Why 666 Isn't Cursed, But 6[6]6 Might Be

[@ComboClass]

Sorry, this episode is a bit cursed (haha?). If you do hate the number 666, please watch the whole thing before judging. In any case, I love you all, and check out the description for more info and cool links.

[@HHHjb_]

sandwich is a fun name for that idea, also you made me hungry

[@wyattstevens8574]

4:21 Squared- even 11³ is too much!

[@BaseSixBasics]

Hey domotro! What do you think about base six representing composite numbers versus base ten? What’s the pattern at larger and larger numbers?

[@ComboClass]

Yeah I accidentally wrote/said cubes instead of squares, but added a clarification in the description@@wyattstevens8574

[@ComboClass]

Base six is way better than base ten! I think it's the ideal base for humans. I think people could figure out many reasons why by studying some of my previous episodes, but I'll definitely also make an episode specifically about base six sometime in the future@@BaseSixBasics

[@calmkat9032]

Fun fact: 666 is probably considered the "number of the beast" because in Greek, if you assign 1 - 24 to Alpha - Omega, and you add the letters' values of Nero's name, it adds up to 666. This is supported by the fact that early transcripts of the bible when it was first translated to latin use the number 616, which is the value using that language. Also, this was often done by Jews back in that time, called "Gematria". So, there's not just the version of 666 to be afraid of in other bases, but also other languages!

[@cameronbigley7483]

I'm happy to finally have a potential reason for 666'a significance. Thank you.

[@tilnation14]

I found this, "Nero, whose name in Hebrew has the numerical value 666, if it is spelled nrwn qsr." but that isn't Greek and idk how that's supposed to "have a numerical value of 666", even with Gematria I took his full name, in Greek, and did what you described, but it ended at only 482; Nero Claudius Caesar Augustus Germanicus -> Νέρωνας Κλαύδιος Καίσαρας Αύγουστος Γερμανικός, 13 + 5 + 17 + 24 + 13 + 1 + 18 + 10 + 11 + 1 + 20 + 4 + 9 + 15 + 18 + 10 + 1 + 9 + 18 + 1 + 17 + 18 + 1 + 20 + 3 + 15 + 20 + 15 + 19 + 15 + 18 + 3 + 5 + 17 + 12 + 1 + 13 + 9 + 10 + 15 + 18 = 482, so I started looking for actual sources, like above

[@litigioussociety4249]

It's not representing 1-24. It's using a system like Roman numerals but with Greek or Hebrew instead. If you use the Greek or Hebrew system it's the addition of (200+60+100)+(50+6+200+50)=666. Using Roman numerals one fifty drops out, and it's 616, which at least one early manuscript of Revelation contains instead. Regardless, it's not a direct reference to Nero, because Christian and secular scholars unanimously agree that Revelation was written after Nero was dead. The apostle John is instead using it as a comparison to say the antichrist will be like a worse Nero. This is a common thing in the Bible, because the Old Testament has many people who have similar lives in regard to delivering the people, but not fully doing it as the Messiah is promised to do.

[@DuringDark]

​@@litigioussociety4249damn, if Nero's famous for his fiddle I wonder what instrument the antichrist plays. Extrapolating from satanist culture my guess is a mean electric guitar

[@sinom]

​​@@tilnation14as to how that is greek. It is Greek transliterated (aka letter for letter replacement into a different language based on the sound they make) into Hebrew. The original is pronounced "Neron Caesar" which is then transliterated into נרון קסר which if you write it in Latin script is Nrwn Qsr because Hebrew does not write most vowels. נרון קסר can then be interpreted as numbers, since every one of these letters represents a number in ancient Hebrew. This results in 200 60 100 50 6 200 50. Adding all of those up gets you 666. If you instead of using the Greek "Neron Caesar" take the Latin "Nero Caesar" this means the Hebrew transliteration becomes נרו קסר or Nrw Csr. As you can see the only letter that disappears is ן which represents the number 50. This means we now get 200 60 100 6 200 50 which sums up to 616. Now you might ask why ר and ן both represent 50. Both of them are the same letter, just ן is the version used at the end of a word while ר is the version used everywhere else (think the two different ways of writing s in cursive for in a word and at the end of a word).

[@luckss4659]

please do not burn down your house

[@connorgibes709]

Fr, we will all still watch even if every video isn't a fire hazard

[@ComboClass]

OK thanks for the suggestion, I have now decided to not burn my house down. Just kidding, yeah I'll be safe haha.

[@TymexComputing]

Nor garden and for sure not that squirrel :)

[@asheep7797]

@@ComboClass"i will not burn down my house. just kidding."

[@itisALWAYSR.A.]

End of video: "maybe it's cuesed because after making this video I burned myself" Well I certainly couldn't have seen that coming

[@KirkWaiblinger]

This man is a landlord's worst nightmare

[@Giantcrabz]

good

[@sootish]

fun fact: whenever you upload, i go into my friends dms and tell her that 'CLOCK GUY UPLOADED' thank you for the wonderful video, clock guy

[@17388]

i love ur channel so much i cant believe how underrated u are. even w viral shorts i guess people resist jsut how fun math can be. truly one of the best channels out there right now

[@pujalte5508]

That's actually so true. He makes incredibly interesting videos that don't get as much attention as they should.

[@dj_enby]

The 666 coincidences coming out of your jacket were so cool! I love fun patterns like that

[@iamdigory]

I'm a Christian. I do believe that 666 is the number of the beast. It is meant to help Christians identify the beast (it was probably Nero). But that does not mean it's evil. No number can possibly be evil, all of them perfectly fit together in the beauty of math, which itself is part of God's own character. In addition, if it helps point out who the beast is, than it's a really helpful kind number, like an antibody or a fire alarm.

[@ComboClass]

While I don't agree that 666 represents the "number of the beast" in numerology or otherwise, I do appreciate the comment and your thoughts! :)

[@yeahaddigirl]

You'd both get excommunicated from my previous church lol

[@eugeneimnotgonnatellyoumyl5513]

Speaking of fire alarms...

[@Willy_Tepes]

The anti-Christ has not yet come and claiming that is was Nero is just a way of fooling people. Revelation is clearly about our time.

[@sykoe360]

Awesome content and hilarious as always 😂 Love your stuff bud keep it up

[@ComboClass]

Thanks! :)

[@KStarPR]

I'd love to see a series where you tell fun facts about whole numbers, starting from zero and such. Even more props if non-mathematic stuff like superstitions and pop-culture phenomena like 4 being Japan's version of 13 for us, 420 being "the weed number." or something like how octo is 8 but October is the 10th month.

[@ComboClass]

Yeah I've considered doing a series where I try to go up analyzing hundreds of whole numbers one at a time from zero upwards (or perhaps another number downwards) haha, although it would probably be in the form of shorts or a podcast or something. Hopefully I'll find a way to incorporate that before long

[@KStarPR]

@@ComboClass Wow I honestly didn't expect a reply, nonetheless the fact you'd considered exactly that. I wanted to do something like that myself, but in my current situation it'd be a bit too tall of a task (plus I don't have nearly the mathematical knowledge & understanding you do 😅) Regardless, best of luck! It'd be neat to see how the chaotic nature of your videos would translate to other formats.

[@Krishna-Govender]

But what happens when he gets to rule... er... I mean number 34? 😂

[@ComboClass]

Feel free to try an "analyzing whole numbers" series yourself too if you'd like! I don't know when I will, but it's a goal for someday. Also, I do actually have a "bonus" channel (with more subscribers than this one) where I put out shorts and livestreams and stuff in somewhat different formats than this "main" channel. In case you haven't seen that it's @Domotro @@KStarPR

[@smergthedargon8974]

@@ComboClass Not shorts, please. I hate shorts.

[@iamdigory]

I love 27 because it's 3[3]3, which is 3 3s, but it's not boring like 1, or unimaginable like 5[5]5[5]5

[@simonwillover4175]

Me, my friend 7[7[7[7]7]7]7, and my best friend 13[13[13[13[13[13[13]13]13]13]13]13]13 sitting on the porch, eating some ham & cheese sandwiches: 😄

[@tristantheoofer2]

hell yea 3^3. aka 27. and then theres 4[4]4... which is already 10^(8.072304726*10^153)... what the fuck

[@Willy_Tepes]

555 is pronounced hahaha in Thai.

[@cameronbigley7483]

Googology is extremely interesting. There's an online database called "Pointless List of Gignatic Numbers" or something of the sort that shows many googology concepts. And a Fun Fact: No standard integer has a "j" or "k", and "c" is the last letter to appear, as in octillion.

[@Ak-sm2qu]

Can't believe they forgot about kajillion smh 😔

[@barrianic4]

what about killillion and mejillion

[@cameronbigley7483]

@@barrianic4 Those aren't "standard" numbers. I can't think of the exact definition, but I know the googology ones don't classify.

[@christopherknight4908]

6[6]6 seems like one of those numbers that perfect knowledge it existing within a human brain would result in a black hole.

[@mr.duckie._.]

you cannot grasp the true form of 6[6]6 !!

[@TheMagicFellow]

Love these videos focusing on a single number, like the golden ratio episode! Also was not expecting 18:46 lol

[@pe1900]

please go further into insanely big numbers, i would love a whole video explaning how BEAF works

[@littlered6340]

WHOO IT'S MY FAVOURITE MAD MATHS GUY

[@littlered6340]

Mans stopped bases at 12 instead of 16 😭, the best base 😭

[@Frisko555]

Are there negative hyperoperations? -1 being subtraction, -2 being division, and so forth?

[@thecameron3996]

And would they be called hypooperations?

[@AutumnWynds]

Hello Combo Class, you are always a delight to encounter on my feed. I have loved speaking about topics similar to this with friends, and the way your videos run you seem like you would fit in with my friend group as well haha. At any rate, one topic I haven't been able to figure out how to breach and properly build up to is 0#. I am absolutely enamored with the idea that a number can be proven with ZF but once you add the axiom of choice (ZFC), it no longer becomes a possible number. I usually leave it at that, but I do like the construction of the number as well. Anyway, no idea how to end this comment. Love your content!

[@anglaismoyen]

What's 0#?

[@AutumnWynds]

@@anglaismoyen 0#, or zero sharp, is an uncountably large cardinal number. It has a lot of interesting implications about constructibility, specifically the relation between all sets possible and all sets that can be constructed. I suggest reading more in Cantor's Attic, and there are a couple papers on arXiv about the topic as well. I wish I could explain better, but that is what I mean by my original comment lol there is a lot of foundation to it that is pretty technical

[@ryanoftinellb]

6[6]6 is an unlucky number. That's why I always avoid the 6[6]6th floor in my building.

[@itisALWAYSR.A.]

It's like the Eagles sang that time: You can check out of the Infinite Hotel any time you like, but you can never leave

[@trenza2566]

15:48 and it's still closer to 0 than infinity

[@rose_no]

I never realized six hundred sixty six had so many properties! (I wonder which number is the first number without any properties. Would be an interesting property to have. /j)

[@CastorQuinn]

For the first time I think I actually grasp what happened to Georg Cantor.

[@mistafizz5195]

I love how you always just have random shit burning in the background I also love your channel

[@oli1181]

Fun fact: there are 666 fun facts about the number 666, but does that include this fun fact?

[@815TypeSirius]

I swear @acollierastro used your funky music in a video. Shes cool.

[@hkayakh]

I like the aesthetic you setted with the candles

[@xyz.ijk.]

I love your channel, and we all enjoy the entertainment, but not at the expense of your safety and good health. It takes the joy out of it if you go too far. We’re not your parents, but we’re also not children. I don’t know how else to put it without overstepping, but there it is.

[@stanimir5F]

A fun episode! The amount of chaos in our videos grows faster than the numbers in your Sandwich sequence! :) Although I was surprised to see how many different "types of numbers" there are and how pointless some of those properties are. For example "polite" number?!?!?! I have never heard of it and when I googled to see what this is: according to wikipedia it is: "In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers. A positive integer which is not polite is called impolite. The impolite numbers are exactly the powers of two, and the polite numbers are the natural numbers that are not powers of two." And even that is wrong because not all squares are "impolite" but only the even squares which shows how little people care about them otherwise it would have been corrected :D

[@floppy8568]

16:14 the time he actually panicked due to his class being in a mess, and that's on FIRE

[@ComfyBasilisk]

"probably no human will ever know the first digit of 6[6]6," huh? well, if represented in binary, the first digit is definitely 1.

[@juliavixen176]

Do you know how many digits come after that one?

[@ComfyBasilisk]

@@juliavixen176 of course! that's floor(log2(6[6]6) -1) c:

[@docopoper]

I wonder if numbers this large have interesting numerical properties like 666 does.

[@ComboClass]

Smaller numbers have “more” cool facts we can describe about them, so numbers like 6[6]6 might not be as simple as being things like sums of consecutive squares or primes, but I’m sure they do have some fun facts of their own!

[@oida6599]

Awesome! Just to make sure I understood the concept: Does that mean that, while 1[1]1 is 2, 1[n]1 is always 1 for n>1?

[@ComboClass]

Yeah, hyperoperations have some interesting properties, like 1[n]1 for n>1 does equal 1, and 2[n]2 alway equals 4, and then the describable properties start to dissolve as the larger numbers emerge haha

[@littlered6340]

This post (specifically the 2[n]2) shocked me so I found this Wikipedia page, which lists some of the notable cases. en.m.wikipedia.org/wiki/Hyperoperation

[@ChiefMakes]

Knowing math there is probably some super advanced logical reason for all those number patterns equaling 666

[@muhammedsaiduzun8725]

"666 is not cursed" Gets seconds away from burning his house down multiple times

[@briangronberg6507]

Is that the Basel problem and the Riemann zeta function I see!?

[@kittybeans8192]

Something I've wondered about off an on, what about using noninteger values for the hyper operation? Such as 3[1.5]3 or 3[2^0.5]3 or 3[pi]3? I originally wanted to plot a graph of integer hyper operations so I could try to find some kinda best fit curve but well, it's hard to do anything meaningful with like 4 data points... I bet there's a sensible answer, but I'm not smart enough to figure it out yet. At the very least, I feel kinda confident to claim that 1[x]1 for x from 1.0 to 2.0 must go from 2 to 1. Seemed kinda interesting. Since 1[1]1 is 2, but 1[2]1 is 1, so the result is actually decreasing as x increases in that range. And of course for any x greater than 2, 1[x]1 is 1. If [0] is division, then we could think about graphing 1[x]1 for x from 0 to 2, as this tiny blip that starts at 1, rises to 2, and returns to 1 for the rest of infinity on the x axis. Another neat thing I suppose, is that 2[x]2 for any x greater than or equal to 1, is always 4. 2+2 is 4, 2*2 is 4, 2^2 is 4. It's like this little stable column of 4's that runs infinitely through this 3D space of numbers, but at 2[0]2 it comes back down to 1 of course... Though I guess I'm making a few assumptions here, first is that the results for a[x]a for x from one integer to the next integer, must all be somewhere between a[x]a and a[x+1]a. I imagine that's a reasonable assumption to make but if I'm being strictly honest, I don't really know. (And that those values are in ascending or descending order) And second is that [0] is division. It probably is, or should be, but remember addition is just shorthand for repeatedly adding one. I just struggle to imagine some operation that is the "building block" of adding 1 in the same way that addition is the "building block" of multiplication, etc.

[@peppermann]

Great video, loved all the 666 identities! And the googology too 😎👍👏

[@unilajamuha91]

Pretty bold words for someone who said that connect 4 is too hard for a human to play perfectly

[@nartoomeon9378]

I've heard of an interesting hypothesis about a Burnside groups : if we have 2-generated group < a, b | xⁿ=id >, it may be infinite, if n=665 or greater odd integer. Not 666, but very close😅If in one day someone proove, that < a, b | x⁶⁶⁵=id > is finite, we can write " it may be infinite, if n>666 and n is odd".

[@JimmyMatis-h9y]

"Layers of representation" reminds me the tenant of philosophy wherein trying to describe something with words is just a layer of abstraction rather than the thing itself. I wonder if this wouldn't serve as a basis for settling the debate over whether or not it's possible for us/our physics (science) to eventually know/understand everything given sufficient time to study the universe?

[@JimmyMatis-h9y]

Reminds me of *

[@orisphera]

I think the layers of distancing is a bit like ordinal numbers. I mean the generalisation of the number of things to well-ordered sets

[@ultimateo621]

This would have been a perfect halloweeen special

[@fermata4425]

Another fun property of 666 (although one could argue it's more of a property of 665) is that the quotient of (3/2)^666 divided by 3/2 times a certain power of 2 (namely 389) is incredibly close to 1. An interesting musical consequence of this is that 665-tone equal temperament (in which the octave is divided into 665 equal intervals instead of the usual 12) contains a better approximation to a just perfect fifth (represented by a frequency ratio of 3/2) than any equal temperament before it! In the world of advanced music theory, such tiny differences between rational numbers are called commas, and this one, due to its relatively close ties to the number 666, is called the *Satanic comma.*

[@Sam_on_YouTube]

And of course, as with any number of that size, if you could hold the whole thing in your brain at once, the amount of energy used to store it in that space would cause your brain to collapse into a black hole. It would literally destroy you from the inside out.

[@machitoons]

the whole 666 and 616 thing sprung up from counting the letter values together of various names, so really it IS about the quantity 666 and not the numerical representation alone, at least how far I understand

[@dizzylilthing]

I'm a history/arky/anthro major minor, the concept of base 10 and stuff makes my skin crawl this is a greater perversion than macroeconomics

[@bradmitchell3831]

666 is polite and pernicious you say? That seems like the definition of evil to me ...

[@VelaiciaCreator]

I was gonna say that the fire in the intro was a bit on the nose, then I remembered what channel this is and that fire doesn't really mean much here.

[@barrianic4]

11:54 that 4[4]4 is called tritet jr.

[@meepletpie1234]

some of the fastest clicks of my life

[@mr.bulldops7692]

Big ups to Carlo for putting is life on the line, and having a garden hose at the ready.

[@ComboClass]

Yeah it’s Carlo (not carlos) by the way, but he certainly deserves a huge shoutout!

[@mr.bulldops7692]

@@ComboClass Thanks! Fixed! Sry, Carlo!

[@ДмитрийБаженов-ш6т]

4:26 squared, not cubed

[@username_not_found6926]

14:43 what about 1^6

[@awlomthesheepermen]

>talks about a cursed number >has giant fires in their fire openly

[@awlomthesheepermen]

Was I tired?

[@albertodelaraza4475]

Might be beyond the scope of this video or perhaps this channel, but I've always wondered what is the formal process of comparing insanely large numbers such as 6[6]6, Graham's number, or another popular number on KZbin, Tree(3) with each other? For example, we're told that Tree(3) is way bigger than g64. How did mathematicians determine that? And, BTW, how does 6[6]6 compare to Tree(3)? It's just curiosity for its own sake.

[@ComboClass]

I have been looking into questions like this to try to compare the “sandwich sequence” I hinted at with other sequences. With some comparisons, it is currently nearly impossible to compare. With others, it is possible to find inequalities based on hierarchies of sorts. This will probably show up in a future episode

[@AjanBaftiari-hi3zp]

17:45 had me stutering in amazement

[@Giantcrabz]

i find a like to view ratio > 5℅ is an indicator of Great Success and Prosperity

[@menjolno]

12 might be a better base, but you end up losing your ability to choose random numbers due to how easy the divisibiliy rule is to coincide

[@ComboClass]

Not sure which type of random number generating you're talking about, but in general switching to base six or twelve wouldn't dramatically change anything of that type. Ten is a relatively divisible number for its size too, just not as much as six or twelve

[@menjolno]

@@ComboClass human generating random numbers. In base 12, people would fear too much that their number that they thought of would be too divisible or something. It is just like how so many people choose 3 when asked about a random number 1-10

[@levoyant1754]

Will you talk about the theories on number ?

[@Salsmachev]

Biblically speaking, 666 is just a coded reference to Emperor Nero. In fact, some ancient copies of Revelation contain a scribal error where the number is not 666, because the writers of those copies used the Greek name Neron instead of the Latin Nero. The numerical equivalent of the name was slightly larger when it was based on the Greek version to account for the added n. Basically the entire book of Revelation is a coded political text about the Roman Empire's past persecution of Christians and newfound tolerance for them under Constantine. So unless you're worried about Roman Emperors who have been dead for centuries, 666 really needn't be that concerning.

[@Fire_Axus]

4:00 also base dependent

[@EvanEscher]

How can you tell your two cats apart?

[@DuringDark]

where are the really big numbers domotro, you can't hide them from me forever

[@xx-go8yh]

I remember as a kid when my dad opened up his wallet and showed me his google plex math proof sheet showing it would take ~8 universes full of onionskin to print that number out. And to think other kids' fathers just cracked their wallet open and then showed their kid their condom they didn't use, leading to the kid's existence. I didn't completely get it so I got beaten again, It was another bad day in 1st grade.

[@mr.x991]

Almost the last Combo Class video 💀💀

[@Sam_on_YouTube]

Those who fear 666 for religious reasons fear the quantity, not the symbols. The number comes from an additive system from Hebrew. It is the same size in our standard Indo-Arabic base 10 numerals or any other system.

[@floppy8568]

What would 6 hexated to 6 look like?

[@apersonwhowantstoread4137]

the number 666 is a symbol in the bible, the number isn’t evil it just represents something evil (sometimes in some translations 616) 7 represents completion, 7 doesn’t mean complete but it represents it because of 7 days in a week. I quite like the number 666. good video

[@Enlightenment0172]

is 666[666]666 even more cursed?

[@justfeeldbyrne2791]

I wanna code something that calculates these numbers accurately

[@mysterfan7649]

I will keep on mind : 4 or 13 . I am not Christian but refer 666 as devil's number as unintentional. The reason I was try to find an another unlucky number that isn't devil and then my teacher ending up giving me 13. I have ending up saying a 100 time for devil's number. Some did Satanism and I just throw off a fib.

[@demonking86420]

Why 4? That's only a pernicious number in East Asian cultures because for some reason the Chinese used the same word for death...(Which led to the Koreans and Japanese importing that loan concept when their civilizations started, but Japan at some point swapped the word for 4)

[@mysterfan7649]

@demonking86420 i am not that numbers any nore. I don't have an unlucky number

[@somewhatblankpaper1423]

Now, time to consider 9[9]9 the Australian counterpart of 6[6]6

[@bjorntorlarsson]

One day, that cat will eat the squirrel.

[@morssocio8324]

*in the name of crossed swords* "or something else other then swords,like how the ancient eqyptains used in depictions or is it the scythe and wheat" i dont think the number 666 matters its just the entrance to an labyrinth of thought which is also connected to the beast,the beast waits in the middle. or jus maybe te malaria outbreak that was happening back in the day and other things inspired revelations.

[@Felipe-sw8wp]

Is your cat's first name Pete by any chance?

[@ShaneSemler]

Hobbit mad scientist living in filth with cats. Subscribed!

[@JohnWayne-hq1ns]

6[6]6 has... about 6[6]6 digits. Taking log_10 of such a large number loses meaning. For an analogy, adding 1 to a googolplex is "about googolplex".

[@EllyCatfox]

Gteat video. I came from a video about internet math that had 666 comments and this was the "next up" video.

[@Baseded]

Despite my fairly Biblical beliefs ''that are not so orthodox'' I actually don't know why people fear the number 666. If 666 made a good enough number base I may consider it but my favorite base of all time is base 120. In this base 666 would be written as 5 followed by what ever symbol you choose to use for the numerical value of 66. With a mixed radix it may be written as 556 that's 120 x 5 + 12 x 5 + 1 x 6

[@barnabasrsnags4828]

Because some bible passage says the mark of the beast is 666. Thing is what they meant probably wasnt even 666 but something that was later on interpreted as such

[@kygrus]

you should do a crossover episode with numberphile

[@lePirateMan]

As an avid incremental game player I know my exponentially

[@qondonyon]

0:00 what WHAT WHAT THE FIRE ON WOOD AND OTHER FLAMMABLE THINGS

[@kenaniahmc]

so what's the first digit? ikyk

[@netiosys4677]

Technically, if you used base 6, you'd know that 6[6]6, or 10[10]10 as it'd be written in base 6, starts with a 1 and ends with a 0.

[@ComboClass]

True, the first digit of n[x]m in base n would be simple, but in most bases would be nearly impossible to check

[@samuelgonzalez8480]

Gee you were pretty lucky those base 11 and 12 numbers didnt happen to have their hypothetical 11th or 12th digit

[@williamhills6927]

so, you know that type of infinite number where the number of types of infinite number that are smaller than it is that type of infinite? aleph base aleph base aleph etc.. if you applied it to x[x]x, how would you represent the number of types of infinity smaller than it? is that even a valid question?

[@juliavixen176]

Aleph⁰ and Aleph¹ are not really "numbers" and are more like a logical statement about sets. So, using them like a you would use a regular (finite) number isn't really defined, as far as I know. But... there is the power set operation, which, in a sense, allows you to combine infinite sets together to create even "bigger" infinite sets. You can make Aleph², Aleph³, ... up to Aleph^Aleph or something, and then an infinite tower of those, I forget the exact details now, but there is a Wikipedia article about this.

[@sicko_the_ew]

Ah! But the encoding contains a secret message that only becomes clear when a something like a prophecy comes true ... (Try Greek or Roman digits - maybe with some adaptations to cope with their limitations and then notice that Ramanujan has not yet arrived.) (Hmm ... what were the Hebrew digits, I wonder?)

[@charlievane]

6[6]6 is just 10 in base 6[6]6

[@seanewing204]

∞ [∞] ∞ = ∞. But, some infinities are bigger than others. The largest of these would be ℵ ͚.

[@michaelwinter742]

666 is each of the Roman numerals added together. 1000 is DD = M

[@wyattstevens8574]

6^^^^6 is huge: n arrows in a row means x[n+2]x.

[@Nik.leonard]

How many sandwiches will be needed to reach TREE(3) size?

[@ComboClass]

I don't know! TREE(3) is very hard to compare to other hyperoperation-esque heirarchies of sequences. But when I show my sandwich/supersandwich numbers further in another episode, maybe some commenters will have some educated guesses. There are some sequences I've developed where I think that their 3rd element would possibly be bigger than TREE(3) but hard to say

[@davidfinton]

Based on what little I know from this video, it would take approximately TREE(3) sandwiches to get to TREE(3)

[@Xnoob545]

​@@ComboClasshave you seen "Ultimate List of Large Numbers 2024" by Douglas Shamlin Jr. TREE(3) seems to be smaller than I expected.

[@X3MgamePlays]

Aaaand yet another way: 6*6*6 + 6*6*6 + 6*6*6 + 6 + 6 + 6 = 666 Now I can only wonder what 6[6]6 would be like.

[@lordmaster6667]

aren't all square numbers polite numbers?

[@stickfiftyfive]

No.. but all of them are except for those which are powers of two. All Triangular numbers >1 are polite though.. Triangular numbers are the subset of Polite numbers which begin at 1.

[@lordmaster6667]

@@stickfiftyfive triangular numbers is what i mean, thank you.

[@stewartbugler]

Ya gotta be kidding me... A few weeks ago I was exploring this method I came up with for building areas for games. Essentially if Ya go by a level progression of rooms. Level 1 is a room level 2 is 2... etc... You could only build certain ways to be a square area. N this adding 1 to 8 gets ya 36 the first plausible area of exponential room size. It had me wondering though where is the next one... It took a while to find the next one and I noticed 36 would always be a part of a lot of things like this... So I wondered what's a 36² level progression up to... I left it at that but your telling me it's 666? I must build this hell.

[@Spikeba11]

6[6[6]6]6 has a last digit of 6.

[@thebrownfrog]

Great video!

[@PSwayBeats]

1 ^ 10 ^ 10 ^ 10 ^ 123 the probability of us and our universe existing the Penrose number is by far my favorite

[@japanada11]

Yes I suppose it is true that we exist with probability 1

[@TheRenaSystem]

WE WANT THE SANDWICH SEQUENCES

[@NyanCat-dn5jb]

What is the black cat's name. Edit: SASSAFRAS.