listen to what I say at exactly 0:40

-So can we count to Infinity? -ℵₒ

1:00 How to count according to Michael: 40, 41, 42, 43, a billion, a trillion

The seemingly random "post credits" scene was incredible. "Omega + one" indicates a number that is in order after the "last" of the natural numbers. Having that bit play AFTER the "end" of the video was absolutely genius and wonderfully creative.

9 year old me: *Infinity plus one.*

How to count past infinity: Dumb people: infinity+1 Smart people: you can’t Top mathematicians: infinity+1 lmao

16:03 "we’re cooking now". I didn’t know people said this 7 years ago I thought that only came out last year?? How ahead of vsauce’s time was he?

This video is 7 years old yet still feels like it was uploaded yesterday

40: exists 41: I'm about to end this man's whole career

"There are numbers bigger than 40.. 41.. 42.. 43.. *A B I L L I O N* *A T R I L L I O N* " Man that escalated quickly

21:00 and this is why i absolutely love and adore mathematicians they're just like me "oh this is absurd that makes no sense but yknow what let's keep going anyway let's see how far we can go"

00:03 Infinity is not a number, but a kind of number. 02:41 Aleph null is a big amount, bigger than any finite amount, but we can count past it using supertask. 05:05 Ordinal numbers are used to label an infinite collection beyond the naturals. 07:30 The order type of sequences and different infinities explained. 09:56 Diagonalization method creates new subsets beyond infinity 12:20 Mathematics is based on axioms and is unreasonably effective in natural sciences 14:53 Axiom of replacement allows construction of new ordinals without end 17:13 The continuum hypothesis is an unsolved mystery. 19:15 Inaccessible cardinals represent a number that cannot be reached from below. 21:25 Infinities may exist beyond the physical realm. Crafted by Sarthak Naithani *i understand everything albert einstien*

This confused me, then pissed me off, then made me feel so relaxed

"Mom, Vsauce glitched my brain again!"

Important note about the continuum hypothesis (CH): It's not just that it's unsolved, it's actually unsolvable. CH has been shown to be logically independent from the ZFC axioms of set theory - that is, you can show that CH is not a theorem of ZFC and that the negation of CH is also not a theorem of ZFC. This is ultimately a consequence of incompleteness - any set of axioms and system of proofs must contain propositions which are neither provable or disprovable

Man, for some reason no matter how hard I try, I cant bring myself to stop watching. I ask myself, "When will i ever use this knowledge?" and my answer is never. But still its so entertaining to watch numbers over numbers of complexity and pretend i comepletely understand and I believe I understand too just because of his amazing teaching. Well Vsauce, you just gained another VERY big fan and subscriber. I got notifications going.

Never discuss infinity with a mathematician, they can go on about it forever.

Vsauce videos Title: Is fire hot Answers:Yes Talks about birds for the rest of the video

“All we have to say is ‘Let there be Omega’, and it will be good.” Why does this sound like a quote from a fantasy movie lmao He would definitely be the cool wizard guy that guides the hero

we had dimensions in objects (e.g. 2D, 3D), and the way vsauce described infinities, i think we also found them number dimensions

Fun fact: infinity+1 is bigger than infinity. Source: 7 year old me arguing with my siblings

i remember, this was the first ever Vsauce video i watched, at my Grandmas house on a laptop. i came back here to say that. ok bye

Talk to Chuck Norris. He counted to infinity twice before his first birthday.

Nobody: Vsauce: How to taste the color 7.

God: how many years do you want to live? Queen Elizabeth II:

Ima make my own inaccesible ordinal and call it “this is the last inaccesible ordinal stfu and live with it”

Michael, i must thank you, enytime i have a test, i watch your videos and my head suddenly starts to hurt.

Michael: “how to count past infinity” 6 year old me: *_infinity and one._*

Person: what is your IQ? Me: θ

Something cool to mention is that is that there are TWO infinite sets and 0 is a transfinite gateway keeping positive/negative omega times/power/root of whatever as the same set but anyone that disagrees, I am entitled to my opinion and same for you.

I'm in tears (I exaggerated. Actually, better than in tears) and with thrills (shivers? I don't know English) each time I watch this video and the Theta is reached. Really big thanks to you, Michael, for having brought me joy, having brought me sense, after I discovered that atoms are not so tiny, galaxies not so big, the universe not so old (recent history is comparable with the history of life and Earth), that anything material is not surprising but that there are things, actual logical things (don't know how much this counts), that can go even way beyond what satisfies me, my hunger for the greatness and the epicness, and Sense. Sense of life to me is merely complexity. I discovered the magnitude if Graham's number and felt shocked. I discovered these "numbers" in the video, in respect to which Graham's is totally nothing (actually infinitesimal) just in comparison with the first one, the numeral infinite, aleph_0. I will take refuge in the ideal world. Mathematics, with its total rigor, the minimal starting points and its complexity, hasn't disappointed me much, yet.

"0=1" Yup, I've had enough of math today.

In high school I was telling my friend about omega and I got a detention for drawing "balls" on my paper ....

5:00 the infinate hotel explains how an infinste hotel has infinate rooms and if they are fully booked, you can simply just move everyone down one room to open up a slot

I watched this video a while back. Brings back good times.

The largest number is “error” you can ask the calculator

Michael: well, there's 41 Me: ok Michael: then there's 42 Me: yea Michael: and then 43 Me: mhm Michael: a billion Me: now I'm not sure about this, but I think you skipped a few Michael: a ᵀʳᶦˡˡᶦᵒⁿ

I think a set of all naturals is N1 because you could divide N by N to get 1. Then 2^1 is 2. Multiply that by N again and that is N2.

There will be a finite number of atoms in the uni verse timeline there will be a practical biggest number in terms of the universe but to calculate it you would need to know 1. The approximate death date of the universe, and two the universes current size meaning that it is theoretically impossible to answer this question.

This literally, physically, mentally, emotionally, spiritually, chronologically, theoretically, socially, psychologically, metaphorically, and exactly hurt my brain.

“I love you infinity +1.” “I love you 40.” “Damn”

I love coming back here year after year, just for the exhilarating and visceral vertigo.

"What's your favorite number?" *proceeds to fully break down the quantum physics of þe universe*

Mom: take a break Me: Do you even exist?

short answer: No long answer: Yes

I think the universe is audacious enough that it does contain the infinities described by math

3:27 written out I believe that would be [((10^10^100)!)^((10^10^100)^(10^10^100))]^2 x Graham’s Number (Sorry if some of the parentheses were redundant) Graham’s number alone is so big there literally isn’t enough space in the universe to write it out in any normal algebraic capacity. Even googolplex, as gigantic as it is, can be written pretty easily as 10^10^100. Graham’s number might as well just be infinity, but if it’s multiplied by all that, it would get even MORE incomprehensibly big somehow. Even that incomprehensible number Michael named, however, might as well be 0 compared to Aleph Null, which is just the first of a number of infinite infinities which go on forever just like the cardinal numbers did before them. My head hurts

How to count past infinity: *40*

Me explaining my parents that u cant pause an online game:

Love this so much! It's a blurring of math & myth.

When you look away for 1 second in class:

What they teach in class: 12*5 What they ask for exam: (This Video)

The video I always come back to when I think about infinity

Bro really said to infinity and BEYOND

ah finally a way to measure your mom's weight

Therapist: So how much stress are you dealing with. Me:

3:34 that drop hits HARD

This might be the coolest video on KZfaq

Here's how you count higher than infinity: *Infinity one, infinity two..*

rip brain

Vsauce you were in the Australian academy of science for this video!!!

4:19 zoom in those numbers are actually in order idk why but it’s cool

Omega+1 isn't bigger than Omega, it just comes after Omega. This was when my brain really broke.

My brain broke when he said "Hey Vsauce"

It's been 7 years and I STILL don't under stand how this man is this smart.

He just makes me question my existence and then says "and as always... thanks for watching"

"I like your funny words magic man."

Mathematicians: “Now... reality can be whatever I want”

If people who are dealing with insurmountably large sets are getting 0=1, I think its important to note that it doesnt suggest its true. It may be that its a sign they're wrong, or something they assumed, concluded after large amounts of work to be incorrect. Take for example the expression 3x = 2x. You can try to reduce it by removing the x from both sides, or dividing one side by the constant then the other by x, but either or you will be left with 3 = 2, 2/3 = 1, or 3/2 = 1. This doesnt mean that 3 is equal to 2... It simply means the expression I initially wrote is in its entirety, incorrect. 3 does not equal 2. Excluding 0 as a solution, 3x will never equal 2x for any real number x.

I am a CS student and your content is absolutely priceless. I took a course about this subject and you helped me to understand infinity better. Complicated and interesting topic. Love your work

“Why didn’t you do your math test?” *”I don’t believe in numbers.”*

waiting for myself to have a son, then I will wait for my son to say “I love you times infinity” and I pull up with the “I love you times Inaccessible Cardinal”

dude the end is always the best part

His explanations are so understanding and so good❤

This video is the only video I've seen where Michael stays on topic.

Nobody Vsauce: How to disable fall damage in real life

10:40 you just wrinkled my brain man

The recursive nature of a compressed and uncompressed infinity...viewing two well-known infinities from inside and out. Version 1 revision 1 - 25th of October, 2023 This simplifies and supersedes a previous document named "An alternative way to visualize infinity". ====================================================================================================================== 1.Take what are considered two different and well-known infinities: a. the one that exists between zero and one consisting of uncountable infinitesimal points b. the one that exists from zero onward consisting of uncountable integers With "a", infinity is enclosed by limits at both ends, yet somehow through Cantor's 'parlor trick' it's said to be a larger infinity than "b". Cantor's proof attempted to show that "a" is larger but I say his logic is flawed because it did much more to obfuscate reality than showing it and his was not a head-on approach to reality but a misleading sidestep. It is that because infinity if not carefully dealt with defies normal arithmetic and easily leads to errant conclusions. I intend to disprove Cantor and show both infinities memberships are absolutely equal through a much 'purer' method that treats both types of infinities in the same manner by declaring they are two opposing views of the same infinity. 2.Basic properties of the two infinities: a. consider 1a shows an infinity that has two 'ends', zero and one and that the smallest value above zero can never be determined using the normal convention; this is what I consider a 'compressed' view, typical of this form of infinity. b. consider 1b shows an infinity that has only one 'end' and that the largest member below infinity can never be determined using the normal convention; this is what I consider an 'expanded' view, typical of this form of infinity. Now, what happens if you allow the thought experiment to expand the first and compress the second, thereby flipping their views? 3.The resulting observation: a. When 2a is viewed from the 'inside' (expanded view), you can distinguish members you could not before. What was '1' now resembles another type of infinity. You can see the first member after zero (before '1'); logically it has to be a number ending with '1' with infinite preceding zeros after the decimal; this by the way is also how the normal integer number line looks, just remove the decimal point. Adjacent members can be plotted; before adjacent members could not be plotted. The number line looks like the integers starting with zero (just remove decimals and leading zeroes). b. When 2b is viewed from the 'outside' (compressed view), you cannot distinguish members you could before. What was infinity resembles another type of '1'. You cannot see the first member after zero (except infinity); all numbers you can name are virtually at the same location as zero. Adjacent members cannot be plotted; before adjacent members could be plotted. The number line looks like the integers zero and '1', any 'fraction' of infinity between behaves like and must be written out like a decimal number between zero and '1'; I suggest creating a new character called a 'super-decimal' to represent such values which looks like a decimal point except that it's at the top of the character block instead of the bottom; its use is to represent a fraction of infinity the same way a decimal is used to represent a fraction of an integer. We say infinity is not a number...in a sense (only because of how we view it) that's absolutely true, but it can look like an integer if the view of the number line is compressed. That integer would be '1'. More accurately using the new character I suggested above, it would look like 1.0 with the decimal moved to the top of the character block (the super-decimal). This new convention would make possible calculations involving a whole or a part of infinity. Notice the two infinities are recursive (the infinitesimally smaller infinity is nested within the larger infinity and is nothing more or less than an enclosed miniaturization). The views of each are essentially a perfect opposite of the other. When both are flipped, the smaller looks virtually like the larger and the larger looks virtually like the smaller. Any differences are cosmetic (decimal vs. no decimal). When you observed 3a and 3b after performing the thought experiment properly, you will see clearly HOW it is possible that the two infinities have the same exact set membership (the size of the sets are absolutely perfectly equal). What is true about both sets yet does not affect my explanation showing how the members are absolutely equal: a.Members are not truly name-able numbers if they must be written out using INFINITE digits; this is true even of decimal numbers in the sense the values reaching the lowest significant digit cannot be reached, and hence named; yes that means irrational and transcendental numbers are not truly name-able numbers, but that does not mean they are not USABLE numbers because we can write out the most significant digits; the compressed view we normally use for decimal numbers allows for that and would not work if the expanded view were used because you would be forced to start writing out the number with the lowest significant digit and could never reach the highest significant digit b.members are name-able numbers if they can be written out using finite digits (This is true regardless if you're talking about membership in either set; infinite digits define un-nameability) Important note on aspect I noticed which can easily be dealt with if you consider the two different views of the number line: The decimal numbers begin naming their 'places' with the most significant digit, making the least significant possible digit un-nameable The integers begin naming their 'places' with the least significant digit, making the most significant possible digit un-nameable (When the views are flipped, it becomes possible to do what was not possible before, and vice versa; the plotting of infinitesimals after zero becomes possible and starts with "1 infinitesimal, 2 infinitesimal, etc... which are now all VISIBLE since the number line was EXPANDED; it now becomes impossible to plot integers because they are INVISIBLE since the number line was COMPRESSED, yet you still know because of our BIAS/TRAINING toward the normal convention that the now invisible integers after zero start with '1, 2, etc...all these integer 'points' exist the same way infinitesimals exist but it is the EXPANDED or COMPRESSED view that determine visibility. It is only our bias/training toward conventional reality that causes whatever is not visible to appear not to exist.) Exploring deeper into why the sets are absolutely, perfectly equal: The expansion of the members between zero and '1' makes it possible to do a 1:1 match to the members between zero and infinity because the memberships both resemble integers starting from zero toward infinity ('1' being a 'type' of infinity) The compression of the members between zero and infinity makes it possible to do a 1:1 match of the members between zero and '1' because the memberships both resemble decimal values between zero and '1' (infinity being a 'type' of '1' Note that there is a 'type' similarity of '1' to infinity as they both represent a 'whole' of something; '1' represents a 'whole' of all the possible decimal values leading up to itself; infinity represents a 'whole' of all the possible integer values leading up to itself; in that sense they are two ways of describing the same concept

Random Guy : How to kill a brain without using any weapons? Me :

Dad:From a scale of 1 to 10, how hard did your brother hit you? My brother:

So is it not possible to reach the inaccessible number even using recursion. Because no matter how long you will use recursion to reach that number, it will still not get remotely close to θ. But i would argue that if the recursion is used ℵ0 time that you would probably reach it, right?

Every time I scare myself with the grin I am having when rewatching and realising unlimited power of axioms and infinities

Why am I so obsessed with watching videos that make my brain dissolve itself

Micheal: What is the biggest number? 1 billion! INFINITY! A googol! Micheal: No its just 40 Oh

So actually not thing bigger than infinity, just arranged differently. And to create a larger infinity we must "multiply" the two infinity together (create an infinite sequence arrangements with infinite elements in a spreadsheet format and reason that there is always an unlisted sequence arrangements). I personality don’t think we can even do that cause how can we list end less thing and arrange them end less time? Or just imagine? In fact, infinity is already INFINITE. Creating something larger than infinity is just a recognized concept that speaks to human imagination (although I think people still haven't imagined what exactly infinity is) but they still want to get over it.

Wait.... what about.. Replace the "0" in "aplph null" with another "alaph null" and continue the process for a 'alaph null' times

Video starts at ∞:∞, thank me later.

"How much do you love your homies?" Me:

at 11:45 i remembered the infinity hotel, and this was a WAYY BETTER WAY to explain it

This video is one of my inspirations for getting a degree in mathematics

If I was a teacher I would, as punishment, have students write a summary or report about this video.

"there's always a bigger fish"

Funny thing about these numbers is that literally even though they all have different quantities of things in them while literally all being the same amount, infinity.

This is truly one of the best KZfaq videos and lessons ever.

"infinity is not a number" 8 year old me : impossible...

It makes sense that 40 is the biggest number. It's extra large (XL is 40 in Roman Numerals).

I like your work with your new numbers 🎉❤

Axiom = I made it the f up My source: Axiom of axioms

The highest number is 420

teacher: the test isn't that hard the test: