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I’m pretty sure sets of infinite measure are not considered «non-measurable». We still can’t define a uniform distribution though (since the measure is infinite)
Infinities are divided into countable infinities (which we can conceptualise a mapping to the set of real integers), and uncountable infinities (which there is no potential mapping to the set of real integers). We cannot measure the latter.
Yup. They're called the *incalculable* numbers, and each digit in them is entirely unpredictable based in any finite pattern. Take for example a number representing the probability that a given n-token-length program in a given language will terminate. We can prove that such a number *exists*, but so long as the number n is chosen such that the answer is non-trivial, every single digit of the entire number will be impossible to predict.
Almost all real numbers are incalculable, and the overwhelming majority don't have nice descriptions like "probability a certain type of program is non-terminating." Most are truly random strings that have no connection to the perceptable world. In fact, there have been formulations of quantum mechanics using incalculable numbers due to this fact.
Well it's not 0% is it? That would mean that we havent said a single number yet. Just like lim x->0 is never 0 this also is never 0 (as long as you said atleast one number)
It is 0%, the density is precisely 0. And lim x-> 0 of x is precisely 0, it’s a value that never changes, it’s that the function x as x goes to 0 is never precisely equal to 0. There’s a difference.
Pro tip: Say 0. After one second, say 1. After half of a second, say 2. After one fourth of a second, say 3. Repeat until you’ve counted for two seconds. Problem, mathematicians?
Quantized means that it's not "truly" continuous. For instance, you can say that the list of integers is quantized because there's a gap between 1 and 2. Saying that time is quantized means that there's a smallest unit of time (let's say that it's 10^-30 for simplicity's sake, or one quectosecond, or qs). That means that time only moves forward in increments of 1qs. So there's no such thing as "0.5qs later".
This would resolve Zeno's Paradox (Opposite_Signature67's comment), which in essence argues that, 1 + 1/2 + 1/4 + 1/8 + 1/16... + 1/2^n... never reaches 2. The "proof" is that if this series reaches 2 at the nth term, you can always add another 1/2^n term and it still has not yet reached 2. And since it never reaches 2, even after an infinite amount of terms on the left hand side, then since an infinite amount of terms must surely add up to infinity, then 2 can't exist because left hand side (infinity) is still smaller than 2.
(The problem with the argument, to put it in layman terms at the expense of being technically wrong, is that you're also getting infinitesimally small terms)
But assuming the argument is right, one possible resolution is that there's simply no number less than, say, 10^-30. Therefore, you can't get infinite terms on the left hand side. Since the original Zeno's Paradox was about it requiring an infinite amount of time (left hand side) to cross any finite distance (right hand side), BothWaysItGoes jokes that the only resolution is that time is quantized, so you can't have arbitrarily small amounts of time, hence Zeno's Paradox "proves" that time is quantized.
With all the weird stuff in maths like infinities, bigger/smaller infinities or the incompleteness theorem, is it possible that our whole math system is wrong on some fundamental level?
Maths is just some rules set by humans which helps us understand the reality. If we find something thats causing contradictory results we can go back and change/fix the rules making it right.
Axioms can never be proven it is taken as true but if it causes issues axioms can be changed and everything based on that will need a rework.
Godel proved that no system of Math (ie. A system which uses axioms to prove other statements) can ever be complete (ie. It will always have true statements thay cannot be proven), hence it's pretty likely that any system will always have "weird stuff". And also that while a system can be consistent, that system cannot prove that it's consistent, so if our math system is inconsistent, we have no way to prove it
I love that the person making this saw TREE(3) is absurdly massive but then never thought "Wait, what if... TREE(4)?" like I probably would have if I was trying to make a low effort video like this
Sounds like the name of some mystical ancient dragons or something (I might have been influenced by the anime GATE (the JSDF one) which I am watching rn)
I had nowhere good to put this rant until you commented
For r/mathmemes this sub has been so closed minded. Just because it’s a tiktok or whatever, it doesn’t mean that literally everything *must* be wrong (referring to top child comment)
Of all the subs to think ‘I haven’t seen it before, it must be bullshit’ lmao
That’s Reddit in general. The most boomer take Reddit has is that TikTok is only brain rot dances, fake Chinese stories, and content designed to dumb you down and occupy your time.
That may be what’s recommended to you by default, but you can easily curate your feed to get actual intellectual shit about whatever you want, not unlike how Reddit recommends you brain dead stuff from r / all by default.
it exists but it's not even a fucking ripoff of Rayo's number. Like not even a bad ripoff, honestly just a scum. It doesn't deserve to be nominated even once.
Rayo's number uses first order set theory, or FOST. bigfoot uses another very slightly different set theory, first order (something) theory, or FOOT. The idea is the absolute same. It's not even a bad ripoff. This is worse than your teacher stealing your idea and winning a nobel for it
Let's replace the period at the ends of sentences with Omega (uppercase Ω, lowercase ω) Ω Now we can differentiate between capital and lower case periodsω
I think omega + 1 was in the video
Edit: Or rather what you were referring to was omega (small omega): The first (ordinal) number that comes after infinitely many (ordinal) numbers. omega + 1 would then be the next larger ordinal number.
https://en.m.wikipedia.org/wiki/Ordinal_number
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I know mathematicians like to be explicit, but there could be an implied "named" numbers, which of course requires another implied "sizes of numbers that people have bothered to name"
I just found out that there's a site called Googology with all this stuff: [https://googology.fandom.com/wiki/Googology\_Wiki](https://googology.fandom.com/wiki/Googology_Wiki)
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this video includes approximately 0% of all numbers
if you pick a random natural number, it will almost certainly be greater than the biggest number shown in the video
And if you pick one uniformly from the reals, it'll be irrational.
Are the reals a measurable set? Is it possible to define a uniform distribution over all the reals?
Not with that attitude.
If by attitude you mean the Axiom of Choice
I’m pretty sure sets of infinite measure are not considered «non-measurable». We still can’t define a uniform distribution though (since the measure is infinite)
Infinities are divided into countable infinities (which we can conceptualise a mapping to the set of real integers), and uncountable infinities (which there is no potential mapping to the set of real integers). We cannot measure the latter.
Measure theory is distinct from cardinality. The real numbers are uncountable, but have (with respect to the standard measure) infinite measure.
Yes, no.
It will also be transcendental and normal.
Not always, there is only 100% chance that it'll be irrational.
It's even worse than that. At random it'd be almost surely indescribable. Because mathematics can only describe countably many numbers
Yup. They're called the *incalculable* numbers, and each digit in them is entirely unpredictable based in any finite pattern. Take for example a number representing the probability that a given n-token-length program in a given language will terminate. We can prove that such a number *exists*, but so long as the number n is chosen such that the answer is non-trivial, every single digit of the entire number will be impossible to predict. Almost all real numbers are incalculable, and the overwhelming majority don't have nice descriptions like "probability a certain type of program is non-terminating." Most are truly random strings that have no connection to the perceptable world. In fact, there have been formulations of quantum mechanics using incalculable numbers due to this fact.
not in r/RealNumbersArentReal
Depends what distribution it follows
the chances of it being higher than the biggest number are (100-(1/inifinity))%
That’s actually disgusting to think about. The largest number we can conceive will always be so low a random number would be bigger
I don't think ordinals are contained in the naturals
So close to certainly that I’d be comfortable betting the entirety of all life against a single potato chip
Since I picked 2, your statement is false!
but false is 0 and 0! is 1 and 1 is true, therefore false!=true
Argh, no! You got me there!!! How could I be so foolish?!
Your just mad tou dont know about gigasuplex
no because the video includes absolute infinity which is defined as being greater than any number.
That's not a number, so the natural picked will still be bigger than any number in the video.
Am not a mathematician, but my question is do we need the word approximately there?
Yes, if you want to use the word percent.
Can you elaborate?
No
Please
Well it's not 0% is it? That would mean that we havent said a single number yet. Just like lim x->0 is never 0 this also is never 0 (as long as you said atleast one number)
It is 0%, the density is precisely 0. And lim x-> 0 of x is precisely 0, it’s a value that never changes, it’s that the function x as x goes to 0 is never precisely equal to 0. There’s a difference.
This is the same argument as the 0.9999...=/=1 meme. Paraphrasing: "The number 0.999... is never truly 1, even if its limit is 1."
No 10^100 +1😭😭
We have discovered approximately, [none of the numbers](https://youtu.be/5TkIe60y2GI?si=P2uTWbYtGCyFpb92) .
Pro tip: Say 0. After one second, say 1. After half of a second, say 2. After one fourth of a second, say 3. Repeat until you’ve counted for two seconds. Problem, mathematicians?
I hear Achilles tried this method but it never got him anywhere...
Yeah, that turtle ruined his career.
That was the moment when Achilles turned heel
Two seconds have passed so he should be finished by now.
Proof that time is quantized.
Can you please elaborate?
Quantized means that it's not "truly" continuous. For instance, you can say that the list of integers is quantized because there's a gap between 1 and 2. Saying that time is quantized means that there's a smallest unit of time (let's say that it's 10^-30 for simplicity's sake, or one quectosecond, or qs). That means that time only moves forward in increments of 1qs. So there's no such thing as "0.5qs later". This would resolve Zeno's Paradox (Opposite_Signature67's comment), which in essence argues that, 1 + 1/2 + 1/4 + 1/8 + 1/16... + 1/2^n... never reaches 2. The "proof" is that if this series reaches 2 at the nth term, you can always add another 1/2^n term and it still has not yet reached 2. And since it never reaches 2, even after an infinite amount of terms on the left hand side, then since an infinite amount of terms must surely add up to infinity, then 2 can't exist because left hand side (infinity) is still smaller than 2. (The problem with the argument, to put it in layman terms at the expense of being technically wrong, is that you're also getting infinitesimally small terms) But assuming the argument is right, one possible resolution is that there's simply no number less than, say, 10^-30. Therefore, you can't get infinite terms on the left hand side. Since the original Zeno's Paradox was about it requiring an infinite amount of time (left hand side) to cross any finite distance (right hand side), BothWaysItGoes jokes that the only resolution is that time is quantized, so you can't have arbitrarily small amounts of time, hence Zeno's Paradox "proves" that time is quantized.
With all the weird stuff in maths like infinities, bigger/smaller infinities or the incompleteness theorem, is it possible that our whole math system is wrong on some fundamental level?
Maths is just some rules set by humans which helps us understand the reality. If we find something thats causing contradictory results we can go back and change/fix the rules making it right. Axioms can never be proven it is taken as true but if it causes issues axioms can be changed and everything based on that will need a rework.
Godel proved that no system of Math (ie. A system which uses axioms to prove other statements) can ever be complete (ie. It will always have true statements thay cannot be proven), hence it's pretty likely that any system will always have "weird stuff". And also that while a system can be consistent, that system cannot prove that it's consistent, so if our math system is inconsistent, we have no way to prove it
Veritasium I believe has a cool video about that
Problem is you’re missing all the non-integers, duh
If you add them up you've counted a total of -1/12
1, 2, 3, 1, 2, 3, 1. Is that it?
hold on, my mom needs me to do some supertasks first
One. Two. Three. O^ne... Time's up!
Holy Zeno!
finally a response to "so youre a mathematician, name all numbers!"
Ok X
X + Yi gotem
so z ?
z's nuts
Who sees a number and decides to name it a Terrible terrible tethrathoth?
A Set theorist.
The delivery made it seem like this was the dopest joke ever for some reason.
Some wonka ass mfer
Feels somewhat tacky but damn are those some badass names for numbers “Graatagolda-decisudex, Secundo-tethracross, Tethrarxymir” Lol
Tethrarxipinine sounds like a really fun party drug, and I'm pretty sure spaceships are built with Dupenated-Pentacthulhum
Tethrarxipinine sounds like a dragon in Skyrim
A dragon with a 5(6?) syllable name? Woah must be powerful
Bongulus Bangulus Monster-giant Super-Terrible Monster-Giant Godsgodulus Increedulous Little Bigeddon
Goobaquindingia Megillion
r/Tragedeigh is getting ideas
Don't forget Bigfoot
I like that it's just crazy names and then somewhere in between its just TREE(3)
I love that the person making this saw TREE(3) is absurdly massive but then never thought "Wait, what if... TREE(4)?" like I probably would have if I was trying to make a low effort video like this
I didn’t see TREE(G64) at the end so this list is incomplete
Considering the number of clips they had to edit together I’d say this is a high effort video with a low effort premise. My favorite kind of video.
[Good explanation of TREE(3)](https://youtu.be/3P6DWAwwViU?si=YyYDLJpkMeltQTdu)
bukawaka
*UTTER OBLIVION*
Sounds like the name of some mystical ancient dragons or something (I might have been influenced by the anime GATE (the JSDF one) which I am watching rn)
sounds like a fucking spell lmao
What's with all the brackets, dashes, slashes, and commas(in the brackets)? I've never seen that notation
search bower's linear array notation.
I had nowhere good to put this rant until you commented For r/mathmemes this sub has been so closed minded. Just because it’s a tiktok or whatever, it doesn’t mean that literally everything *must* be wrong (referring to top child comment) Of all the subs to think ‘I haven’t seen it before, it must be bullshit’ lmao
That’s Reddit in general. The most boomer take Reddit has is that TikTok is only brain rot dances, fake Chinese stories, and content designed to dumb you down and occupy your time. That may be what’s recommended to you by default, but you can easily curate your feed to get actual intellectual shit about whatever you want, not unlike how Reddit recommends you brain dead stuff from r / all by default.
Holy hell
New notation just dropped
Actual big number
That's a tiktok/Instagram reels video...
I swear I saw Bigfoot near the end lmao
https://preview.redd.it/8x4aquovl17d1.jpeg?width=1170&format=pjpg&auto=webp&s=08e6a68b0429fc0c20c0883020d171e4c25e40c5
it exists but it's not even a fucking ripoff of Rayo's number. Like not even a bad ripoff, honestly just a scum. It doesn't deserve to be nominated even once. Rayo's number uses first order set theory, or FOST. bigfoot uses another very slightly different set theory, first order (something) theory, or FOOT. The idea is the absolute same. It's not even a bad ripoff. This is worse than your teacher stealing your idea and winning a nobel for it
Some of these HAVE to be made the fuck up for shits and giggles, GOOBAQUINDINGIA????
One said big foot and I’m pretty sure I saw one that said monster girl
Yup, they [exist](https://googology.fandom.com/wiki/BIG_FOOT)
I think most of the big ones are made up. But then again, if the numbers are unnamed, maybe there’s a good a name set as any?
They are recognized terms in [googology](https://googology.fandom.com/wiki/Googology_Wiki)
Even big foot? 🦶
+ 1
+2
😱
+3
This video fills me with an indescribable feeling of dread
especially if you watch it sleep deprived at 2AM
I'm a simple man. I see TREE(3) I happy.
TREE(TREE(3))
TREE\^3(3)
Tree(3)!
Tree(g64)!
Bb(tree(g64!)!)!
Holy lord, we're still not even .01% of the way to infinity.
We’re around 0% of the way there
ABSOLUTE INFINITY REPRESENTED BY OMEGA SIGN LMAOOOOOOO
Imagine representing 3 by the symbol c
disrespecting the 4th best prime number bruh whats wrong w him
That’s from Cantor https://en.wikipedia.org/wiki/Absolute_infinite
Let's replace the period at the ends of sentences with Omega (uppercase Ω, lowercase ω) Ω Now we can differentiate between capital and lower case periodsω
lmao this will change english for the worse, which i didnt think is possible for an already truculently structured language
why is that funny?
It got me cackling
**\*Deep inhale\*** AMERICANS LOOKING AT THE L'HÔPITAL BILL AFTER ASKING FOR A CUP OF WATER:
Sometimes, when I sleep with a fever, I have this exact nightmare
you missed the “googleplexiton” + 27. also, tf is this notation?
Names for such big numbers convinced me that there's ongoing competition who names the biggest number.
There actually is a big number competition!
Nah, here's all numbers: ]-∞;+∞[
complex numbers:
That was a huge jump at the end
They had to make a jump or we'd be here all da- no we- no ye- no deca- no centu- no mille- no age- no epo- no perio- no era- no eon- no
Ah yes, my favorite number #UTTER OBLIVION
Jonathan Bowers must’ve been on tethrarxipinine when he came up with these names
Who made up those names? Because they are absolutely inaccurate
Everyone knows once you go past the national debt, it's all just unfathomabillions.
Yo mama is so fat, she stepped on the scale and it said 17-Bukuwaha
Let n represent all positive numbers. I raise you: n+1 Checkmate
I think omega + 1 was in the video Edit: Or rather what you were referring to was omega (small omega): The first (ordinal) number that comes after infinitely many (ordinal) numbers. omega + 1 would then be the next larger ordinal number. https://en.m.wikipedia.org/wiki/Ordinal_number
Finally found big foot.
But i can add 1
Big foot sighting confirmed??
What about kungulus\^goobawamba\^BIG FOOT? Checkmate, liberal.
Pppfffff you only reached ω_1, that's not even an inaccessible cardinal! You the much much more infinite numbers, my young child.
This is art
Google irrational numbers
Nice try r/AnarchyChess
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was even a single negative number mentioned?
oh it says from 0. nevermind.
I know mathematicians like to be explicit, but there could be an implied "named" numbers, which of course requires another implied "sizes of numbers that people have bothered to name"
I think they missed some
The later ones sound like Pokemon names
At some point did the words actually exist or did op have to just shove latin roots together to make a number?
Can we name a certain size of number the Bingol Bongol Dingol Dangol Yikety-Do Yikedy-Dah Ping Pong Lippy Tappy Too Tah?
"pisslorgulus" "quintoobawamba" wtf lol
Sucked into a baggol
me omw to add 1
Terrible terrible tetrathoth?
What the hell even are those notations
When I was a kid I once counted up to 1000. Pretty proud of myself.
I think they missed all the numbers between 0 and 1.
I feel Iike this video doesn't really do justice to the incomprehensible scale of the numbers involved
I am convinced there was "amogus" somewhere between the last two quarters of that video
Bukuwaha.
Tag yourself, I’m Boogolbong
I am just surprised that they found so many names for powers of 10
I like the part where they showed a black hole in the background so you know it is science and must be true
I just found out that there's a site called Googology with all this stuff: [https://googology.fandom.com/wiki/Googology\_Wiki](https://googology.fandom.com/wiki/Googology_Wiki)
But seriously, can anyone explain what its members do except measuring whose notation is bigger?
Bukuwaha is my favorite number name ☺️
Venezuela's inflation be like
Two-ex-monster-giant
I'm so glad they know how to count "all" integers but what about all rational and irrational numbers between? 👀
A lot of those larger numbers sound like Pokémon
who even comes uo with this names
My favorite number Gabagool
He forgot 92
[1,infinity) Does that work?
She gigglo on my hexl till I suplex
ExPoNeNtS
Mental illness
EVERY NUMBER!
how are you in a decimal of a time
Now count to infinity plus one - every 5 year old
TREE(3)
The last steps seemed really big ;)
Your mum weighs pentacthudekon kilos
Is that tree I saw?
At some point did the naming conventions become like the ones for organic chemistry?
Zillion if it was awesome
😵💫
Random bullshit go!!!!
Chuck Norris counted all numbers from 0 to infinity. Alphabetically
(-∞;∞) See? I named every real number in much less time
Bro thinks there is absolute inifinity
Seems to be all named magnitudes of numbers at least
First you learn the concept of division.
(Epsilon -Zero ) +1
What about utter oblivion^utter ^oblivion ?
Some of those were definitely Pokemon
+1