I Found Out What Infinity Factorial Is 

No

Good point!

Except when they use it for calculation in quantum physics then it becomes valid application.

@@kazedcat bruh 😂

uhh math math, um zeta alpha pi tau stuff i understand 100% definitely uh i dont feel dumb at all right now

@@opalb9006 It would cost you exactly $0 not to write that comment

But apparently that spurious result is quite important to string theory.

@@simongross3122 Not just to string theory. And the result is not spurious; there are precise ways to justify it; none is (truly) elementary, unfortunately.

@@dlevi67 It is rubbish. There are ways to make any non-convergent series apparently equal anything. Still, if you want to believe it, I can't stop you.

@@simongross3122 It is not rubbish and it is - or can be made - rigorous. Not in the way (e.g.) the Numberphile video from a few years ago did, but Mathologer did a much better work (for example). Still, if you don't want to believe it can be made rigorous, I can't stop you. 😁 There is a theorem (Riemann's rearrangement theorem) that proves that a certain type of series can be made to converge to any value, but not "just any non-convergent series".

@@dlevi67 I wonder if Bri the Math Guy can settle this.

Did you ever hear the tragedy of Darth Plagueis the Bris?

I understood everything until whatever that dirichlet eta thing is

Damn y'all seriously assume all kids have the same mindset

@@Chadniger ever heard of a joke

Haha ^^

Oh it definitely lacks rigor :) Glad you enjoyed it anyway!

This uses the Reimann Zeta Function. Every result is gonna lack rigor. It's like saying 1+2+3+... = -1/12

@@georgestrvanger6878 :-)

Maths is enjoyable when you leave out the rigour.

@@Jehannum2000 as are most pursuits.

😅

Don't tell them about 2^2^x^2^x^1/pi as x approaches infinity.

*Infinity! = Infinity and that's it.* Really, now? Can you prove that this is true? You cannot. You would say that lim n! (n -> ♾) = ♾, but you are assuming lim n! (n -> ♾) and ♾! represent the same thing. You cannot prove that, you are just making an assumption. This is just as much a sleight of hand as the video itself. *This is basically some manipulation to try to assign an "alternative value" to something that should have been infinity, but it's not actual its actual value.* How do you know it is not its actual value? What determines the actual value of ♾!, then? I wish I had the self-control to refrain from ranting about how much I hate it when people pretend to be well-informed about a topic, only to very thoroughly demonstrate that they are not. Your comment reveals that what little knowledge you have on the subject comes entirely from reading people's comments about Numberphile's video, instead of having read any actual mathematical sources on the matter. And the dismissal is, as some would put it, "all talk, no bite." You have not appealed to a single mathematical concept or any formal theory or provided a single meaningful correction. Your deliberation boils down to "this is wrong because it is wrong." Meanwhile, there actually is a lot of work that shows that these results are indeed perfectly justified. These results are used in physics. But even beyond just talking about physics, it has plenty of meaning in various disciplines in pure mathematics. I would recommend that you do some reading on the theory of Banach limits.

Same to you!

Cool!

Aleph null factorial, more specifically.

@@isospectral3537 Lol aleph null factorial is actually a mindblowing concept because it is a weakly inaccessible cardinal so you can't really subtract from it and ever get a finite result. Nice.

@@farrankhawaja9856 You cannot subtract cardinals, period, so that is redundant.

I feel like this video was made to get people interested in math and the wierd things that can happen sometimes. yeah. for example every time there is an infinity symbol instead of a limit. so many hand-waving arguments, it hurt my brain

2pi is tau, its sqrt(tau)

@@oyungogdfrust4136 what's tau used for?

@@danielarnold9042 almost every equation you use 2pi in is a lot simpler with tau used instead of 2pi, for example the classic 2piR is just tauR with tau

@@oyungogdfrust4136 ok thanks

π^2 = 9.8(g)

I really appreciate your honest feedback. I'm always trying to improve my videos so I hope you will continue to provide constructive criticisms in the future. Thank you for watching!

@@BriTheMathGuy Thank you - and best wishes for the Holidays!

@@dlevi67 You as well! :)

Analytic continuation is enough of a disclaimer.

A good observation!

Well, ya. It's no different than saying 2 = 3 since 2*0 = 3*0. I'm fond of creativity in math, but not when it's presented as having any tendrils to reality. Simply put, if the answer is inconsistent with the prediction, you have made a mistake in the answer or in the prediction.

@kasuha , @Qermaq 1+2+3+4+... Is a *divergent* series. However there's ways of assigning numbers to divergent series, just like the Cauchy Principle Value is a way to assign a value to a divergent integral. If you assign the divergent sum a value based on the Ramanujan summation convention, you'll get -1/12. I'm considering to make a video about it next week if there's enough interest. I'm a fairly new RU-vidr!

@@NikeDattani I assigned names to the house plants. The ficus was assigned the name Larry. The fern was assigned Janet. But is there any VALUE to us in naming the house plants? Or tacking a number onto a divergent series?

@@Qermaq that's a very good point. However Ramanujan's sum is not completely arbitrary, there's a few different justifications for it. You don't get -1/13 with that sum and the Riemann zeta function, you get -1/12. The y-intercept for a certain plot related to that sum, has slope = -1/12, not infinity or +1/13 or something else. Furthermore it has its "value" when studying the Casimir effect!

@@NikeDattani I vaguely recall bprp did a few videos where he shows 1 + 2 + 3 + ... can take other values like -1/8 and -1/9. Can't find them at the moment. So your video would have to convince me not that -1/12 *can* be a value of the sum, but *should* be the value.

Glad you enjoyed it!

Yeah, since it's a weak convergence, you can basically get a number as big or small as you like as a result of those manipulations

Yes, there is a definite relationship between the two results. Both use Ramanujan's Theorem outside its specified domain.

Because it diverges, one considers the analytic continuation, where on 0 is regular. So when taking derivatives, the analytic continuation also is regular at 0.

That's the idea behind these operations, of course these series are divergent, but just as an experiment, the idea is treat them as convergent series, it makes no sense, and of course the result obtained is not the true result of these operations, that's why you can obtain -1/12 of the addition of all natural numbers. Addition which diverges and of course has no sense as there is no decimal neither negative number to obtain such result.

I think this is more of a "you converge because I said so" scenario.

this is basically trying to compute S by making S = S + S - S and say yo look at this S + S it s actually the log of the wallis product which is equal to ln(pi/2) so S = S + S - S = ln(pi/2) - S so 2S = ln(pi/2) so S = ln(pi/2)/2 the prank is that S was a serie adding and subtracting bigger and bigger quantities which is mathematically illegal

@@raphaelnej8387 It isn't mathematically illegal at all. Banach limits.

@@TheTruemanBoi Why should it matter that there is no decimal or negative quantity? This is a series, not an addition of finitely many elements. Did you know that you can have a series of infinitely many rational numbers that converge to π? According to your incorrect assumptions, that should be impossible.

I'm in 8 class n I'm still trying to understand these things 🤣

one way to analyse such inconsistencies is to locate the exact step where the value changes, in this case what is the transition step where the expression considered changes value from infinity to sqrt(2pi) . the first few steps have value infinity, the last few steps have value sqrt(2pi), so which step makes the transition possible? analysing possible mistakes at that step.

x^0 is definitely equal to 1 for any object represented by the symbol x :)

@@Lucaazade except infinity, infinity raised to zero is 'not-defined' and definitely it is not 1

also zero raised to zero is not 1

Not only that, but the most commonly accepted extension of the factorial is the Euler Gamma function, which lo! diverges at infinity...

@@dlevi67 the gamma function isn’t the analytic continuation of the factorial. It’s just one chosen generalization. Analytic continuations are unique for each function and the factorial isn’t continuous, let alone differentiable, let alone smooth, let alone analytic.

@@biblebot3947 Sorry - should have said extension - corrected; the gamma function can be analytically extended to the whole complex plane, but that is irrelevant here. (Love the autocorrect substituting a Belgian town for a Greek letter!)

🤯

🤔

Yes

But if you want some cool results that are not rigorous, in the way you just calculated zeta(0)=-1/2. Zeta(0) based on what you doing Mr. Bri is the sum 1+1+1+1.. So yeah you just proved that 1+1+1+1..=-1/2

1+1+1…=1+(1+1)+(1+1+1)… = 1+2+3…=-1/12 -1/12 = -1/2 12=2 6=1 10=5 1=2

It's a cool sum that deserves its own video!

@@NerdWithLaptop **casually rearranges divergent sum**

I laughed so hard at this, spot on summary :-)

HOW?

It certainly has that kind of feel to it!

@@BriTheMathGuy that most probably means you broke a lot of math rules to get to this solution. I'm not a math expert so I can't tell you where you were wrong.

@@BriTheMathGuy ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-5SFHhtoDXOY.html This shows up as the first video about this. You're the 5th misleading RU-vidr using the same calculation.

It's exactly like that, maybe worse

I think the video is in there somewhere 🤔

Thanks so much! 😄

We have perfectly defined pi, as in some magic paint shop you can ask for pi units of paint. The problem with pi is the same as five years old knowing some Mister. Pi but for rhe love of god aren't able to draw him well But it's true that pi has some cool things going on

The sum equals infinity. The Zeta function value of the sum equals -1/12.

Yeah I thought the same

Every time you deal with infinity be prepared for it to not behave as expected. Sometimes infinity just goes bonkers and boom your single sphere is now a pair of spheres.

⛸

and aleph zero is pretty much infinity I think.

🤯

He used analytical continuation aka i-know-what-it-is-but-anyway-let's-do-that

@@darksecret6050 i know, but the analytical continucated has differenet form so we cannot conclude C'(0) = ln(inf!)

You can also use the zeta function to show it, since zeta(-1) = -1/12. I think the sqrt(2 pi) is more related to the Stirling approximation for n factorial (it's the "constant" term).

How do you get from 1+2+3+4... To a geometric series? Honest question.

@@tomkerruish2982 ζ(-1) diverges. Its analytical continuation via Dirichlet's η is -1/12. Another interesting observation (which can be justified and is connected to Stirling's approximation) is that the Gaussian integral value between -∞ and +∞ is also √π...

Actually the exact same method is used for both!