Can you Divide by Zero?

[@SledgerFromTDS.]

Ahh yes the best math channel I've been watching each day is back I love your videos plz keep uploading.

[@dingalong14]

Informative and entertaining as always! Keep it up!

[@erik-ic3tp]

Glad to see you back Derrick Taylor.😊 I hope you’ll upload more often now you’ve moved and made your studio in order.🙂

[@TheTaylorSeries]

Assuming nobody else in my family receives life altering injuries during a pandemic where both my kids stay home, yes. :)

[@tmd9412]

can you repost this video but it's just 5 seconds of you saying "No", that would be amazing

[@TheTaylorSeries]

Hahaha. :) You know, I had considered making a cold open that was me saying 'no' and then cutting to the end. Was *THIS* close to doing it. :)

[@ibji]

One thing I would mention, is that infinity isn't a number, it's an idea. And you can't have a number or equation equal to an idea, that's not mathematics either.

[@RalphInRalphWorld]

Your videos are so inspirational! I really envy your students

[@Sordorack]

What a nicely made video, thank you for that treat. This reminds me of how 0^0 also has its problems as the usual rules of x^0=1 and 0^x=0 kinda dont mix nicely Tho i dont know how that is taken care of :o Do you by chance have covered that (admittedly rather short) topic, or do you plan to given the relative proximity of the topic? ^^'

[@TheTaylorSeries]

I may in the future cover the other problematic expressions. :)

[@Xnoob545]

7:39 Wait I'm thinking 1/4th. You divide a thing into 4 sections and take 1 of them 1/3rd. You divide a thing into three sections and take one of them 1/1st. You divide a thing into 1 section and take it. 1/0th. You divide a thing into 0 sections and take one of them. But wait, you can't, there's only 0 sections and 1 is more than zero Wait what about 5/4ths You divide a thing into 4 sections and try to take 4, bit you can't. So you divide an extra thing into 4 sections and take 1. Now back to 1/0 Ok so there's not enough sections of the thing, so take as much as you can and move onto the next thing 0+0 is 0 So you're still only at 0 of the 1 needed sections So you take another, and another, and wait a minute you'll never finish So infinity? Wait no, it can be proven that it can't be infinity either. So you just can't do it Wait what does it even mean to divide something into 0 sections Honestly, I have no idea Like with a 4th you take 4 sections With 1/1, you take a section, do the whole thing A section in 4ths is 0.25 of the thing A section in 1sts is 1 of the thing But zero sections Does that mean that it's just empty Or is it something else I have no idea

[@carrotmaster8521]

Ah desmos, i like desmos

[@TheTaylorSeries]

I like it the desmost.

[@fritzzz1372]

@@TheTaylorSeries haha😅

[@fritzzz1372]

@@TheTaylorSeries By the way nice Usage of the black hole es a zero!

[@Tiessie]

Really great video!

[@seb_5969]

Missed your viedeos

[@EpicMathTime]

Why did you stop making videos?

[@TheTaylorSeries]

I haven't stopped completely; I'm still around. But it's been very very hard on account of being a stay at home dad, so ... I hope to have part 2 of this published. Sorry. :(

[@someperson8815]

I like the animations. Very cool.

[@hisxmark]

What is the slope of the vector (0, a)? Ans: (a/0) What is the atan(a/0) Ans: +/- (pi)/2 What is 0/0? It is the slope of point (0, 0) So, if (a/0) can be an argument or a result, it must exist. And if atan(a/0) can have two solutions then what is wrong with =/- (inf)? Enquiring minds want to know!

[@TheTaylorSeries]

That vector has an undefined slope. :) We can say it's vertical, and be correct. But the notion of Slope, which works in so many other places, breaks down here. atan(a/0), as written, would be undefined. atan(infinity) is a bit more delicate; we do nail down pi/2 to atan(infinity), but there's logic going on under the hood that keeps us safe from the Insane Clowncar that is infinity. And the reason atan(infinity) has, when it's defined as a relation and not a function, have infinitely many solutions, that's due to tangent's periodicity. :) Great questions tho!

[@hisxmark]

@@TheTaylorSeries It is undefined only in real numbers. It is perfectly defined as a slope, but in any slope some information has been lost. At least one point is needed to determine which of an infinite number of possible slopes it actually is.

[@hisxmark]

@@TheTaylorSeries Strangely enough though, my calculator returns atan(x/0) returns the angle (pi)/2 radians. That would be the correct angle, would it not? And multiplying a complex number by (i) rotates the complex vector by (pi)/2 counterclockwise, and any real number is simply x + i0. So, in the case of the slope (x/0) X i = ix . Slopes can be scaled so that is where the indeterminacy kicks in.

[@notwithouttext]

what about wheel theory? it says infinity and negative infinity are the same thing, so instead of a number line it's a number wheel. then 1/0 can equal infinity just fine, but 0/0 is null. so 1/0 * 0 would equal 0/0, not 1. infinity - infinity is also 0/0, and many other things

[@johnwalker1058]

For a lesson like this, I think it could be helpful to offer a secondary explanation for why division by zero doesn't work by using a purely intuition-based approach. Dividing by zero doesn't work because it is self-contradictory. But the very reason why it is a self-contradictory concept is that it is basically a representation of the act of dividing by not dividing. To divide by nothing, which zero essentially is, is to be the same as not dividing at all. But how can one divide by not dividing? It is impossible for it is a contradiction. Likewise, having a "zeroth" fraction doesn't and can't work for similar reasons. Such a concept implies parts of nothing. But nothing doesn't have anything, and so there isn't anything to be broken into parts. You can't have a piece or part of nothing. Thus, a fraction with a zero denominator doesn't work. It is impossible for it is a contradiction. ---

[@Lopoi]

Great video.

[@Michael-cg7yz]

Nice starting animation. what's 0^^0 if 0/0 & 0^0 are indeterminate? Can we really say that 0^^0 is ind. as well? Also, I'm just passing complex numbers in my curriculum, onto derivatives and integrals next. You know what's coming, Mr. Taylor. Just imagine: i^^I adding one more thing, I derived some formulas for complex numbers: i^x=cos(pi*x/2)+isin(pi*x/2) or cosx+isinx = i^(2x/pi) from the equality i^0.5 = cos(pi/4)+isin(pi/4) wonder if I made any mistakes, but this SEEMS correct, and that's not even using the number e!

[@TheTaylorSeries]

Thanks! It took me a week to make. :) And, 0^^0 would probably end up at 'undefined' as well? But, for perhaps a different reason -- I don't know how to tetrate anything other than positive integers. That may be a definition that could be supplied, though! And ... yeah, i^^i is nightmare fuel :) I haven't mentally processed those equations, but a way to check would be to, and I don't mean this as a pun, check their taylor expansions. :)

[@Sordorack]

for the last part, i'd be careful to say that those are without using e, as cos(x)+i*sin(x)=e^(i*x) ;D

[@Michael-cg7yz]

@@Sordorack yeah, I've heard about the Euler's formula, but if we take i^0.5, and, actually, any i exponent it ends up being on the unit circle. From this follows the simple correlation between {i^a}, a going from 0 to 2 (as i^2 is -1) and the angle going from 0 to π, but my formulas don't use e, even if Euler's does. I'm sure someone knew about these formulas but I'm not sure.

[@Sordorack]

@Michael my comment wasn't meant to lessen your findings, im sorry if it seemed that way :o You're definitely right, just as much as you can use e^(i*x) to move on the complex unit circle, you can also use i^(x) or actually almost any complex number from the unit circle this way to traverse it (as their absolute is by definition 1 and just their angle changes) what i just wanted to say is that because of e^(i*π/2) = i it follows that e^(i*π/4) = (e^(i*π/2))^(1/2) = i^(1/2) Which is basically your found formula. So you were surely right when you found them :D Playing around with maths like this is very valuable, try not to lose that :D

[@Michael-cg7yz]

@@Sordorack oi no worries, i just wanted to explain myself. But i played with the idea of i^x because, frankly, I find math with the euler's number to be confusing for the time being...

[@saburousaitoh]

Our new mathematics are not difficult, but fundamental. You will be able to see many and many evidences: 2th Announcement on DBZC: The International Journal of Division by Zero Calculus: Dear the leading mathematicians and the related persons on the division by zero calculus: For our new journal on division by zero calculus, 1)Please kindly give me your ideas and wishes for the attached basic idea. 2)Please kindly recommend some suitable editorial members and please kindly forward this email with the attached one. 3)In order not to loss our valuable time, we would like to do our best. With some completion, we would like to push our publication more promptly: We have still enough time, however, in order not to loss our valuable time, I imagine for the first volume: Gather survey papers over 20-30 pages as follows: 1.Jan Aldert Bergstra: Computer and Division by Zero, and his theory 2.Wolfgang Daeumler: On Daeumler-Puha Horn Torus Model - 3.Hiroshi Okumura: Geometry and division by zero calculus 4.Saburou Saitoh: History of Division by zero and Division by Zero Calculus Furthermore, I would like to request to write their ideas and results on the division by zero Professors Sin-ei Takahasi, Wolfhard Hövel and José Manuel Rodríguez Caballero and Ravi P. Agarwal. Of course, the editors can submit their papers. I am already requesting to Wolfgang Daeumler symbolic Figures of our Journal that may be used in the covers of the Journal and in others. Please kindly do the above with enough time, however, we do not need to wait our pleasant works. For some prompt publication, I would like to gather the papers following your wishes, however, I would like to look the papers over all and their situations in order to publish our Journal with the publisher promptly. This will mean that we would like to do our best for the publication. Please kindly give me your kind suggestions and good ideas. With best regards, Sincerely yours, Saburou Saitoh 2021.2.26. __________________________________ Nature of the International Journal of Division by Zero Calculus: 1.Introduction. What is a Journal? Of course, the authors will wish to publish their results, promptly and widely, following their wishes. However, sometimes, they will wish to hear from some authorities for their results from the viewpoints of originality, rightness (correctness), and estimation. That is; they will wish to have some estimation for the papers. For the ideal publication procedure of a paper, for example, viXra:2010.0228 submitted on 2020-10-28 21:39:06, Division by Zero Calculus and Euclidean Geometry - Revolution in Euclidean Geometry we have to consider the refereeing procedure, seriously. For this point, how will be?: The appointed editorial member for a paper submitted can give the final decision with two referee’s recommendations for the paper. The publisher and the main editors (in some topics) will give the final decision officially for the publication with the three forms; one editorial member and two referees reports. This procedure, however, is just formal, in the usual many cases. 2.Manuscript form and submitting procedure. These may be given simply, by the publisher. No problem. 3 . Aim and Scope , Instructions to Authors, (the requests of the publisher) The topics in the journal may be identified as the division by zero calculus that is expanded to the whole fields of mathematical sciences. However, the contents may also be related to our serious problems: What is ZERO? What is Division by Zero, in some serious sense? The problems may be related to mathematical philosophy, long history and our culture. Papers and essays by related physicists, computer scientists, philosophers and others are well-comed. Also, some simple examples and evidences of the division by zero calculus may be published in one and two pages in the Short Notes. The spirit of the journal is: fundamental, beautiful and good impact to human beings. Love, passion and fairness are important in the journal. 3.Quality of papers: Many kinds of papers, variety, high quality papers and low quality papers are acceptable. For originality, correctness, quality and others, their responsibility may be considered: the authors 5, the appointed editor 4 and the journal 1 among 10, roughly. The appointed editor is presented by as the communicated member in the paper. 4.Frequency of the journal. In order to loss our valuable time, we do not fix Frequency of the journal. We publish first the paper soon after the official acceptance of the paper on line. With a reasonable set of the papers, the publisher will publish the journal with printed book form. 5.List of the editorial board members, (by the request of the publisher) Tentative, we are looking for the editorial members:

[@TheTaylorSeries]

wat

[@BrianBrecker]

Since any number * 0 =0 shouldn't 0/0 equal a range of any number?

[@TheTaylorSeries]

Alaso, no, that wouidn't follow.

[@ethanzhu8478]

Well, we know that 1/0 violates axioms of rings, but can we toss out/modify the set of ring axioms till division by zero makes sense?

[@TheTaylorSeries]

Oooooh, an abstract algebra question. :) So, the answer is ... not really? Say you want to try. Here's kind of what I see happening. You want division, but the thing you need to build first is multiplication, but the thing you need to build first is addition. So you take your set and your 'addition' style binary operator, and you start proving satisfaction of criteria for a group -- one of which is the additive identity element i+, which, for the reals, is 0. When you go to build multiplication, you have to show that you can get inverses. And, though I forget the process off the top of my head, if memory serves you can show that a * i+ = i+. When you get to multiplicative inverses -- division -- you end up with a gap, namely, division by the additive identity. I think if you start throwing out axioms, then you also start throwing out things like division, which defeats the project. But I may be wrong! I still have a suspicion that there'll be SOME structure out there for which this works, but everything seems to be to the contrary. Man, this would make a cool video. I'm gonna go write some stuff. Thank you for the insightful question. :)

[@dantebroggi3734]

@@TheTaylorSeries en.wikipedia.org/wiki/Wheel_theory is one example of how one can limit `0x=0` and `0x/0` instead of `x/0`. In particular, in a wheel `x/x = 1+0x/x` and the subset where `0x=0` is a ring.

[@fungoose2195]

k so whats with black holes....

[@TheTaylorSeries]

Oh, it's a sort of inside joke -- it looked like a 0, and there's a few memes around that suggest that dividing by zero punches a hole in reality or something equally silly. :)

[@fungoose2195]

@@TheTaylorSeries yeah in a high school physics class i was looking at gravity and the equation seemes to break at diatance zero. which makes black holes confusing and interesting to me. i assumed there was a connection to that.

[@EdwardNavu]

I've heard that you can multiply two non-zero numbers and get zero in the realm of Sedenion, i.e. you can actually divide by zero in that algebra. The catch? Sedenion is a kind of algebra with 15 kinds of imaginary numbers. It can't form integral domain. It can't form divisor ring. It doesn't feel commutativity, or associativity, or alternativity. And it absolutely will not stop!

[@TheTaylorSeries]

I still want someone to invent a 2048-ion, with 2047 orthogonal imaginary numbers. :(

[@bobloudly4733]

When you divide by 0 you don't put the numerator into any groups so the answer is there is 0 grouped and a remainder of numerator.

[@TheTaylorSeries]

So, you're using a model -- groups and such. That model sits on top of numbers, and when those numbers exist, the model works! But with this, one of the numbers doesn't exist -- the zeroth -- and I cover why in the video.

[@SlimThrull]

So, infinity = -infinity = 0. Problem solved! Wait, no, that didn't work well at all!

[@TheTaylorSeries]

hahaha. :)

[@TheHylianJuggalo]

Always was terrible at math. Subscribed for Doom modder. :P

[@tanhay72]

I L'hopital the next video is just as good.

[@TheTaylorSeries]

That is the best pun ever. :)

[@Graeme_Lastname]

My calc has no problem with 0/0.

[@dawnv3436]

Call it "divide into 0" and it becomes really obvious what the question is asking.

[@gabrielgabi543]

And the riman sfere

[@babykosh5415]

found you from 2B1B

[@Sooyush]

The contrast between animation and music is too wide. Classy to cheap generic music. Personally I'd switch off the bgm if I had an option

[@TheTaylorSeries]

That's fair. I admit that while I kinda like the chipper feel of the music, I understand, that it isn't your taste, and that's valid feedback. Thank you for sharing!

[@LethalChicken77]

I can because I'm built different

[@TheTaylorSeries]

f

[@drsquash2003]

Despite your proof. I can't agree. I just can't lol. 1/0 is infity. One day i will prove it

[@TheTaylorSeries]

When you do, remember to laugh maniacally and shake your fist at the air dramatically before you take over the world. :)