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What comes after forever?

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By popular demand, here is a video about infinities. I tried to make this the most comprehensive guide to infinities on RU-vid, so I'm going in depth for both ordinals and cardinals here.
Check out the Googlology wiki: googology.fand...
The music is, in chronological order:
-Time passing
-Time flow
-Thunder-Unison-Dramatic-Action-Epic-Music
-Space ambaint Sci-fi
-Facing infinity

Опубликовано:

4 сен 2024

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Комментарии : 467

@RandomAndgit Месяц назад

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 Месяц назад

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

@RandomAndgit Месяц назад

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

@omarie5893 Месяц назад

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

@derekritch4360 Месяц назад

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

@derekritch4360 Месяц назад

But worth a new subscriber

@karrpfen Месяц назад

‘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 Месяц назад

Wow, I may need to watch doctor who.

@guotyr2502 Месяц назад

What season tho ?

@karrpfen Месяц назад

@@guotyr2502 season 9

@Rohit_Naga. Месяц назад

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

@AlmostAstronaut Месяц назад

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

@thescooshinator Месяц назад

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 Месяц назад

Wow, thanks very much!

@sakuhoa Месяц назад

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

@stevenfallinge7149 Месяц назад

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.

@user-ce6ig1tv3k 14 дней назад

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

@Mikalinium Месяц назад

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

@patkirasoong1102 Месяц назад

lol

@SWI_alt_to_avoid_comment_ban Месяц назад

it's closer to absolute infinity than anything we know

@BRAVETOASTA Месяц назад

buccholz ordinal

@imnimbusy2885 Месяц назад

All muscle, baby!

@CLASSSSSSSIED9781 Месяц назад

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

@Gin2761 Месяц назад

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

@RandomAndgit Месяц назад

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

@AbyssalTheDifficulty 27 дней назад

@@RandomAndgitis sams number bigger than utter oblivion or not

@WTIF2024 24 дня назад

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

@user-cj2zt3zu1t Месяц назад

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

@RandomAndgit Месяц назад

Damn, I wish I'd thought of that.

@BRAVETOASTA Месяц назад

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

@RandomAndgit Месяц назад

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

@Chest777YT Месяц назад

Omega is bigger than infinte

@RandomAndgit Месяц назад

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

@WTIF2024 29 дней назад

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 29 дней назад

Yet that isn’t even the worst of it 💀

@Succativiplex 27 дней назад

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 27 дней назад

pretty sure that IS the worst of it

@Polstok2024 25 дней назад

@ScorchingStoleYourToast Месяц назад

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

@crumble2000 Месяц назад

me: "your number plus one!"

@WTIF2024 29 дней назад

You just summoned the entire fictional googology community

@RealZerenaFan 29 дней назад

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!

@ERRORRubiksZeraBrand Месяц назад

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

@RandomAndgit Месяц назад

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

@stevenfallinge7149 Месяц назад

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 Месяц назад

@@RandomAndgitwhat about Absolute Infinity - 1?

@polymations Месяц назад

@@robinpinar9691 surreal ordinals moment

@RandomAndgit Месяц назад

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

@coolio-46 Месяц назад

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

@RandomAndgit Месяц назад

Thanks so much!

@cartermarrero9431 Месяц назад

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

@HYP3RBYT3-p8n 29 дней назад

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

@the-unsweatiest-player 26 дней назад

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.

@Chlo3Gaming Месяц назад

this channel has every fact EVER CONFIRMED

@Psi385 29 дней назад

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

@meatman6908 Месяц назад

damn this channel is underrated af

@Jacobghouls2024 14 дней назад

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.

@jobgeorge1216 7 дней назад

@2:42 - [BIG BRAIN MOMENT] Actually, Rayo's Number is being defined as being the largest number that is smaller than Alpeh Nol. If there was a number in between Rayo's Number and Alpeh Nol, that number would be Rayo's Number.

@RandomAndgit 6 дней назад

Actually, unless I'm mistaken, Rayo's number is defined as the smallest positive integer bigger than any finite positive integer named by an expression in the language of first-order set theory.

@omegaplaysgb 18 дней назад

best youtube channel ive ever seen about math so far

@julianstories8933 Месяц назад

You actually can’t count to 6,542,124,659 in 1 lifetime because you can only count to about 100 million in 1 lifetime

@ZerWubbie Месяц назад

No lt 3x10^9

@catloverplayz3268 Месяц назад

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

@Dauntlesscubing Месяц назад

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

@stormmugger4719 Месяц назад

What a massively underrated channel

@R5O_63O8 Месяц назад

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

@RandomAndgit Месяц назад

Thanks very much!

@judgemanamacarsanar3626 4 дня назад

Yet it is still closer to zero than… Caseoh’s weight

@Octronicrocs Месяц назад

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

@crimsondragon2677 Месяц назад

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

@BookInBlack Месяц назад

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

@RandomAndgit Месяц назад

That's my favourite Kurzgesagt quote, actually.

@WTIF2024 29 дней назад

so like half a second?

@WTIF2024 29 дней назад

@@BookInBlack hello fellow ewow contestant

@BookInBlack 29 дней назад

agree

@Fennaixelphox Месяц назад

"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

@simeonsurfer5868 Месяц назад

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.

@DTN001. 11 дней назад

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.

@donkeyhobo34 Месяц назад

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

@Rainstar1234 Месяц назад

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

@MCraven120 Месяц назад

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 Месяц назад

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.

@ThePendriveGuy Месяц назад

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 Месяц назад

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

@KaijuHDR 14 дней назад

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

@ThePendriveGuy 14 дней назад

@@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 14 дней назад

@@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 14 дней назад

@@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.

@theyobro1843 Месяц назад

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

@RandomAndgit Месяц назад

Por qué no los dos, as they say.

@denorangebanan Месяц назад

this is just mathematicians' version of infinty plus one

@SleepyPancake-rm2jr Месяц назад

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

@Gamma929 23 дня назад

Oh wow!!! its me in the thumbnail!

@RealZerenaFan 29 дней назад

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 28 дней назад

Hello There! FG

@WTIF2024 24 дня назад

@@dedifanani8658this person gets it

@SoI- 29 дней назад

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

@nocktv6559 Месяц назад

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 Месяц назад

Thank you very much!

@Spiton7714 Месяц назад

ΤΗΕ ΕΝΔ

@bokikoki7 Месяц назад

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 Месяц назад

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 Месяц назад

@@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 Месяц назад

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

@Pupetmantheguywhoisminus. Месяц назад

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.

@also_nothing Месяц назад

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

@IzincZaduel Месяц назад

Simple answer. Still forever. It's endless and it doesn't stop there. Forever will still be forever after forever.

@callhimtim3188 Месяц назад

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

@RandomAndgit Месяц назад

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

@trcsyt 29 дней назад

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

@RealZerenaFan 29 дней назад

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

@RandomAndgit 29 дней назад

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 28 дней назад

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

@nobodyatall9999 Месяц назад

What comes after CASE-OH’s Weight in Solar Masses Uploaded on April Fools, 2025 Script: Start N O T H I N G Like and subscribe for more! END SCREEN

@acechesterfernandez4770 19 дней назад

I love how there is one RU-vidr that made a number bigger than omega 1 and infinity combined and its absolute infinity that is this Ω also that same RU-vidr absolutely destroyed his record with NEVER or ? is there any bigger number than number? Well we can tetrate that with never and make that tower but ive hit a roadblock theres this huge gap between the next number invented by another guy since you can tetrate any number how about NEVER tetrated by NEVER tetrated by NEVER tetrated by NEVER tetrated by NEVER and so on but this number is so gigantic it would probably take 41 eons the number is PROTOCOL BARRIER but whats bigger than it? I mean it's too big to comprehend now imagine every millimeter was PROTOCOL BARRIERs of universes possible we could even just even make our universe inside a parallel universe thats the same as our real universe that has PROTOCOL BARRIERs universes and so on i couldnt even see the number... Edit: the same creator made a bigger number than PROTOCOL BARRIER the end of numbers... Or so i thought the same creator made another number bigger than the end of numbers its B̶̠̤̊Ě̸̢̨̮̙̞͌Y̷̧̘͇̘̿̍ͅO̷̡͕̹̾Ṋ̶̪̬͒̌͒̌̀D̴̝͑ then copying that with the protocol barrier function i just said it comes to the null point... But gigantic numbers can be confusing i mean negative numbers are strange... But can we do the same thing to the null point like the protocol barrier?

@Googolplexianthattoll3141 18 дней назад

There's known as the average size ordinal call the first uncountable cardinal

@taheemparvez8195 Месяц назад

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

@annxu8219 Месяц назад

btw φ(1,0,0) to φ(1,0,1) is very tricky to look closely

@dominiqueubersfeld2282 Месяц назад

It's like with washing powder advertising: what comes after whiter than white?

@user-ce6ig1tv3k Месяц назад

Its a shame you didnt explain innacessible cardinals tbh

@RandomAndgit Месяц назад

I wanted to keep the video within that 10-15 minute mark but I might make a brief followup explaining innacessibles and other even larger ones like 0# and almost huge.

@robinpinar9691 Месяц назад

@@RandomAndgiteventually reaching absolute infinity

@user-ce6ig1tv3k Месяц назад

@@RandomAndgit youre gonna need a few parts to explain everything, ciz theres the inaccessibles which you didnt even explain, mahlo cardinals, Inaccessible, weakly compact, indescribable, strongly unfoldable, omega 1 iterable and 0^# exists, ramsey, strongly ramsey, measurable, strong, woodin, superstrong and strongly compact, supercompact, extendible, vopenka's principle, almost huge, huge, superhuge, n-huge, 10-13 and finally 0=1

@Unofficial2048tiles Месяц назад

Tbh ω_x is kinda like inaccessible cardinals beta

@iheartoofs Месяц назад

@@robinpinar9691 by eventually you mean after absolute infinity time?

@cyanidechryst Месяц назад

underrated channel real

@metamusic64 Месяц назад

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

@L3g0_99 Месяц назад

I have been summoned: 2:10

@acearmageddon4404 Месяц назад

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.

@uhimdivin Месяц назад

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.

@ninas8238 Месяц назад

Funny thing is a number named Utter Oblivion is so utterly vast that it is a finite number but surpasses almost all inaccessible cardinals and uncountable infinities

@RandomAndgit Месяц назад

That doesn't work mathematically. Aleph null is, by definition, larger than all finite numbers and all other infinities are, also by definition, at least as large as Aleph null.

@ninas8238 Месяц назад

@@RandomAndgit If **Utter Oblivion** is a very, very, very large finite number, it would surpass even uncountable infinities in terms of magnitude. This is because its size is constructed to be beyond any typical infinite measure, placing it at a scale larger than any uncountable infinity.

@ninas8238 Месяц назад

@@RandomAndgit While uncountable infinities describe sizes beyond finite numbers, a number like Utter Oblivion, it is finite and designed to be beyond any typical measure, would exceed even the largest forms of infinity in terms of magnitude.

@ninas8238 Месяц назад

@@RandomAndgit By definition, Utter Oblivion is intended to be larger than any uncountable infinity. It is designed to be so large that it exceeds the size of infinite sets, including those with uncountable cardinalities.

@RandomAndgit Месяц назад

@@ninas8238 Ahh, I see. Yeah if you're talking magnitude rather than actual size that does kinda make sense. I still don't think I fully understand how that's possible but it could just be me.

@MathewSan_ Месяц назад

Great video 👍

@cuberman5948 Месяц назад

the fact he never mentioned absolute infinity is uhhhhhh

@RandomAndgit Месяц назад

Absolute infinity is ill defined and is also neither a cardinal nor an ordinal and, as such, is entirely irrelevant to this video.

@Succativiplex Месяц назад

@@RandomAndgitit's the limit of logic. Every number is a property of it. Even if a number claimed to go larger than absolute infinity, it'll still basically be a property of it.

@cuberman5948 24 дня назад

@@RandomAndgit but you showed the symbol for Absolute Infinity

@RandomAndgit 23 дня назад

@@cuberman5948 No, I showed capital omega which is used both as the symbol of absolute infinity and of omega 1.

@Skivv5 Месяц назад

Yeah but what if i add one more

@RandomAndgit Месяц назад

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.

@SJ-ym4yt Месяц назад

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

@roma45721 Месяц назад

There are numbers bigger than inaccessible cardinal

@nocktv6559 Месяц назад

weakly Compact Kardinal K

@roma45721 Месяц назад

@@nocktv6559 AND ABSOLUTE INFINITY

@HomieNukeMarkRealNoFake Месяц назад

Church-Kleene Ordinal

@ServantOfTheAlmighty0 Месяц назад

Don’t let power scalers watch this video

@IbiActive Месяц назад

@@ServantOfTheAlmighty0Its funny that you mentioned that because that is exactly what I was thinking about wondering if any powerscalers has caught on to this video yet or if they have wrote anything in the comments section regarding it here

@_-___________ Месяц назад

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 Месяц назад

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.

@_-___________ Месяц назад

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

@stevenfallinge7149 Месяц назад

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.

@KyleTang-my5sn Месяц назад

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@caseylynrodriguez342 Месяц назад

Copied and pasted

@tylerrichter6760 Месяц назад

I know your ass didnt do this

@erenerbay Месяц назад

@@caseylynrodriguez342 you dont expect him to write all of that do you

@FaizThe-kc6dk Месяц назад

Plus its not related

@RicetheShoplifter Месяц назад

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

@RandomAndgit Месяц назад

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

@annxu8219 Месяц назад

υ_α=φ(1,0,0,α) yay

@ZTGAMERYAY 28 дней назад

Let’s just rap this up and say x is the biggest number. As a variable, it can be the highest number.

@Googolplexianthattoll3141 18 дней назад

{²ω(0)-35,46}=first uncountable cardinal={-ω(1.2,69,29)5}")_}

@anneliesoliver8705 Месяц назад

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 Месяц назад

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!

@Googolplexianthattoll3141 18 дней назад

ωx_ωx_^ω¹⁰⁰⁰⁰⁰⁰=inaccessible cardinal^ω=mahlo cardinal

@pr0hobo Месяц назад

every one just loves remaking vsauce videos dont they

@RandomAndgit Месяц назад

Actually, the reason I made this video is because of how little that Vsauce video actually covers. He only goes into Omega, Aleph and Epsilon and almost completely skips the ordinals which is why this video focuses on them.

@pr0hobo Месяц назад

@@RandomAndgit fair enough and the video was of course a very different style than his. its just sad how many times ive seen youtubers make a video like this about ordinals and follow almost the exact same path as vsauce or at least take extreme inspiration and not credit or even mention him. This has to be like the fourth video ive seen do this. I appreciate that hes amazing inspiration and that you added much to the discussion but if you remove his discussion in the intro about 40 and your discussion about eons the first halves of the video follow almost the same plot. Im not saying dont make a video and bring awareness of this awesome part of math to the pubic (also the video you made was really good), im just saying its sad not to credit or mention him for making a video on the topic years ago. I did really appreciate your discussion about the different phi functions and linking googolology tho you definitely added more than others have when making videos on this topic.

@RandomAndgit Месяц назад

@@pr0hobo Crediting is a very good idea actually, thanks. Sorry I didn't think of it.

@dccisco9515 Месяц назад

@@RandomAndgitadd some ordinals between the small veblen ordinal and omega 1

@pr0hobo Месяц назад

@@RandomAndgit thank you, I think you did a great job presenting the information and i think it complements vsauce’s video quite well actually.

@Diamond13428 Месяц назад

Number is a Endless❤

@Diamond13428 Месяц назад

Is not end yet

@aleksanderwierzbicki7998 Месяц назад

4:01 omega

@RandomAndgit Месяц назад

That is, indeed, omega.

@user-dt7mz5bz7z Месяц назад

2+2=4 2x2=4 2^2=4

@Spiton7714 Месяц назад

2 2= 2^2^2= 4^2= 16

@imfumrsaqjed Месяц назад

@@Spiton77142^^2 = 2^2

@KinuTheDragon Месяц назад

@@Spiton7714No, 2 tetrated to 2 = 2^2 = 4.

@batsen3777 Месяц назад

hyper(2, 2, k) = 4; ∀k ∊ N Upd: hyper(a,b,1) = a+b hyper(a,b,2) = a*b hyper(a,b,3) = a^b hyper(a,b,4) = a^^b etc

@robinpinar9691 Месяц назад

@@KinuTheDragon2^^^2, 2^^^^2, 2^^^^^2 Even 2{∞}2 equal 4

@user-lf8hz9st6d 21 день назад

1 2 3 4 5 6 7 8 9 10 11 12... 122 123 124 125... 6542124657 6542124658 6542124659... Infinity!!!!!!!!!!

@qMAXi Месяц назад

Really underrated....you can compete with 3b1b at explaining

@RandomAndgit Месяц назад

Wow, thanks very much.

@supayambaek Месяц назад

honestly, anything that comes after omega is can be reduced into a function within itself which can go on forever. kinda unimpressive and ironic because this is an attempt to encapsulate 'forever.'

@RandomAndgit Месяц назад

Mathematicians love trying to reduce esoteric ideas to functions.

@AllYourMemeAreBelongToUs Месяц назад

And I thought Aleph 1 was big.

@jhanschoo Месяц назад

I'm not particularly fond that this video names so many transfinite ordinals, and yet there is no good discussion on how you typically construct these ordinals. The way it is explained, with supertasks, is kind of loosy-goosey. It's easier and more formally accurate to say that we have generalized the notion of being able to take the smallest finite ordinal greater than any set of finite ordinal (e.g. the ordinal after {2nd, 16th, 13th} is 17th) into sets of any size containing ordinals. This is called the well-ordering property. So the smallest ordinal greater than any finite ordinal is omega, the smallest ordinal greater than omega is omega + 1, and so on.

@Dauntlesscubing Месяц назад

it's a good critique but keep your personal opinion out of it, you can make a critique without stating your personal opinion abruptly and unkindly.

@RandomAndgit Месяц назад

While that may be true, I feel that the well ordering property is a little more difficult to explain to less mathematically experienced viewers. Thanks for your feedback though.

@stevenfallinge7149 Месяц назад

Construction is actually very simple and easy, you just take the union of all those ordinals. For example, consider 3 = {0, 1, 2}, 4 = {0, 1, 2, 3}, and 5 = {0, 1, 2, 3, 4}, so the union of the set {3 ,4, 5} is the set {0, 1, 2, 3, 4}=5. The union of any set of ordinals is another ordinal, and equal to the sup of that set of ordinals. Of course, one needs to first prove that the union of a set of ordinals is indeed an ordinal.

@oflameo8927 Месяц назад

I think infinity towers are stupid because they don't describe anything. I want a proof that you can't always map your infinity tower to the continuum.

@stevenfallinge7149 Месяц назад

They are described rigorously as the union of all the finite towers. But that first requires understanding ordinals as sets (in considering them as Von Neumann ordinals), and then proving that the union of any set of ordinals is another ordinal, and in fact equal to the sup (least upper bound) of that set.

@Malachite_Jab Месяц назад

After Forever Is The End Of Math

@MrTrueseventh Месяц назад

excellent !

@huhneat1076 Месяц назад

adds one

@user-he2bo4zg9c Месяц назад

You deserve another sub

@robinhammond4446 Месяц назад

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 ?

@hongkonger885 Месяц назад

Damn, what kind of drugs are these methematicians smoking

@RandomAndgit Месяц назад

Cold hard math.

@superboiz50 Месяц назад

how about tree infinity

@ho-mw6qp Месяц назад

Forever after

@laylabaez5153 Месяц назад

60 seconds make a minute 60 min makes 1 hour 24 hours in 1 day 7 days in 1 week 4 weeks + 3 days in 1 month 12 months in 1 year 31 days in a month 365 days in a year 10 years in a decade 10 decades in a century 10 centuries in 1 millenium 1000 milleniums in 1 meganium 1000 meganium in 1 eon/giganium

@leethejailer9195 12 дней назад

Now talk about inaccessibles

@kachetofes Месяц назад

Please no bright backgrounds

@AbyssalTheDifficulty 27 дней назад

its not bright

@boscoyuen8970 Месяц назад

Where is absolute infinity?

@Axislimit2024_fg_and_more Месяц назад

ψ0(2) - Mahlo Cardinal - M ψ0(3) - Weakly Compact Cardinal - K ψ0(ψ0(ψ0…ψ0(K)….) K. K = Ω Absolute Infinity

@andersjimmy7368 28 дней назад

Meta Absolute Big Omega=Meta Absolute Infinity

@waffler-yz3gw Месяц назад

forever implies everything to happen ever, if anything came after it then "it" isnt forever, so the answer to the question posed by the title is no

@RandomAndgit Месяц назад

"What comes after forever?" "No." The whole point of the video is that there theoretically could be more after infinity which you would know if you actually watched the video.