

Would be interesting to learn of more properties of zeta!

@Dexuz

4 күн бұрын

Have you talked about zeta yet?

I’m so glad you brought light to this, because I’ve been thinking about this concept the exact way you mentioned it, and I’m really happy that this concept is out there, being explained so masterfully yet simply.

Math is one of the few things that can make adults feel like children again

@BriTheMathGuy

3 жыл бұрын

😀

@dailysacrificedoublee

2 жыл бұрын

We’re all such nerds.

@Enderia2

Жыл бұрын

key word: can

@kneecapz7385

Жыл бұрын

@TurboGamer 0/0 is indeterminate since n•0=0

@GotSwissd

Жыл бұрын

@@Enderia2 key word: your mom

4:02 Problem solved. Right? Vsauce2 (Kevin): WRONG!

@dominicstewart-guido7598

3 жыл бұрын

Or is it...?

@anawesomepet

3 жыл бұрын

@@dominicstewart-guido7598 Look! Look! Look! There's still 1 way to get around this. . Idk how to do a Jake impression.

@duncanhw

3 жыл бұрын

because every good punchlines has a qualifier in parentheses.

@novaace2474

3 жыл бұрын

@@dominicstewart-guido7598 *vsauce music plays* Michal: I mean think about it...

@NicoPlayZ9002

8 ай бұрын

*vsauce music plays*

I've been puzzling over 1/0 for quite some time; it does feel like you should be able to treat it in a similar fashion to sqrt(-1) by creating a new axis of complex numbers, but I've struggled to imagine what such a function would graph. The idea of the "terminus" makes me think it should be treated more like the center point of a sphere. 1/X becomes the distance from the center, with 1/0 being the true center. 1/1 would then be the shell where "normal" numbers lie. I'm a philosopher, not a mathematician, so this might be a dumb way of looking at it. I don't know. Still, thanks for posting this; it was interesting.

@danc.5509

Жыл бұрын

Hello. I thought I'd like to comment that square root is just the inverse of a square. So X to the power of 2, is the square, the inverse is to the power of a half, or 1/2. The importance of odd and even numbers comes into play with a cube root, such as to the power of 1/3, and odd powers such as 1/5, 1/7 etcetera. This is because a negative squared is a negative multiplied by a negative which makes a positive. This is not the case for cubic functions (to the power of 1/3) or other odd root functions. ( Like to the power of 1/5, or 1/7 etc) The cube root of -2 is -1.259921. But the square root of -2 does not exist. This theoretical anomaly has perhaps been where the visualisation of things has led to the idea of black holes and negative particles, and string theory.

@realcreative3334

8 ай бұрын

@@danc.5509 the square root of -2 does exist, just not within the real numbers

@whimbur

7 ай бұрын

I'm not a philosopher or a mathematician, but it seems like pretty interesting idea. "j = 1/0" I can't think of any real world uses, but the same was said about negatives and square roots of negatives.

@otter502

7 ай бұрын

@danc.5509 Well is kinda depends First off if you limit yourself to the reals you can't solve sqrt(-4) but if you expand to allow complex numbers Then you get 2i i is defined as i =√(-1) It doesn't "exist" but using it you can solve for a lot of things and has some real world applications @whyme1698 While there are some ways to have x/0 not be undefined using a variable like "i" is because it can be used to make two different numbers equal each other which means that it can't exist (1/0 = j) Is because there are a lot of ways to mess with it So: (1/0) = j Assuming absolutely nothing about j: So then: 1 = 0j And because any number times 0 is 0 1 = 0 Which is a contradiction

@yosefmacgruber1920

6 ай бұрын

You can not just define your way out of 1/0, because division is the undoing of multiplying. Since most any number n * 0 is 0, we just do not know what the original number could have been. Higher-dimensional numbers (complex -> quaternions -> octonions) become more problematic with division, because there is just too many ways to get the same product.

i had no idea this was released today a year ago and that just makes this better

"...and if you divide by zero, you go to hell." Cit.

@BriTheMathGuy

3 жыл бұрын

I sure hope not!

@mr.rabbit5642

3 жыл бұрын

You go to the "bottom" of it. Hahalmao so funny

@fasebingterfe6354

3 жыл бұрын

guess i go to hell

@bobdull3148

3 жыл бұрын

@@BriTheMathGuy see ya in hell i guess. I'll make sure to bring a 6 pack and some hotdogs for the tasty hellgrill

Oh my gosh! Brian! You were my math professor last semester! Hope you’re doing well!

@BriTheMathGuy

3 жыл бұрын

Hey Reggie, I am! Hope you are too!!

@use2l

2 жыл бұрын

Brian Brain

@SolstitiumNatum

2 жыл бұрын

He just solved ÷0 as a mathematician. He's living the dream baby

@ketchuptakeshi

2 жыл бұрын

@@SolstitiumNatum he's living the 80's American Dream lol

@RDani223

2 жыл бұрын

it would be funny to see my math teacher have a popular yt channel

4:00 Problem solved, right?? Not quite. Me ragequitting the video

I like the approach of how everything equals everything else, its almost like it too the definition away and left everything undefined

Here's another way to put it: If you want to define a new set of numbers, you need to show that it's possible to start with already-defined numbers, go into the undefined set, and come back out the other side into already-defined numbers. If I gain 5 apples and lose 3 apples, I make a net profit of 2 apples. This holds true even if I went into debt because I lost 3 apples *before* I gained 5. This shows we can go into negative numbers and come back out, which means we can define the set of negative numbers. We know that the area of a triangle is bh/2. Knowing this, we can easily prove that if we have two isosceles right triangles, and we put them together as halves of a new isosceles right triangle, the new triangle has an area equal to the side length of the original triangles. If our original triangles had side lengths of 1, this shows we can go into irrational numbers (since the hypotenuses have lengths of sqrt(2)) and come back out with the rational number 1, which means we can define the set of irrational numbers. And though I forget the exact formulas involved, imaginary numbers were proven valid the same way. There was some known formula to solve a certain kind of polynomial, but it was found that if instead of just using the formula outright you worked through the *proof* of the formula, you would end up having to evaluate negative numbers under radical signs at some point in the process, even though you might start and end with real numbers. Conversely, the video demonstrates that the idea of "nullity" swallows numbers like a black hole from which there is no escape, since you have to "give up some rules of algebra" in order to use it. In other words, this new system is demonstrably incomplete and likely has no practical use.

@irrelevant_noob

3 жыл бұрын

i wouldn't call it "incomplete" just because it includes an "error state"...

@finnfinity9711

2 жыл бұрын

Why not invent a set of numbers then that become their "real" counterpart when multiplied by 0. Eg. 2÷0 =[Nullity sign]2 [Nullity sign]2 x 0 = 2

@nomic655

2 жыл бұрын

That's pretty much the best way to put it, and the reason why division by zero is impossible. Unlike other mathematical elements, you can't define it without breaking the laws that already exist. If assuming that giving up the rules that solidify 99.99% of Maths is worth to justify one insignificant operation, why even keep on playing with maths?

@nomic655

2 жыл бұрын

@Remix God In the real world you actually can divide a singular piece into more pieces. There's a whole scientific field that came out of that, known as Chemistry, but even if you want to go into something simpler, imagine a slice of bread. Now cut it to 4 pieces. You just divided 1 by 4 in the physical world. Just because the set of natural numbers doesn't allow that doesn't mean it doesn't exist. In that case, 1/1 is just 1. That also involves the concept that dividing anything by 1 gives you the same thing. If I have a cake and zero people on my birthday party, the only one left to eat it is me, and I will, that's a 1/1 in the physical world. A nullity, at least as described in the video, is an absorbing element. *That* doesn't exist in the physical world because, by physics laws, energy is not lost. It just becomes something different. Yet a nullity can absorb every other number it's given with any operation. 1/1 can't do that.

@riccardoboa742

2 жыл бұрын

@@finnfinity9711 I mean, I guess you could. But aren’t you still breaking some rules? [Nullity]2 * 0 = 2 You’re multiplying something by 0 and getting something out that isn’t 0.

4:58 Literally my facial expression when solving math problems 😂

@pandakekok7319

2 жыл бұрын

His face is when you think "wait, am I really solving this right or bullshitting myself?"

@youtubefire_5263

2 жыл бұрын

@@pandakekok7319 yes

i wont tell my teacher, im graduating

You could also map out quaternions, octonions, and so on to multidimensional donuts. Great video.

1:30 i'm officially using the word "outouts" instead of "outputs" forever now.

@jamieg2427

Жыл бұрын

i came here to say this, only to discover: i already had. 😮

@lynettemurray1331

Жыл бұрын

@@jamieg2427 lmao

@microwave856

5 ай бұрын

⁠@@jamieg2427its been another year do it again

I've just watched this video and I'm gonna subscribe straight away because that is mind blowing

@BriTheMathGuy

3 жыл бұрын

Thanks a ton!

When I was in college I studied projective geometry and homogenous Cartesian coordinates. So, (x,y) would be expressed as (x,y,1) or (2x,2y,2) etc.. We determined that that there was a single point at infinity in each direction of x/y. Further, all the points at infinity formed the line at infinity. The notation would be (x,y,0) for any particular point at infinity. In addition, using the General Projective Transformation, we could transform a point at infinity to become local, but losing a point previously local to become inaccessible. This was done by matrix cross products. For example, a simple addition nomogram, with three parallel lines, could become three concurrently intersecting lines, with the point at infinity now appearing as the common intersection. As the three lines approached the central point, the associated scales grew greater from both the positive and negative directions. As far as I know, the GPT is how the math behind computer graphics is handled. It allows for a single technique to be used for scaling, rotation, magnification, etc.. And the transformations can be stacked and reversed. But I've never seen this used to handle the points at infinity.

I've always been told by my math teachers (since the 90s) dividing by 0 results in "null set" not 0 technically but functionally it's 0. Thanks for explaining why!

@I_am_Raziel

7 ай бұрын

It is wrong. First of all, how do you devide by nothing? And second deviding by an infinitely small number != 0 will get you an infinitely big number (approaching infinity). So it cannot be 0.

"Can't have two definitions for one thing" Square root of all numbers being both negative and positive:

@jamieee472

3 жыл бұрын

I get your joke (don't whoosh me), but the square root is a function (which means only one output) defined to give only non-negative outputs for real inputs. It's when you try to solve x^2 = a that results in x=±√a where √a ≥0

@shinjiikari4199

3 жыл бұрын

No it is |x|

@h-Films

3 жыл бұрын

@@jamieee472 r/wooooshwith4osandnoh

@Shaper-bx9kb

3 жыл бұрын

@@shinjiikari4199 yeah, what changed?

@technoultimategaming2999

3 жыл бұрын

This kind of explains the quadratic formula. (-b ± sqrt(b^2 - 4ac))/2 Square root takes the positive and multiplies it by + and - making two answers. So square root on it's own doesn't have 2 answers, but ± does

I like that you come to the exactly same conclusions as I did when I first learned about the symbol i from complex numbers and had the idea to check what happens if we define a symbol standing for the division by zero.

Consider infinity to be like an "edge" instead. What happens when you cross it? (like in your Infinity +1 example). It wouldn't "absorb" it like you say - but rather the perspective moves beyond, into another "measure" of infinity. Using the stereographic projection point of view, it is like crossing into a different 2-dimensional plane, where if you were to stereographically project this new plane onto the initial plane, the sphere that it forms would have a point at zero which would map to *the same point* as the point at infinity/at 1 on the initial sphere. Imagine it stacked on top with the only intersection between the two spheres being the point which represents infinity on the first sphere and 0 on the second sphere. Then when we consider dividing by zero, we can understand it from a new point of view in that what we are actually doing in the process of dividing by zero is like "crossing the edge" and moving between different measures of infinity. IDK how useful this point of view is yet, but its another way of looking at it that I thought of. I've been mulling over an idea relating this to complex numbers/quaternions, where the additional measures of infinity are represented as a form of complex number.

After some thinking, I found this to be an interesting idea: 1/0 = 0^-1 There's probably some flaws, but here's my thought process: If you multiply each side by 0, you get 1/0 * 0 = 0^-1 * 0 Division and multiplication of 0 cancel out, and you're left with 1 = 0^-1 * 0 Every time you multiply a number by itself, its exponent increases by 1, so 1 = 0^0 And 0^0 = 1, therefore 1 = 1

why do you look so displeased whenever you're drawing something 😄

@Very-Uncorrect

3 жыл бұрын

"God I hate writing backwards, why do I do this to myself?"

Finally someone makes a video on something related to the Riemann Sphere, which isn't a lecture. Can I also request a video on looking at complex functions and transformations on the Riemann Sphere, because they're really mind-blowing and eye-opening. What functions correspond to reflexions across the 3 main axes of the sphere, and stuff like that. Thanks for this video!

Well, IEEE floating point numbers work a little bit like that. Except that they distinguish between +infinity and -infinity, but then there are also different representations for +0 and -0.

@weetabixharry

6 ай бұрын

The different binary representations of +0 and -0 are really just an implementation detail. They are two different ways of describing the same number in the sense that +0 == -0 is required to evaluate to true. But you're right about how all the indeterminate forms (0/0, 0*Inf, Inf/Inf and Inf-Inf) all evaluate to NaN ("not a number") in IEEE 754. And I think NaN shares several other properties with the "nullity" in the video (like NaN-NaN = NaN).

@lifthras11r

4 ай бұрын

​@@weetabixharry +0 and -0 were there because you still want to retain a sign even when the truncation caused the number to be zero. It can be even argued that they really represent infinitesimals in some sense. The actual implementation detail is that they are kinda aliased to the real zero, which was considered an acceptable tradeoff.

We can define 1/0 as another imaginary number, say "j", forming another complex plane and a complex 3d space. Multiplying by i rotates numbers 90 degrees counterclockwise around the j axis, and multiplying by j rotates around the i axis. We can create extra dimensions for more undefined numbers.

Actually on the playground I would say infinity times infinity, infinity to the infinite power, or if I was feeling really petty, infinity plus two

@BriTheMathGuy

3 жыл бұрын

You're so right!! Wish I had put that in the video instead!

@shauncook3405

3 жыл бұрын

The aleph series

@HOLDENPOPE

3 жыл бұрын

Anyone who says that is talking about transfinite numbers. AKA, they're smart without knowing it.

@kupa121

3 жыл бұрын

Yeah, but isn't ∞ × ∞ = ∞?

This is a similar line of reasoning that I used back in middle school, the teachers weren't convinced but I thought it was pretty intuitive.

@josephjoestar953

2 жыл бұрын

Yeah same here, since zero could go into any number forever without filling the gap. But it's more fun when you start to involve things middle schoolers wouldn't be able to figure out normally.

@AngelNearDestruction

Жыл бұрын

@@josephjoestar953 personally, I have always argued with my teachers that if we think of it algebraicly, that as long as we don't use imaginary numbers that division by zero is simply a conserved absolute value addition problem using an infinite series. If you were to graph a negative and positive infinite series with the same absolute value, they would be identical graphically except for which side of the graph they were on. If you think about this way, X + -1/0 is actually X - |1/0|. If we think about it this way, 1/0 is a smaller infinity than 2/0 and so on, but the negative counterparts conserve the value without being defined in the opposite direction. Similarly, an infinite series of zeros is still zeros so zero/zero would simply be zero. 0-D is just zero, 1-D is an infinite line, -1-D is also an infinite line, 2-D is an infinite flat grid, as is -2-D, so on so forth.

@seanb6478

Жыл бұрын

Teachers probably didn't know this type of math...too busy teaching Common core math which makes far LESS sense than anything.

@One.Zero.One101

9 ай бұрын

It introduces more problems than it solves, meaning it's useless.

@yosefmacgruber1920

6 ай бұрын

Be careful, dinosaurs destroyed their world when a dinosaur wrote 1/0 on its chalkboard. Then the asteroids crashed to the ground. According to a Far Side cartoon.

Very good but there’s still a problem. If 1 = infinity * 0, and we say that infinity * 0 = the nulity, then 1 = the nulity. If you divide 2/0, you get 2 = nulity. So if you substitute for the nulity, you get 1=2. You can’t really just get rid of some of the rules of algebra. Throughout all the proofs out there, I think it’s best to just keep it undefined. Maybe it will be defined one day, but it’s true definition must keep math consistent.

incredible video. super fascinating

BIG OUTOUTS :)

@BriTheMathGuy

3 жыл бұрын

😂 that’s what I get for trying to break rules

We focused so much on whether we COULD do it that we never stopped to think whether we SHOULD do it.

Sharing this to my teacher🏃‍♂️

For such a simple question I did not expect such a complicated answer

Makes sense honestly. Infinity is a quantity not a number, and if 0 has no sign it makes sense that infinity doesn't too

Very happy to give this video the 1000th and more than deserved like, This is a really interesting qubject

@BriTheMathGuy

3 жыл бұрын

Thanks so much!!

Wow, thanks! You really blew my brain this time! :D

@BriTheMathGuy

2 жыл бұрын

Glad to hear it!

I think it's quite interesting to look at x/0 as a unique set of numbers outside the reals such that 0 * (x/0) = 0 holds, but (x/0)/0 = x, and also is somehow logically consistent with all other known arithmetic properties of elementary operations. Also the only place I can think of right now in which every number is equivalent would be if we permitted x modulo 0 where the residue of x is 0 for all x; then consider that: mod(x, y) = x + y floor(x/y) for the residue class x (mod y), then the floored coefficient is floor(x/0). I haven't really looked into this idea of divide by 0 much, but now I kinda want to...

Turning Ian Malcolm's quote on its heels toward his own profession: The mathematicians were so preoccupied with whether or not they could they didn't stop to think if they should.

2:22, "You can't have 2 definitions for one thing". English: *has 430 definitions for the word "set"*

@manioqqqq

Жыл бұрын

Xd

@allstar4065

8 ай бұрын

Yea but numbers should never be contextual

There are few other ways to handle divisions by zero, and these are practical. 1) use replacement symbol (like with "i") and do the math; sometimes these entities cancel each other out or produce tangible results 2) conditional statements in programming languages is also a form of math. Sort of. "If something = divby0 then print something else" 3) in DSP fhere is a problem called "denormals". One way of handling them is to add some small offset to the computation.

@williamwilliam4944

9 ай бұрын

In the first case, this works in very specific cases with very specific rules. For example, the degree of the 0 polynomial is often denoted by -infinity, a formal symbol satisfying: -infinity + -infinity = -infinity For all natural numbers x (including 0), -infinity + x = -infinity etc We do not have general rules for multiplication involving -infinity.

Never gonna give you up!

Just like how we assigned a undefined number to the square root of -1, anything divided by zero could be _z_ for example.

@williamwilliam4944

9 ай бұрын

Not so simple. The problem is that division is multiplication of a multiplicative inverse. To say we can divide by 0 is to say that 0 has a multiplicative inverse. Hence, if _z_ = 1/0 and _z_ = 2/0, we get that 1/0 = 2/0 (equality is transitive) and hence (1/0) * 0 = (2/0) * 0, implying that 1 = 2, a clear contradiction. That is, _z_ * 0 would not be well defined.

I still see problems with this first since (like told in this video) you can sometimes make sense of terms like infinity - infinity specific to a function and can get normal numbers (but also +-infinity). That means the nullity can be equivelent to any number. second when you transform equations with variables you can sometimes get plain wrong results when not accounting for the case that the variable may be 0 when dividing through the variable

He looks so sad when writing stuff down, but so satisfied when he's done

The zeroth root of 1: °√1 = a, with "a" being every number, because every number to the power of zero is equals one: a^0 = 1 5^0 = 1 23^0 = 1 (-2897,3401)^0 = 1 °√1 = 5 °√1 = 23 °√1 = -2897,3401 And so: 5 = 23 = -2897,3401

@gabrielgabi543

Жыл бұрын

Lol

"Don't tell your teachers" Teachers that are watching this video: you have become the very thing you swore to destroy

The thing about -∞ = +∞ is that it actually has some physical significance. I'm referring to the absolute (Kelvin) temperature scale.

@angelmendez-rivera351

3 жыл бұрын

Well... yes, but actually, no. (I say that as a physicist)

@maxthexpfarmer3957

3 жыл бұрын

@@angelmendez-rivera351 Wait! I need to know more about this!

@angelmendez-rivera351

3 жыл бұрын

@@maxthexpfarmer3957 In statistical thermodynamics, we work with the quantities temperature (T) and entropy (S). One thing you probably have heard a lot is that we cannot reach absolute 0 for temperature. This is true,... but despite that, we can actually reach negative temperatures in Kelvin. The idea is that some physical systems have a highest energy U they can attain. This energy U is a function of the entropy S of the system. Entropy, energy, and temperature are related by the equation T = dU/dS. Now, if that physical system attains its maximum energy possible, what happens if you increase S even more? Then U obviously cannot keep increasing. It can only decrease from there. If S is increasing while S is increasing, then dU/dS 1. Because T = dU/dS is only an approximation. It is well-known today that at very high temperatures, statistical thermodynamics does not describe reality accurately. It is also likely that there exists a highest temperature attainable, the Planck temperature, and if that is accurate, then that means that there is no such a thing as infinite temperature, and that temperature could never loop around the way it is described here. Besides, in reality, entropy changes discretely anyway. Entropy is defined as S = k·ln(Ω), where Ω is the number of microstates corresponding to the macrostate of the system, and k is Boltzmann's constant. Ω is necessarily a positive integer, so it can only change from Ω to Ω + 1, there is no smaller possible change, making it discrete. So the smallest possible change in entropy is k·ln(1 + 1/Ω). However, we can approximately these discrete changes as continuous changes, because given how astronomically small k as a constant is, and given how even smaller 1/Ω is, these changes in entropy are so small, that we can approximate them with continuous changes, so using derivatives gives a remarkably accurate model for low temperatures. 2. Also, this idea of unsigned infinity does not correspond to physics because absolute zero is still unreachable, and thus the analogous of division by 0 is still not possible in it. So again, there is some very superficial similarity if you ignore the rigor, but otherwise, it is not really analogous.

@kadenhesse9777

3 жыл бұрын

​@@angelmendez-rivera351 I had no idea!!!!! Thank you for taking the time to let us know

@Yolwoocle

3 жыл бұрын

@Angel Mendez-Rivera your comment motivates me to continue persuing physics :)

In the largest number question I alwys threw them infinity raised to infinity power. BTW, Yes I took calculus. For my major of Meteorology I had to take one course past calc. I took differential Equations. BTW, I'm 76, worked for A.F. as a meteorologist for almost 36 years, retired in 2009.

One thing you lose in replacing positive and negative infinity with unsigned infinity is the differentiation between functions which blow up n the positive direction versus blow up in the negative direction. You’re basically replacing “becomes unboundedly positively large” with “becomes unbounded in some direction.” It’s useful to be able to, for example, have the notion that positive infinity is strictly greater than any finite number. Of course you can define singularities like in the video, but I suspect in most contexts it’s better to keep positive and negative infinity as separate concepts.

1:16 So this is probably why people think something divided by 0 is Infinity

We could define a constant that multiplies with 0 to produce 1. Such a number would be irrational, but actually is conceptually identical to how remainders work in integer division (remainder division actually can define a division by 0, as everything is simply dumped into the remainder; 1/0 = 0r1 = 0 + (1 * 1/0)), just extracted into a constant.

Moving the parentheses in that way so that 0 • ∞ = 1 would violate the associative property in this expression anyway since (2 • 0) • ∞ = 0 and 2 • (0 • ∞) = 1, (a • b) • c ≠ a • (b • c) But I suppose as long as we're at it, maybe we can treat multiplication like division in that order matters and it's not associative? I wonder if that works, like when we "pretend" that a square root of a negative number can exist or that parallel lines can intersect. Pretty cool

Great video!

@BriTheMathGuy

3 жыл бұрын

Glad you enjoyed it!

Really great video I'm French guy but I understood your video

@BriTheMathGuy

3 жыл бұрын

Glad you liked it! Thanks for watching!

you're under arrest for destroying the universe

When we normalize the divided number to be unsigned - then why not? Then when we have a physical limit to the result, again, it's pretty useful. The physical result will light all bits in our output register. So we can predict how the digital circuit would behave when we put zero somewhere as a short circuit. Or a software bug. So - considering some constraints - division by zero is pretty straight forward and simple. JS allows it and produces a result that can be used. It doesn't make sense in any given context, but in some it does.

I never tell my students they can’t divide by zero I always remind them of the idea of new number sets. Aside from wheel algebra there are also the hyper real number sets. Good job

@edomeindertsma6669

2 жыл бұрын

Can't divide by zero in the hyperreal number system either, but still cool.

@aawiggins314159

2 жыл бұрын

@@edomeindertsma6669 Technically no but very close to the real thing

@supC_

2 жыл бұрын

It is absolutely true that division by zero is undefined (impossible) on the field of real (and complex) numbers, which is the only field any high school or lower students will ever work with. In fact, tons of students get things confused because they don’t really understand that certain functions (especially trigonometric ones) have entirely different results based on what they’re defined in. I’ve seen a perfectly intelligent (probably too clever) kid disbelieve that 0.99…=1 because they heard about the hyperreals and said that 1>0.99…1>0.99… without really understanding how it actually works. I don’t even know if that statement is true in the hyperreals, but in the real numbers 0.99…=3/3=1. And indeed, anything else would cause problems.

@kyarumomochi5146

2 жыл бұрын

Because its immposible

Can you do this in math: yes, as long as you're being consistent. Should you: only if it's useful. Done.

4:57 the way I like to think about it doesn't involve infinities at all. You see? The interesting thing about the zero is it nullifies everything; it voids info from any numerical expression it gets multiplied with. So any R*0 would be 0. But inverting that, i.e., dvividing expression by 0, would yield that R, but we knew beforehand anything times 0 is zero. Whst does that mean? Any R is = any R. Which is the same point you mentioned. It isn't unique to zero as a number either. If you think about the zero as a relationship of 2 to 1 (as opposed to 1 to 1 relationship, i.e., a function) then that becomes clearer. If we have the functions (rather, the values themselves) x turned/mapped into x², and please let's be real for a second, you would not know which values you started with. That is what I mean by (losing information). Now instead of mapping values to x², map them to a constant.l, and try to find what you started with. The zero does that exact job. But instead of defaulting to a value of c, say the functions to map to is y=5, we default to a arithmetically neutral value.

Wow good😊

Thank you for your brilliant question and intelligible video about it. I had been asking myself this question in mid-November 2021 and finally found an answer that led to a new paradigm. I call it HyperMath, "Math 2.0" Math 20-21 (and 22 :) ), a contemporary math that "goes beyond" and unifies different branches of math in a single uniform vision. I share the same idea, that we should consider a space of numbers as a sphere (not a 2D-plane), so we treat "infinity" as a single point, just opposite to 0. "Plus inf" and "minus inf" differ just as path/direction to a single point ("infinity" itself IS really a single point, however there are many types of "infinities" in different "operator worlds"). Well, that answer is in short... and is... you can't divide a number by a number "zero", because THERE'S NO "number zero" in the "Multiplication World". What MW is? Consider a "product" as bijective mapping of (x,y)->z, where x,y,z are "numbers" (real positive numbers), z is a product (smth new "made from"/"based on" x and y) of multiplication. We can consider an equivalent mapping in MW. In a simple way, let's consider pairs (x,y), where y is "inverse/opposite in terms of multiplication" (reciprocal) to x and vice versa. Let's stay simpler and limit "number x" to a natural number (1,2,3..). Consider x as a natural number, and y as an inverse to it, so x*y=1. Members of our "Multiplication World" are grouped in pairs: (1, 1), (2, 1/2), (3, 1/3), ... Not that "1" is a special element. Call it as "self-applied"/"central" (stays the same during transformation)/"idempotent", so 1*1=1. It is just as "number zero" in a world of addition: 0+0=0 (and there are another ones in another "worlds"), by the way. Note that there's no "number 0" between members of MW: (1, 1), (2, 1/2), (3, 1/3), ..., (N, 1/N). "1/N" is no way 0, while N is a natural number. We can legally divide X to "1/N" and get X*N for any X,N in natural nums (MUL and DIV and opposite operations, so div(x,y) means mul(x,1/y)). But we can DEFINE a special element "INFTY", which is not a natural number, which means a "limit" of N. Then we must DEFINE its inverse as "1/INFTY" and represent it as "0" to match the pair (INFTY, 0). Then MW is extended by two mutually inverse items: (1, 1), (2, 1/2), (3, 1/3), ..., (N, 1/N), (INFTY, 0). These items are not "numbers" (natural or harmonic, e.g 1/N, numbers), I call them "pole". So they have a special meaning and special rules in multiplication world should be applied to them. This way, we DEFINE INFTY as inverse to 0, and 0 as inverse to INFTY. Simply put, we define 0*INFTY=1 (note that we define it just here. In a different place, we could define it differently). But how can we apply the pole to a number? We can define mul(x, ZERO) = ZERO (pole ZERO is a "killing" element, a very bizzare beast, breaking a bijective mapping mul(x,y)=z, so pole ZERO is different from "number", because a legal number keeps this bijection), mul(x, ZERO) = mul(x, 1/INFTY) = div(x, INFTY). This rule introduces UNCERTAINTY (just as shown in the video), which is "smth (that can be anything at once) in a range". We can invent "U(X)" is "anything" from "set X" ("everything at once"). Sometimes, the UNCERTAINTY is in range 0..1. Let's consider a graph of x^(1/100). When it comes to extreme (e.g. x^(1/1000), x^(1/100000), ...), then the graph goes close to a vertical segment (0,0)-(0,1). This is a sample of UNCERTAINTY(0..1). Another example of UNCERTAINTY is zero-vector. It is said, it has NO certain direction (or all directions at once). So, div(x, ZERO) = div(x, 1/INFTY) = mul(x, INFTY). But how we treat "x*INFTY"? The first approach is to treat it as UNCERTAINTY(0..INFTY), e.g. any number: x*INFTY = U. You can depict it as a vertical line x=y. So U/INFTY="any X"=U. The funny thing is that our "defined" rule "0*INFTY=1" gets a broader sense: "0*INFTY=U" (and not only "1"). The second approach is to define a "hyper-natural" (in terms of multiplication), that "goes beyond" the natural number, so there's a bijection between "x" and product of (x, INFTY) = x*INFTY or single-term "x*INFTY", so div("x*INFTY", INFTY) = x. And we don't have to give up some basic algebra rules, but invent extended ones. If we are lied that's impossible, just remember imaginary i. MUL( 5, i) = 5i. It's smth that is not a number (in sense of naturals), but it is defined. And hence... exists!

@andreybaluevsky4485

2 жыл бұрын

"vertical line y=x" shoud read a line x=const. More accurately: (x, y), x=const, y=any

@MappingRobloxAnimations

Жыл бұрын

I aint reading allat

@esajpsasipes2822

Жыл бұрын

I have some (groups) of questions: 1) You invented the concept of uncertainity (U). Is U also part of the multiplication world (bacause some things are equal to it, i'd figure it should be, but i could be wrong), and if so, is U also one of the "poles"? What can you pair with U in the inverse pairings? 2) In the addition world, i suppose that the diffirent pairs of inverse numbers would always be a number and their negative. Zero is self pairing. Now - what can you pair infinity and U with? Or do they not exist in the addition world? They probably should exist there, if they exist in the multiplication world...

Very interesting !

@BriTheMathGuy

3 жыл бұрын

Glad you thought so. Thanks for watching!

Personally, since 6th grade I have always defined division by zero as an absolute infinite series. What I mean is the rather than divding by simply zero, division by zero simply functions as a fraction where the value of the number is defined in absolute value and the sign of the numerator simply becomes a +/-. In standard algebra, there is no difference between X - 2, X - (2/1), and X + (-2/1). If we replace 1 with zero, the easiest way to fix the problem is to solve for the total numerator over zero, adjust the +/- in the equation to fit the numerator, and then divide that number by zero. Then, we end up with an infinite series where we have an infinite series is defined by the numerator. 1/0 and 2/0 are both infinity, but the numbers contained within 1/0 are half the value of 2/0. This is hard to conceptualize, but it is similar to defining a dimensional plane. 2-D is infinitely larger than 1-D, 0-D is finite 0, 3-D is infinitely larger than 2-D, and -1-D is equal in valie to 1-D but has a different, and is infinitely smaller than 0.. If we think of a dimensional plane as division by zero in an infinite space where we only use real numbers, this makes perfect sense. The only issue is using imaginary numbers, and if I knew calculus better I think I could define it better. In any case, whatever you divide by zero except for zero ends up as a value of infinity equivalent to the largest possible infinite series involving the root number. The direction really doesn't matter if you define it as an absolute value that conserves the numerators sign this way. I'm pretty sure this solves all the problems but idk

my first brithemathguy video

Thank you... Very informative and generous .. And yes i will not tell the prof or teacher.. 👍👍👍👍👍

@BriTheMathGuy

3 жыл бұрын

You bet! 🤫🤫

I think maths needs a solution/ definition for 1/0. This one sounds quite interesting. It would be nice to see some long existing problems solved by that

@rhubaruth

2 жыл бұрын

What problems for example?

@tehnoobleader7673

2 жыл бұрын

@@rhubaruth the amount of biscuits I have eaten in my life

@atharva2502

2 жыл бұрын

@@rhubaruth IDK but I heard somethings in physics are unsolvable like singularities, which maybe solved if we can divide by 0, though I have absolutely no idea because I don't know anything about it

@ninjaboy3232

2 жыл бұрын

@@atharva2502 Although you said you have no idea, I do think there is a significant point in your statement. I think its obvious through the study of calculus and real analysis that the idea of 0 is very closely linked to the idea of infinity. In that respect I could see a solution regarding infinities in physics (such as center of black holes ie. singularities) being related in some way to the idea of dividing by 0.

@Gutek8134

2 жыл бұрын

There is a tiiny wiiny clumsy detail we're forgetting here: 1/0 = INF 2/0 = INF 1/0=2/0 WTF? And, by the rules of expanding fractions: x/0 = x*k/0*k = x*k/0 From which: x = x*k This contradicts basics of math. So, no, Infinity isn't that good of a solution. Not in common algebra at least. If it was, why wasn't it implemented yet?

practically, i have to ask the follow-up question: what is the difference between this "nullity" and the concept of undefined? "nullity" is an overflow number meant to stop questions beyond our current understanding, but is that not the exact purpose of undefined? We have yet to define the term, so anything that interacts with said term becomes beyond our comprehension. With this logic in mind (if you can make sense of it), the conclusion of "use nullity" is just "undefined by a new name".

Actually we can divide anything by 0, but we won't get an end, so that means it's infinity, like this: 1 / 0 -0 1 8 = Infinity that never reaches nothing Another way is: 1 / 0 -Ind Inf Ind = Indeterminate Form So in both ways the answer is Undefined, because "we must agree that Answer × 0 is 1, and that cannot be true, because anything multiplied by 0 is 0."

I think people said to not divide with zero in order to make the final exams in 12th-13th grade easier. There is always a question where you have something like x+1/x and if 0 would be a possibility for that, than there would be a huge number of answers (I think, Im not that trained in maths).

Switches: 2:40

Or divide by 0^2. The problem is the 1/x function, but by using a 1/x^2 function you are assuring it only approaches infinity since negative numbers squared become positive.

1/0=undefined/infinity, since undefined is a concept that is used to represent an unmeasurable value, and infinity is used to define an unmeasurable value too, perhaps infinity=undefined.

Math is even more broken when you prove the sum of all the counting numbers equals -1/12

4:28 "Infinity + 1 is infinity!" Lol. At my school people would just keep going with "infinity + 2" (3, 4 wtc) followed by "2x infinity" (3x, 4x etc)) followed by "always 1 more than you" followed by "always 2x as much as you" (then 3, 4 etc.). The worst part is the incorrect grammar in those sentences. In German, they would say "Immer zweimal mehr wie du!", Which is like saying "always two times more as you"

@buglerplayz7497

8 ай бұрын

Infinity to the power of infinity

I like your faceexpression during writing on the whiteboard

Yes; that's why we have "calculus". since "infinity" is more of a "concept" rather than a "number". both positive infinity and/or negative infinity. That's why we have "L'Hopital's Rule", for example. And the Zeno's paradoxes.

I'm glad there is another Bri the Math Guy out there! Well, I'm not really a math guy as much as a science guy. So I guess you could call me Bri the Science Guy! That feels taken somehow...

Finally, someone understood the art of dividing by zero

You would also have to lose the something divided by itself is one, and the 0 divided by something is 0. So instead of 0/0 bing 1, because it is 0/itself, or 0/0 being 0 because the numerator is 0, we insteas say it is infinity, which as my teachers have said numerous times, is not a number, and when we take limits it is only approaching infinity. But since infinity is not actually a number, 0/0 cannot = infinity. So undefined still seems to work best to me.

For some reason I always thought couldn’t zero technically be defined as something like neutral infinity. It just sounds the most natural to me as to what you would call it.

There is a poetry to infinity in the Riemann sphere in that infinity has "arbitrary direction" just as 0 does.

I knew about stereographic projection (or, alternatively, one-point compactification) but this is the first time I've seen wheel theory explained. It seems like we preserve all the field axioms except the existence of inverses. Neat. At 6:55 Why are we squaring? x - x = 0x seems to cover all the cases.

The big issue I think would be the fact that if we tried to divide by 0 we would run into an issue with the relationship between 1/x and ln(x). Currently the derivative of ln(x) is 1/x. However, if you define division by 0 than the derivative of 1/x is 1/0. Therefore ln(x) and 1/0 would technically be the same thing, which obviously is not true. Is there a way around this?

5:19 I liked using this proof to “prove” to people that 1+1=3 by treating the ones like variables, and replacing them with 1.5, because with this logic, 1=1.5. The only thing I did differently was inside of using stereo graphic projection, I left the answer as +/- infinity

Nullity is “strange matter” of numbers

@angelmendez-rivera351

3 жыл бұрын

Huh?

@Marcelelias11

3 жыл бұрын

@@angelmendez-rivera351 Strange matter is a theoretical form of matter that converts any other type of matter it touches into itself. Imagine a gray goo scenario, only waay worse, since theoretically, if even one particle of strange matter touches something like a planet, it converts the entire thing into strange matter. Pretty freaky if you ask me.