What comes after forever?

[@RandomAndgit]

Notes and corrections: I mispronounced the atom cesium at the very beginning of the video, pronouncing it 'Kasium' I said that Omega ^ Omega x Omega is the same as Omega^ Omega ^ Omega when that's actually very wrong. At 6:11 I used a coefficient with an ordinal when really ordinal multiplication is non-commutative so that could cause problems. There are several minor phrasing errors around that amounts of alephs and omegas when I'm saying how long to wait. I had the original idea for this video ages ago when watching a Vsauce about infinity and noticing that it went past many of the ordinals. (Go and watch that video if you haven't, by the way, it's quite a bit more comprehensive than this one.)

[@tomkerruish2982]

Well done! Subscribed! At 6:10, you momentarily forgot that ordinal multiplication is noncommutative.

[@RandomAndgit]

@@tomkerruish2982 Oh, right! Sorry. Thanks for pointing that out.

[@omarie5893]

​@@RandomAndgiti watched that "powersetting" video of infinity!

[@derekritch4360]

6:00 so far this sounds a lot like Vsause’s video

[@derekritch4360]

But worth a new subscriber

[@Gin2761]

I can only accept that these concepts were invented by two mathematicians arguing in the playground.

[@RandomAndgit]

Hilariously, there was actually a real event just like what you described called the big number duel. Mathematicians are just very clever children.

[@AbyssalTheDifficulty]

​@@RandomAndgitis sams number bigger than utter oblivion or not

[@WTIF2024]

⁠@@AbyssalTheDifficultyit’s not a serious number, it’s a joke between googologists

[@victoriamitchell413]

​@WTIF2024 Whoa stella, you're in this video?

[@deannaszmaj9806]

@@RandomAndgit°-°😮

[@karrpfen]

‘There’s this mountain of pure diamond. It takes an hour to climb it and an hour to go around it, and every hundred years a little bird comes and sharpens its beak on the diamond mountain. And when the entire mountain is chiseled away, the first second of eternity will have passed.’ You may think that’s a hell of a long time. Personally, I think that’s a hell of a bird. (From Doctor Who)

[@RandomAndgit]

Wow, I may need to watch doctor who.

[@guotyr2502]

What season tho ?

[@karrpfen]

@@guotyr2502 season 9

[@Rohit_Naga.]

I think that's actually from a story or poem called "the Shephard boy"

[@AlmostAstronaut]

the episode is called heaven sent from season 9 if you want to watch it

[@thescooshinator]

Ever since vsauce made how to count past infinity 8 years ago, I've wanted to see another video that goes into more detail about the numbers larger than the ones he described, as he jumped almost straight from epsilon to the innacessable cardinals. I've finally found one. This is probably my new favorite video to do with numbers in general.

[@RandomAndgit]

Wow, thanks very much!

[@sakuhoa]

Go check out "Sheafification of g" I'm sure you'll love his videos.

[@stevenfallinge7149]

It's rather difficult to make ordinals describable to the general public. That's because the larger you go the more you simply describe them via logical conditions. For example, a "weakly inaccessible cardinal" is one equal to its own cofinality (shortest possible ordinal-sequence converging to it) and is a limit cardinal (not a successor cardinal). And to describe cofinality, one must describe limits of ordinals, and so on.

[@hillabwonS]

The sad thing is vsauce didnt explain the cardinals shown at the end in the roadmap and neither did andigit

[@serraramayfield9230]

@@hillabwonSBecause it gets significantly harder to explain

[@ScorchingStoleYourToast]

"but there are ways to force past this barrier too!" me: *"USE MORE GREEK LETTERS!"*

[@crumble2000]

me: "your number plus one!"

[@MatthewConnellan-xc3oj]

@@crumble2000But, on an ordinal scale, +1s don’t matter.

[@CatValentineOfficial]

@@MatthewConnellan-xc3oj r/woooosh

[@DWithDiagonalStroke]

Beta Nought and Sigma Nought both exist as extensions to the greek letter sequence.

[@Sirlacran-z6f]

​@@MatthewConnellan-xc3ojordinals is the scale of order, in CARDINALS it doesn't matter, in ordinals yes

[@WTIF2024]

back in my day these numbers were big. kids these days with their autologicless+ struxybroken DOS-ungraphable DOS-unbuildable nameless-filkist catascaleless fictoproto-zuxaperdinologisms

[@LT_Productions1]

Yet that isn’t even the worst of it 💀

[@Succativiplex]

We had rkinal-projected number definition with the definition of Aperdinal (Ω∈) isn't FMS-chainable, but can't be RM()^♛/Я^♛-cataattributed to any (cata)thing in Stratasis today

[@Istamtae]

pretty sure that IS the worst of it

[@Polstok2024]

Ik

[@DWithDiagonalStroke]

FG Wiki moment

[@coolio-46]

this is the kinda content id see from a 100k sub channel surprised you arent big yet your contents awesome

[@RandomAndgit]

Thanks so much!

[@cartermarrero9431]

Holy cow I thought you where a big channel until I read this comment! Keep it up dude your content is great

[@HYP3RBYT3-p8n]

"Hey, are you ready to go on that date we mentioned?" "Sure, just wait an aleph null seconds."

[@נועםדוד-י8ד]

😢

[@frankman2]

🤣 or ... are you ready to go out now? just omega seconds darling!

[@HYP3RBYT3-p8n]

It’s funny just how lightly he uses aleph null like rayo(rayo(rayo(10^100))) isn’t octillons times closer to 0 than to it

[@Whybruh-q5b]

@@HYP3RBYT3-p8nWtf is Rayo. I've heard of Tree and Hexation

[@HYP3RBYT3-p8n]

@@Whybruh-q5bThe Rayo function describes the number after the largest possible number expressed in however many symbols (of first order set theory, whatever that is) the function describes. So, Rayo(10) is the number after the largest number that you can write with 10 symbols. Rayo’s number is Rayo(10^100), or Rayo(Googol).

[@ΓεώργιοςΑθερίδης]

1:24 I'm sad that you didn't say "this is taking forever"

[@RandomAndgit]

Damn, I wish I'd thought of that.

[@AIternate0]

​@@RandomAndgit what's the biggest number that's not infinite that you can think of?

[@RandomAndgit]

@@AIternate0 Good question. There isn't really a largest number I can think of because you can always increase.

[@Chest777YT]

Omega is bigger than infinte

[@RandomAndgit]

@@Chest777YT Yes. That was kind of the point of the video.

[@steppindown6874]

Idk but the idea of inaccessible cardinal seems so fucking badass to me. Been learning bout the continuum hypothesis on youtube to know whether the size of the set of real numbers is Aleph 1 or larger, and the nuance on it is beautiful. Guess this video tackles more on its general idea of larger infinities. Great job!

[@bloxrocks5179]

You weren't meant to count this high. Turn around

[@Dauntlesscubing]

incredible! this is an AMAZING VIDEO I learned a lot and am glad that the stuff I already knew will be taught to people who don't know it yet, thank you! this is an amazing video that deserves MILLIONS OF VIEWS

[@WTIF2024]

You just summoned the entire fictional googology community

[@RealZerenaFan]

if you're wondering what "Fictional Googology" is, it's essentially a version of googology that contains Very ill-defined, if not, completely undefined numbers that should not exist in any possible capacity, which is more of a communal art project about "What if you can count beyond Absolute Infinity" if anything! Even a well-known googologist by the name of TehAarex is in that Community!

[@DWithDiagonalStroke]

​@@RealZerenaFando you know if Aarex has a YT?

[@Chomik-np8rv]

When the numbes go from 0 to ¥¥|^£{§¥§™==`}®×¶=I ¥` :

[@Mikalinium]

I like how mathematicians attempted making ordinals that can describe Caseoh's weight

[@patkirasoong1102]

lol

[@SWI_alt_to_avoid_comment_ban]

it's closer to absolute infinity than anything we know

[@AIternate0]

buccholz ordinal

[@imnimbusy2885]

All muscle, baby!

[@CLASSSSSSSIED9781]

WHY IS THIS STUPID COMMENT ON A ACTUAL INSTERING VIDEO THE MOST LIKED IM MAD

[@omegaplaysgb]

best youtube channel ive ever seen about math so far

[@R5O-63O8]

Another amazing video! Great. I was here before this channel blew up (which I'm sure it will from the quality of content).

[@RandomAndgit]

Thanks very much!

[@meatman6908]

damn this channel is underrated af

[@simeonsurfer5868]

It's interesting that you take the ordinal approach, i've seen a lot of video that talk about aleph 0 and C, but not so much about aleph 1 ect.

[@Octronicrocs]

I’ve watched your videos since the simple history of interesting stuff video, you’ve earned a new subscriber! I really like your content

[@stormmugger4719]

What a massively underrated channel

[@MarioSqeegee]

i love that all this has no actual realistic use at all lol

[@DWithDiagonalStroke]

12:03 this is the smallest Inaccessible Cardinal: Omega Fixed Point. It is defined as the limit of the aleph function, an infinite nesting of alephs.

[@MCraven120]

I legit did not know tetration was an actual thing! I remember coming up with a very similar concept back in middle school and thinking it was an insane idea. The way I visualized it was "x^x=x2" then "x2^x2=x3", repeat ad infinitum

[@RandomAndgit]

Oh, yeah tetration is really cool. You can do it with finite numbers too, it's part of how you get to Graham's number.

[@ERRORRubiksZeraBrand]

Imagine you said "there is no biggest cardinal!" But Mathis R.V. said "absolute infinity"

[@RandomAndgit]

Absolute infinity isn't a cardinal, it transcends cardinals. Also, Absolute infinity is ill defined.

[@stevenfallinge7149]

If you allow things such as "proper classes," then a proper class can be thought of as absolute infinity. However, proper classes don't exist in standard set theory, they can only be reasoned with as propositions instead.

[@robinpinar9691]

​@@RandomAndgitwhat about Absolute Infinity - 1?

[@polymations]

@@robinpinar9691 surreal ordinals moment

[@RandomAndgit]

@@robinpinar9691 Absolute Infinity - 1 is still Absolute Infinity.

[@RealZerenaFan]

I Like how we showed up to a video about Apierology... I mean, you did summon us, so yay free engagement which means algorithm boost.

[@dedifanani8658]

Hello There! FG

[@WTIF2024]

@@dedifanani8658this person gets it

[@callhimtim3188]

I think THIS is my favorite type of KZbin video. The type that gets you excited to learn about something.

[@RandomAndgit]

Mine too, I try to make all my videos like that so I'm glad you thought so.

[@assumingsand6352]

this gives the same energy as kids fighting on the playground trying to come up with bigger and stronger weapons than each other. but with math.

[@Psi385]

good job u just did the summoning of all of the fg members

[@makowiecmakowiecki4565]

Infinity so infinite there's infinite infinities, as if it's so infinite that it's infinite.

[@Whatdoido-b8c]

0:50 Wouldn’t that make forever finite?

[@RandomAndgit]

No, actually! It's really weird.

[@Whatdoido-b8c]

@@RandomAndgit HOW

[@RandomAndgit]

@@Whatdoido-b8c Excellent question. We can actually prove that some infinities are larger or smaller than others using either the powerset or diagonal proof. Essentially, some infinite sets can be matched up to other infinite sets and still have members remaining. For example, the number of fractions is greater than the amount of numbers because you can match each fraction to 1/any number in the set of numbers and then still have lots left over (Like 3/7 which cant be written as 1/x)

[@FishYellow3]

​@RandomAndgit technically yes, but any infinite number is still infinite, unless there is a tier for transfinities where the infinity we know, is the smallest transfinity

[@enigmatv5641]

the universe is 1 forever

[@Rainstar1234]

yknow i still wonder who woke up and decided "yknow, what if the 90 degree rotated 8 wasn't the biggest number in the universe?" which caused THIS amount of infinities to be made

[@zdelrod829]

I think I had a stroke trying to wrap my head around this about halfway through

[@Lucygoosey719]

"Imagine you're an immortal being floating around in the universe for Aleph Null seconds" *proceeds to make an OC out of this concept and names him Aleph Null*

[@Jacobghouls2024]

Actually there's bigger than Gamma Nought: If we use the MDI notation saying that there's nothing bigger by calculating this: {10, - 50,} it can be so big that it reaches gamma. But if use the Gàblën function we can do this: G⁰(0) = 0 G¹(0) = 10^300,000,000,000,000,000,000,003 G² = Aleph null. G³(0) = ε1. G⁴ = Gamma nought... Until we reach GG⁰(0) Or G⁰(1) = I Or incessible Cardinal. So big that nothing in a vacuum is bigger than this. or is it? By using Gàblën function again. We can do GGG⁰(0) Or G⁰(2) = M or Mahlo Cardinal. This is so big that if we use the Veblen function: φ0(0) It would take Epsilon nought zeros to make it. but we can go farther by GGGGGGGGGGG...⁰(0) Or G⁰(10^33) = K or Weakly Compact Cardinal but If we do GGGGGGGGGGG.....⁰(0) or G⁰(ε0) = Ω or ABSOLUTE INFINTY THERES NOTHING AFTER THERES FANMADE NUMBERS AFTER ABSOLUTE INFINTY. ITS SO BIG THAT NO FUNCTION CAN BIGGER THAN THIS BUT JACOBS FUNCTION.

[@Fennaixelphox]

"There’s this emperor, and he asks the shepherd’s boy how many seconds in eternity. And the shepherd’s boy says, ‘There’s this mountain of pure diamond. It takes an hour to climb it and an hour to go around it, and every hundred years a little bird comes and sharpens its beak on the diamond mountain. And when the entire mountain is chiseled away, the first second of eternity will have passed.’ You may think that’s a hell of a long time. Personally, I think that’s a hell of a bird." --The Twelfth Doctor

[@flameendcyborgguy883]

One of the best monologue in history of fiction in my opinion.

[@theyobro1843]

Can't tell if this killed or fed my infinity anxiety

[@RandomAndgit]

Por qué no los dos, as they say.

[@matthewhall5571]

@@RandomAndgitSchroedinger's infinity

[@gravitrax3287]

I'll never ever look at those greek letters in physics class the same way again...

[@NeilAnaiahBuhayo-q2h]

Although the Inaccessible Cardinal is too big to be Accessed, we still found a way to go past it. Besides that, Stronger equations were made to go past it Nowadays, we have numbers like Absolute Infinity, Never, Endless, The Box Number, Absolute Fictional Numbers, Even Omegafinurom! We also have equations like BFN(n), T[t]->n, PX[n], ???[n], and Numbertomin: n

[@Bronathan251]

very much enjoyed the TREE(3) reference to your giant numbers video

[@liamismath1]

The end. 12:24 talking about ψ_1(ω) 14:32 talking about ψ_x(y) 16:37 (heres a rule for this part: y>ωωωωωωωωωωωωωωωωωωωωωωω… [ω times] [or Ω {absolute infinity}]

[@cyanidechryst]

underrated channel real

[@nocktv6559]

i love videos like this Very great representation, explenation also with the music! Also writing "The End" in greek letters and aleph 0 was very cool :D

[@RandomAndgit]

Thank you very much!

[@Spiton7714]

ΤΗΕ ΕΝΔ

[@lmlimpoism]

i feel like nothing can happen after forever, since forever is well, forever. you fill an endless pool with more water, well, you have an endless pool still.

[@unsweatbear]

No. The real biggest transfinite number is if you make a function called CALORIES() and put the incomprehensible number, ‘NIKOCADO’ into the function. CALORIES(NIKOCADO) creates a number so big it beats everything else on this video combined very easily, like comparing a million to the millionth power to zero.

[@w8363]

Nikocado is now skinny.

[@unsweatbear]

@@w8363 yeah this comment didn't age well

[@Gwbeditz]

​@@w8363It was fake

[@asheep7797]

Calories(Nikocado) is now around 130,000.

[@macrolocate2443]

How old is he 😨

[@catloverplayz3268]

This bends my brain to the point that this whole thing seems ridiculous

[@Gamma929]

Oh wow!!! its me in the thumbnail!

[@Meandpigeoncoolio]

Congrats litterally breaking physics while being more and not more then infinite at the same time

[@littlefloss._.]

So... this is just a numbers video, its just disguised to make some of us watch this type of video once again. [I mean, works for me]

[@totallyrealnotfakelifeadvi7547]

I’ve never heard of an eon defined as 1 billion years. Is this different than eons in biology/geology which are defined by fossils becoming different (Hadean, Archaean, Proterozoic, Phanerozoic)?

[@RandomAndgit]

Yes, there are a few different eon definitions.

[@totallyrealnotfakelifeadvi7547]

@ so cool! When do people use the billion year version of an eon (btw I just finished the video and I love it)

[@pncka]

I'm interested in the math that you could do with these. I want a sandbox to throw stuff together, like desmos, but infinite.

[@robinhammond4446]

On the point of inaccessible infinities, I prefer the phrasing 'not constructable from the finite.' I've also never seen this topic broached sans the powerset being invoked, was there a reason for that choice ?

[@viktoriatoth5521]

Can you count up to Aleph-Null?

[@bokikoki7]

I love this type of video! Keep up the good work ! Where did you learn these things? Did you study it in school or read books independently or did you maybe watch a different video like this? Im just curious:)

[@RandomAndgit]

A mixture. I first gained interest in infinity from a very old Vsauce video but most of the information comes from books and articles which I read specifically for the purpose of this video.

[@stevenfallinge7149]

@@RandomAndgit Recommend reading is the book "Set Theory" by Thomas Jech for more about this subject, in fact it has everything. A pdf can easily be searched for online. However, note that it presumes knowledge about certain subjects, namely prepositional logic (such as what symbols like ∃ "there exists" ∀ "for all"), formal languages, symbols, formulas, and variables and whatnot, basic knowledge about stuff like functions and relations. Later chapters slowly trickle in additional presumptions, like chapter 4 assumes you know about the existence of "least upper bounds" (supremum) in real numbers, and then "metric" "metric topology" "order topology" "lebesgue measure." If you don't know those subjects, chapters 1-3 are still readable and contain the most important basic info, and one can come back to chapter 4 after knowing those other subjects.

[@RandomAndgit]

@@stevenfallinge7149 Ahh, thanks! That sounds like a great read.

[@anneliesoliver8705]

Thank you for this amazing video, you explained everything well and thoroughly so that everyone can understand the concept of ordinals, including me! I still have one question after this though: I've never seen an understandable definition of κ-inaccessible cardinals, could you please provide me with one/a link to one?

[@RandomAndgit]

Sure! I'll try my best. So, k-Inaccessible basically means that a number is strongly inaccessible, meaning that it: -Is uncountable (You couldn't count to it even in an infinite amount of time, for example, you could never count all the decimals between 0 and 1 because you can't even start assuming your doing it in order) -It's not a sum of fewer cardinals than it's own value, basically, you could never reach it from bellow with addition or multiplication unless you'd already defined it. -You can't reach it though power setting (Seeing how many sets you can build with a certain number of elements which gives the same value as 2^x) The basic idea is that you can't possibly reach it from bellow and the only way to get to it is by declaring its existence by a mathematical axiom. Aleph-Null is the best example of something that's kinda similar because it also can't be reached from bellow but aleph null is countable. I hope this helps!

[@essegd]

good video, however i think it would've been better to continue using analogies relating to supertasks to describe the larger ordinals, rather than talking about "waiting multiple forevers", because that makes conceptually less sense

[@viktoriatoth5521]

That is called the first uncountable ordinal in that bit 😊 ♾️

[@totallyrealnotfakelifeadvi7547]

When they start adding Latin (English) letters to math 😌 When they start adding Greek letters to math 😕 When they start adding Hebrew letters to math 😱

[@RainbowGhost4820]

But one question: How do we reach absolute Infinity(uppercase omega)? Isn't it like, the name of the all infinity set? Including aleph0, low. Omega, Epsilon0 etc.?

[@RandomAndgit]

That's a great question. If I understand correctly, the only way to get to absolute Infinity is to declare it's existence through an axiom.

[@RainbowGhost4820]

@@RandomAndgit oh ok, it's that Im trying to use Omega in a series as like "God" so that helps me understand more of it, Also i love math and thanks!

[@RandomAndgit]

@@RainbowGhost4820 You're most welcome!

[@viktoriatoth5521]

@@RandomAndgit There are Aleph-Null seconds in forever ♾

[@viktoriatoth5521]

Hey, Percy (Andgit) is TREE(3) years an infinite amount of time?

[@RandomAndgit]

No, it's not, but TREE(3) is so stupidly large that it would be long enough for the universe to end and then stay dead for googols of googols of googols of years.

[@viktoriatoth5521]

@@RandomAndgitWhat about 10^^^10^^^357 years and what about 10{36466}10 years these numbers are large

[@donkeyhobo34]

This seems familiar and natural like I've physically been through it before

[@ThePendriveGuy]

For those of you wondering, the reason Absolute Infinity isn't in this is becaue it's ill-defined (basically there's no real and conventional mathematical definition for it that doesn't create problems) Other than that, great video! I would really like to see an elaboration on Large Cardinals if that's a possibility :D

[@RandomAndgit]

It's definitely something I'll make at some point in the future! I'm not sure how long it'll take though.

[@KaijuHDR]

Just say it encompasses absolutely every cardinal, literally every mathematical expression, even mathematics itself. That's not too hard to comprehend it💀

[@ThePendriveGuy]

@@KaijuHDR That's the problem, Absolute Infinity cannot contain everything, if it did, then it would have to contain itself, which makes no sense and causes pardoxes within Mathematics. On the other Hand, if you say "Ω is the set of all Ordinals" there's nothing stopping Ω+1 from existing. Since Ω Is itself another ordinal, thus failing to contain everything.

[@KaijuHDR]

@@ThePendriveGuy Then what's your point? You just told me it can't be anything then what I just said, which means it can't make sense, which means it ignores all logic. And this isn't even the actualized meaning to it. Cantor just defined it as a infinity larger than everything and cannot be surpassed by anything in everything. Not containing everything. Which don't mistake me saying this, is still probably illogical and paradoxical. Because seemingly it's part of everything, but you also just hinted at the fact that it can't be that ordinal one. Also isnt the "set of all ordinals" just Aleph-null btw? Or another one? I'm too engrossed with making a response (since most of my responses I've reread and realized they're just idiotic and stupid💀) and my own cosmology rn.

[@ThePendriveGuy]

@@KaijuHDR My point is, Absolute Infinity isn't a set, or an ordinal, or any mathematical structure for that matter. Absolute Infinity Is better fit as a philosophical Concept, since, like I Said, It causes problems when ported to real math. It's simply something more closely related to the meaning of perfection Cantor also stated himself that it is inconsistent with the definition of a set Also, Aleph-Null Is not an ordinal, nor Is related to Ordinals at all. Aleph-Null Is the set of all counting numbers. While Omega (The "Smallest" infinity) Is simply the thing that comes after all the Naturals. As for set construction, Ordinals and Cardinals are fundamentally defined as sets, so if we invent a new value Larger than any of those, it must be described as a set. TL;DR: Absolute Infinity (Ω) is More of a philosophical concept not meant to make sense in math. It's typically used in your average "0 to Infinity" number videos, which leads people to believe that it is a real number.

[@Qreator06]

Define True Accessor “function” TA: returns smallest ordinal not accessible by its inputs S(x)=x+1 TA(S,0) = ω TA(S,ω)= ω_1 TA(S,ω_1) = ω_2 Make a function out of this TA(S,x)=F1(x) F1^x(0)=A(x)=ω_x A is the basic accessor function TA(A,1) = the inaccessible ordinal at the end of the vid

[@Qreator06]

Is this cheating?

[@Qreator06]

Wait I just realized the final number was a cardinal, not ordinal, eh just replace the omegas with alephs

[@THE_HONOURED_ONE_LOL]

12:12 Arent infinities “too big” that we’ve made up numbers?

[@jayvardhankhatri4084]

They: We have reached another barrier which cant be overcome this time. No matter what!! Me: what is it? They : We are out of Greek letters!!!!

[@HYP3RBYT3-p8n]

If an inaccessible cardinal is like the infinity to the infinities, is there some kind of function to label each level of “inaccessibility?”

[@RandomAndgit]

That's an excellent question! There isn't a function, per say (at least not to my knowledge), but there is something called the large cardinal hierarchy which features cardinals larger than inaccessibles, then those larger than them, larger than those, and so on.

[@HYP3RBYT3-p8n]

@@RandomAndgit all of that sounds like fictional googology at this point lol

[@Qreator06]

@@HYP3RBYT3-p8n my brother, sister or non binary entity, all of math is fictional

[@faclubedosros-2863]

Insane! Thank You!

[@taheemparvez8195]

the way I think omega and No is you switch bases like No is the first set of digits and then omega is next like one and tens except with infinate diffrent digits

[@TStyle1979]

Could you consider turning the music down (or off)? I really struggled to hear and follow you. Thanks.

[@RandomAndgit]

Sorry! Yeah, a few people have said that. I'm turning the music waaaay down in my next video.

[@trcsyt]

"Theres no bugger cardinal" Hey, did you heard of FG? you forgot? _(It stands for _*_F_*_ ictional _*_G_*_ oogology)_

[@RealZerenaFan]

He's talking about Apierology, where There IS no bigger cardinal, besides absolute infinity.

[@RandomAndgit]

I never said that there was no bigger cardinal, I just said that it was too big to reach from bellow. (Which is true)

[@Paumung2014]

​@@RandomAndgitFictional is Fictional¯⁠\⁠_⁠(⁠ツ⁠)⁠_⁠/⁠¯

[@theoncomingstorm7903]

@@RandomAndgit FG is pseudomathematics anyway

[@RandomAndgit]

@@theoncomingstorm7903 Quite so.

[@also_nothing]

Fun fact: everything that is shown in this video is closer to 0 than true infinity

[@StringOfExins]

you should point out the fact that the Infinite stacks of veblen function in a veblen function equals more of a NAN/Infinity relationship, because the Veblen function never gets what it needs in its function slot: A numerical input. It instead always gets a function, which is not able to define the funtion.

[@melly7126]

VSauce stopped at epsilon 0 and i was always curious

[@PhysicsChan]

Are these numbers bigger than actual infinity? What about countable infinites?

[@viktoriatoth5521]

Aleph null is countable infinity ♾️

[@_-___________]

Well... to be fair.... are infinities really actually definitely larger than each other? In a finite sense, yes. But there is always more infinity, so doesn't that mean that even if one infinity is bigger than another, you can still match every number with another from the "smaller" infinity? Even if the bigger infinity includes every number in the smaller infinity, there are always more numbers. Intuitively it seems that some infinities are smaller than others... But remember the infinite hotel? It depends on how you arrange infinity. Infinity doesn't have a size. It doesn't have an end. If you matched every odd number with all real numbers, they are both the same size. That's because neither of them end. The rate of acceleration is different, but infinity is already endless, no matter what it's made of.

[@NStripleseven]

The infinite hotel analogy only works on aleph null many things, because it requires that the collection be countable. That’s how we can prove that e.g. the rationals have the same size as the naturals, because there’s a way of enumerating the rationals that forms a one-to-one mapping between the two sets. However, the argument falls apart for a set like the reals, with cardinality greater than aleph null (maybe it’s aleph 1, nobody is sure), since you can prove that no such enumeration can exist. There are, then, infinities which contain more things than others.

[@_-___________]

@@NStripleseven Oh yeah.... that too. Oh well.

[@stevenfallinge7149]

Main reason this isn't true is something analogous to Russel's paradox (in fact Russel's paradox even says some infinities are too large to exist because they result in a logical paradox), comparing a set S with its power set P(S), the set of all subsets of S. Put it in simple terms, there's no mapping f: P(S)→S in such a way that different subsets of S always map to different elements of S, because if such an f existed, then consider the subset B={a∈S | There exists A∈P(S) such that f(A) = a and a ∉ A}. Then consider f(B)=x. Law of the excluded middle says that x∈B or x∉B. In the first case, if x∈B, then by definition of set B, there exists A∈P(S) such that f(A)=x and x∉A. But f maps different subsets of S to different elements and f(A)=f(B), so A must equal B. Which means x∉B, contradicting x∈B. In the second case, if x∉B, then there exists the set B∈P(S) such that f(B)=x and x∉B, so by definition of set B, x∈B, contradicting x∉B. So both x∈B or x∉B are impossible meaning that such a mapping f cannot exist. So any attempt to map P(S) to S must have overlaps, mapping different subsets of S to the same element.

[@Meandpigeoncoolio]

Smaller and bigger infinites have the same properties almost like they don't even have a size difference

[@_-___________]

@@Meandpigeoncoolio Isn't it literally just an interpretation difference? Like a line and an infinite plane would have the same size because you could basically create an infinite plane with an infinite line if you line it up... you won't ever run out of infinite line with witch to line up to the infinite line.

[@impydude2000]

Well my infinity has the combined total of all of your infinities combined, hmph.

[@Skivv5]

Yeah but what if i add one more

[@RandomAndgit]

I know that this is probably a joke but the answer is actually really interesting. So, for any ordinal, we just put +1 on the end (Omega +1, Epsilon0 +1, ect...) but for cardinals we actually change it to its corresponding ordinal +1 so Aleph 42 would become Omega 42 +1. If you do this with an inexcusable cardinal, you can also have an inexcusable ordinal, so that's pretty interesting.

[@crimsondragon2677]

Close your eyes, count to 1; That’s how long forever feels.

[@BookInBlack]

Yes, that's Optimistic Nihilism from Kurzgesagt to you blud

[@RandomAndgit]

That's my favourite Kurzgesagt quote, actually.

[@WTIF2024]

so like half a second?

[@WTIF2024]

@@BookInBlack hello fellow ewow contestant

[@BookInBlack]

agree

[@norwd]

One of these mathematicians should just announce “Matryoshka’s Number” and call it a day 😂

[@uhimdivin]

well, if the Innascesable Ordinal gets reached in the future, we need to then try to reach ABSOLUTE INFINITY, but i dont know if it is fictonal or not.

[@RicetheShoplifter]

9:39 the ackermann ordinal's symbol should be υ (upsilon) since ive never seen it in math

[@RandomAndgit]

That's not a bad idea, actually. υ could also be good for an ordinal naming scheme after the vebeln function.

[@annxu8219]

υ_α=φ(1,0,0,α) yay

[@barrettkepler7618]

Mathematics had too much fun creating these infinities

[@SleepyPancake-rm2jr]

Sorry miss, I can’t attend school today, STUFF, AN ABRIDGED GUIDE TO INTERESTING THINGS JUST UPLOADED!

[@Rajarshichowdhury5667]

Whats that number called

[@viktoriatoth5521]

If Aleph-Null was the amount of seconds in forever, the amount of time in forever would be countably infinite?

[@RandomAndgit]

That's right, because you can start from the first second and then continue counting forever. An example of something uncountably infinite would be the number of irrational numbers, because you couldn't even start counting because there is no 'first' irrational number.

[@viktoriatoth5521]

@@RandomAndgit but Aleph-Null is not the amount of seconds in forever, because it is countably infinite ♾️

[@SoI-]

waiting for the 17 hour video which DOES explain the most complicated functions xd

[@SJ-ym4yt]

Another great video! Once again I find the music too loud though, you should really consider turning it down

[@anadiacostadeoliveira4]

What's the first song name?

[@RandomAndgit]

All music names are in the video description, in chronological order.

[@viktoriatoth5521]

@@RandomAndgitI know what it is, Time Flow!! Is the correct answer ✅

[@viktoriatoth5521]

Is Utter Oblivion closer to Aleph-Null?

[@RandomAndgit]

Closer to Aleph Null than what? Closer takes 2 arguments.

[@viktoriatoth5521]

@@RandomAndgit What takes 2 arguments?

[@gravitrax3287]

​@@viktoriatoth5521your question, i think what he means is that you didn't specify what you meant by closer, probably closer to 0 or Aleph Null

[@user-dp6gm8ky5p]

ω+G looks so cool

[@tealianmapping]

8:00 whats the music here?

[@RandomAndgit]

It's called, rather boringly "Space-ambiant-sci-fi-121842" It's free to use.

[@tealianmapping]

Now that Im talking about this, what is all the music in order, if you don’t mind.

[@RandomAndgit]

@@tealianmapping Not at all! I'm afraid it might take a little while to find it all again. I'll try to get it all for you as soon as possible.

[@RandomAndgit]

@@tealianmapping All the music is now listed in the video description! Hope this is helpful.

[@NStripleseven]

5:00 Not technically true. Taking omega squared and appending another omega squared just gives you 2x omega squared. To reach omega cubed you’d need to say something along the lines of “and repeat that process aleph null times”

[@RandomAndgit]

Oh, that's very true actually. My mistake.

[@robinpinar9691]

​@@RandomAndgitand also omega lots of omega forevers just goes to omega cubed not epsilon null

[@robinpinar9691]

And also to reach ω⁠^ω⁠ you need to say "ω⁠ forevers" then repeat that for how many seconds forever is Then You have to repeat That again and again for how many seconds forever is and you get ω⁠^ω⁠

[@robinpinar9691]

and to reach ε0 you need to do the "And also to reach ω⁠^ω⁠ you need to say "ω⁠ forevers" then repeat that for how many seconds forever is Then You have to repeat That again and again for how many seconds forever is" Again but this time it's the power of the starting ω⁠ and again and again for how many seconds forever is and you get ε0

[@FarzanaFathima-t4e]

You deserve another sub

[@ainyaku]

1:24 missed opportunity to say this is taking forever

[@metamusic64]

you sound exactly like the narrator in the old flash game "The I of It". i can't quite put my finger on why

[@MathewSan_]

Great video 👍

[@pababulky]

What about Absolute Infinity?

[@bacicinvatteneaca]

I would have left a comment correctng your pronunciation of feferman-schütte but KZbin censors all phonetic symbols

[@RandomAndgit]

Oh, that's annoying. Sorry about that.

[@viktoriatoth5521]

@@RandomAndgitwas that your voice in this video?

[@DTN001.]

I think infinity should behave like tetris game. After some point, it will turn negative, then down to zero again. And this point could have been called absolute point since 1/0 equals this point. If we think about the number line is on a sphere, that would make more sense.

[@HYP3RBYT3-p8n]

Why can’t it? We kind of just invented all of these numbers for fun anyway.

[@acearmageddon4404]

What on earth is going on in mathematicians brains. This all souns so made up, but I'd be surprised if all those different types of infinities didn't have a rigorous proof behind them that justifies distinguishing them from the others. What a fun video.

[@-._Ahmad_.-]

Clicker Games:

[@denorangebanan]

this is just mathematicians' version of infinty plus one