How To Count Past Infinity

  • Published: 09 April 2016
  • my twitter: @tweetsauce
    my instagram: electricpants

    Sources and links to learn more below!

    I’m very grateful to mathematician Hugh Woodin, Professor of Philosophy and Mathematics at Harvard, for taking the time on multiple occasions to discuss this topic with me and help me wrap my (finite) head around it.

    I’m also grateful to David Eisenbud, the Director of the Mathematical Sciences Research Institute (MSRI) and professor of mathematics at the University of California, Berkeley, for his help and for connecting me with Hugh Woodin.

    And of course, big thanks to Brady Haran who created the “mile of pi” seen in this video and connected me with all these mathematicians in the first place. His channel, Numberphile, is superb:

    BOOKS related to these topics that I used:

    “The Outer Limits of Reason” by Noson S. Yanofsky:
    “Infinity and The Mind” by Rudy Rucker:
    “Roads to Infinity” by John C. Stilwell:
    “More Precisely: The Math You Need to Do Philosophy” by Eric Steinhart:
    “Satan, Cantor and Infinity: Mind-Boggling Puzzles” by Raymond M. Smullyan:

    classic book that helps introduce concept of axioms: “Introduction to the Foundations of Mathematics” by Raymond L. Wilder:

    Hugh Woodin speaking about infinity at the World Science Festival:

    Names of large (finite) numbers:


    The biggest number:

    Fovant badges:

    Battalion Park:

    A mile of pi [VIDEO]:

    Wikipedia’s great visualization of ordinals out to omega^omega:

    as seen on:

    this is also a good page about ordinals:


    and: and



    Large Cardinal game based on 2048:

    Other good resources:

  • Science and Technology Science and Technology

Comments • 63 485

  • Jason L0L
    Jason L0L  33 minutes back

    Infinity plus 1

    • HashBrown
      HashBrown  1 hours back

      Mom: From a Scale of 1 - 10 how much do you love me?
      Vsauce : Inaccessible cardinal.

      • HashBrown
        HashBrown  1 hours back

        A guy talking about numbers more exciting than my teacher.

        • Finley Donn
          Finley Donn  2 hours back

          Do the lowest

          • Leon Van Heerden
            Leon Van Heerden  6 hours back

            17:30 well that de-escalated quickly

            • PaintedPerfect
              PaintedPerfect  6 hours back

              How to count past infinity.
              Turn the infinity sideways, *9, 10, 11* ...

              • CliffJumper gaming
                CliffJumper gaming  7 hours back

                mom come pick me up i'm scared

                • wow2 chicken nuggets
                  wow2 chicken nuggets  8 hours back

                  You heard it here folks 40 is the biggest

                  • Teo Sega Sumić
                    Teo Sega Sumić  9 hours back

                    Everytime i finish a VSauce video i fell like ive been high on something

                    • Klapto
                      Klapto  10 hours back

                      Just say infinity and 1

                      • Kocsis Kolos Kende
                        Kocsis Kolos Kende  11 hours back

                        It hurts my brain so much

                        • Connor Clark
                          Connor Clark  13 hours back

                          Vsauce has a hot face, boi

                          • Keira Cloud
                            Keira Cloud  13 hours back

                            Infinity and 1

                            • ThunderWolf 56570
                              ThunderWolf 56570  19 hours back

                              Me: 40, 41

                              I’m smarter than vsause

                              • ToxicRolo
                                ToxicRolo  20 hours back

                                Infinity and 1

                                • No Entity
                                  No Entity  22 hours back

                                  1 is the biggest number because 1 could have infinite 0's and zero doesn't have a value for example, 1=10000000000000000000000000000000.

                                  • No Entity
                                    No Entity  11 hours back

                                    @Caladbolg shhhhhhh the 9 yr olds don't know that

                                  • Caladbolg
                                    Caladbolg  13 hours back

                                    1 cannot have infinite zeroes. By that logic 1=10. No integer can have infinite digits.

                                    Zero does have a value: zero.

                                • flyte
                                  flyte  23 hours back

                                  me researching how you beat exodia

                                  • What The Cinnamon toast fuk

                                    Crush: How much do you love me

                                    • Jonathan Robertson
                                      Jonathan Robertson  23 hours back

                                      Micheal, I disagree with this, here's why.

                                      (I am basing all of this off of the fact that, by definition, infinite means not finite.)

                                      The entire field of mathematics is nothing more than a system of ideas we made up that have to consistently follow rules (which, yes, we made up). Numbers consist of a set amount of characters and a pattern which they follow (cycle through all the characters, add another power, repeat). These numbers don't actually mean anything though, they just represent a value. That value is simply which combination of characters in this set pattern of combinations it is. That's why each number in the base ten system has a corresponding number in binary, base three, base google, or any base n number system. They are all made up, yet they all represent the same values. These values are real, tangible things.
                                      Infinity is not a real, tangible thing. It is an idea. (yes I know that space is as far as we know infinite, but that is a quality of space, not a quantity, and this video is addressing the quantity of infinity) This idea of infinity has one rule, it's definition: not finite (yes I know that's the definition of infinite, not infinity, but by definition infinity is infinite, and the only quality of infinity is that it is not finite).
                                      Following this rule, it is impossible to have a quantity greater than infinity. That is because, by labeling a number as such, a finite value is put on infinity. This contradicts the idea of infinity and thus can not be true. But there are other ways to prove this.

                                      Replacement is wrong because it's nothing more than a base infinity number system. In all that effort to show how replacement goes on forever and ever until it reaches... the inaccessible cardinal, all you showed was that there are an infinite number of numbers, and in reality, aleph null is the inaccessible cardinal. All those aleph and omega numbers you made up were just that, numbers. Numbers which only have a value equivalent to which one of the combination of characters in the pattern you made up they are. Each one with a corresponding number in any other number system. You can continue counting in any number system all the way up to every number you displayed using replacement.

                                      Power sets are literally just binary. The only value that power sets have is the quantity of sets contained in them. You displayed these as combinations of y's and n's. The only way to insure that you go through every single possible set of y's and n's is if you follow a pattern. Lets start with all n's: n... Then lets replace the first one with a y: yn... there aren't any more options for that place so let's switch to the next, then we'll have that option open again: nyn... Now we can do yyn... Then nnyn... ynyn... yyyn...nnnyn... It's an exact mirror image of the binary you're familier with, just with different characters: ...0 ...01 ...010 ...011 ...0100 ...0101 ...0111 ...01000
                                      (Sure there might be four power sets for 1 and 2, and eight power sets for 1, 2, and 3, but the four sets from 1 and 2 are all repeated in the sets for 1, 2, and 3, so they don't count for any new quantity, and two of those are in the power sets of 1 and one of those is the power set of no number and the last set is accounted for in 0. This is because the lack of a quantity and a quantity of zero are represented differently in these power sets and thus both represent a quantity equal in value to one combination of characters from any number system. Therefor every power set is accounted for)

                                      Sure you can make up ways to count past infinity, but the only way to consistently follow those systems is to put a finite value on infinity, which contradicts the whole idea of infinity, which is unfathomably, inaccessibly, existentially..... infinite.

                                      Infinite as a quality of space also proves this. No matter how far out you measure, you can always go farther: it's infinite.

                                      • Caladbolg
                                        Caladbolg  13 hours back

                                        There is no requirement that math have anything to do with the real world. You are also conflating numbers and numerals, as well as mathematical infinity with some philosophical or intuitive infinity.

                                        You are implicitly assuming that a value must be finite, i.e. that infinity is not a value that can be compared. That depends on what you mean by infinity.

                                        Would you agree that {1,2,3,4...} is infinite in some sense? That set btw is omega. Omega has a successor omega+1.

                                    • Zombiewolf 132
                                      Zombiewolf 132  1 days back

                                      I’m telling you
                                      Soon he’s gonna say something that creates a black hole

                                      • Troy Tran-le
                                        Troy Tran-le  1 days back

                                        Infinity is something beyond our universe.
                                        Gbfvgn(fcsftjj,ninhb$egyj(j6rcscfnjjmffaswfgmjmfvxcaxdvgnhmfvsxqxscfnhmjmn fcscfhhmjnttgsc

                                        • Troy Tran-le
                                          Troy Tran-le  1 days back


                                          • HarisPlaysYT
                                            HarisPlaysYT  1 days back

                                            Vsauce: how to count past infinity
                                            Me: *iNfInItY aNd BeYoNd*

                                            • Wrave
                                              Wrave  1 days back

                                              Absolutely Nobody
                                              Vsauce: *hOw tO CoUNt PaSsEd InFiNiTy*

                                              • Wrave
                                                Wrave  1 days back

                                                The way this guy hypes stuff is too much

                                                • juan garcia
                                                  juan garcia  1 days back

                                                  It's rayo number

                                                  • Sean Robertson
                                                    Sean Robertson  1 days back

                                                    Serious question: at this point, is it even mathematics? Or is this philosophy? It’s dealing with stuff that isn’t real and can never be proven, so is it really math?

                                                    • Caladbolg
                                                      Caladbolg  13 hours back

                                                      It is mathematics. Numbers aren't "real" in the sense objects are anyways. They are concepts, albeit useful ones.

                                                      Everything in this video can, and has been proven. Math is the only discipline in which things can actually be proven. "Proof" means a logical deduction from a chosen set of initial assumptions. Natural sciences don't have that - even in physics, everything is just approximations, though incredibly accurate ones. The fact that much of theoretical math doesn't have a real world application (yet) has no bearing on whether or not it is legitimately math.

                                                  • kuba tutak
                                                    kuba tutak  1 days back

                                                    ez, infinity + 1

                                                    • KING _GAMES
                                                      KING _GAMES  1 days back


                                                      • chekystar
                                                        chekystar  1 days back

                                                        izy you start counting while you drive past infinity she is slow driver :P

                                                        • Cooxq - _ - YT
                                                          Cooxq - _ - YT  2 days back

                                                          Infinity and a google and one

                                                          • [Camp] Hot Nuke
                                                            [Camp] Hot Nuke  2 days back

                                                            My mom saying I love you

                                                            Me hesitating to say I love you back

                                                            Takes 23 minutes to say I love you back to her

                                                            • Charles JSB
                                                              Charles JSB  2 days back

                                                              Rip math teachers

                                                              • Clogged toilet
                                                                Clogged toilet  2 days back

                                                                Vsauce is like that one geeky kid that took Rick and Morty way too seriously

                                                                • Phanuroj 37
                                                                  Phanuroj 37  2 days back

                                                                  Is alif null odd or even

                                                                  • DarKStaR Of Legend
                                                                    DarKStaR Of Legend  2 days back

                                                                    Me: watching the vid till end
                                                                    My brain: i want to explode

                                                                    • Julie Ann Luague
                                                                      Julie Ann Luague  2 days back

                                                                      Vsauce is right. 40 is the largest number because 40 in roman numerals is XL, meaning "Extra Large".

                                                                      • CONTENT
                                                                        CONTENT  2 days back

                                                                        Infinity one
                                                                        Infinity two
                                                                        Infinity three

                                                                        • Wiktor Zakrzewski
                                                                          Wiktor Zakrzewski  2 days back

                                                                          I am no matematician but I had some study in logic. And mathematics is based on logic. And this whole omega buisines seems to me to brake the fundamental law of logic. In any moment you add or multiply to infinity, you produce a paradox, so it becomes clear why you can come to 0=1. Logic says that Dog is not cat. 0 is not 1. Only because we defined them so. So the meaning of Infinity is infinity, period. There can be nothing more, because the definition of infinity encompasses everything and more. So any omegas are simply play on language based on nonsense. Nonsense is fun, can't say it isn't. But it's non-sense. Non-logic.

                                                                          • Wiktor Zakrzewski
                                                                            Wiktor Zakrzewski  10 hours back

                                                                            I'm sorry about your headache. Well I said before I am no matematician. I would gladly admit I was wrong, but I fail to understand the omega +1. I will abandon the subject here until I understand more.

                                                                          • Caladbolg
                                                                            Caladbolg  13 hours back

                                                                            @Wiktor Zakrzewski If you knew math, you would see there's no error there. Successors in ordinals are defined thus: successor of x is xU{x}. Omega+1 is a notation used for the successor of omega. Successor of a number is bigger than that number.

                                                                            "Comes after" is the same as "bigger" in ordinals, genius. This topic is clearly way over your head so I don't understand this obstinate refusal to admit you're wrong. The only thing I'm suffering from is a headache from your apparent lack of math knowledge.

                                                                          • Wiktor Zakrzewski
                                                                            Wiktor Zakrzewski  19 hours back

                                                                            And according to Michael Stevens omega is not bigger. It comes after.

                                                                          • Wiktor Zakrzewski
                                                                            Wiktor Zakrzewski  19 hours back

                                                                            @Caladbolg I'm afraid you suffer the thing you claim others do. You define omega as a set of all integers and count past it by adding an integer to it. You clearly made an error here.

                                                                          • Caladbolg
                                                                            Caladbolg  20 hours back

                                                                            @Wiktor Zakrzewski But we don't say that that exists, do we? Besides, that is not even a claim about existence.

                                                                            Also, congratulations on avoiding the explanation. It's clear you have zero mathematical education and don't really care to learn. You don't even understand what math is nor how it works. You just care to play rhetorical gotchas, which only betray your lack of understanding on the subject.

                                                                            Fortunately, math has proofs, so unlike other fields, it's conclusions are certain within a given axiom system. Omega is bigger than any integer, and has numbers bigger than it still. Doesn't depend on intuition, real world, or even scientific authority. It follows from definitions and axiomd taken.

                                                                            Anyways, I have better stuff to do. Bye now.

                                                                        • Barleykid 12
                                                                          Barleykid 12  2 days back

                                                                          Well what could you call omega x 2 instead of omega x 2 like how you call two ones the number 2 and then so on and so on

                                                                          • Foxy - TheMemelords
                                                                            Foxy - TheMemelords  2 days back

                                                                            To the infinity and beyond

                                                                            • Isaac Asmah
                                                                              Isaac Asmah  2 days back

                                                                              Vsauce is the prince ea of science

                                                                              • Aiden Westcott
                                                                                Aiden Westcott  2 days back

                                                                                and i thought 1st grade math was hard

                                                                                • Chronical Kiefer
                                                                                  Chronical Kiefer  2 days back

                                                                                  The last number is...

                                                                                  That’s what I found


                                                                                  • Matt25
                                                                                    Matt25  2 days back

                                                                                    You count to infinity 1 to infinity 1000000000000000000000000

                                                                                    • まだ寒い ッ
                                                                                      まだ寒い ッ  2 days back

                                                                                      Infinity and one

                                                                                      • clorans from clorox
                                                                                        clorans from clorox  2 days back

                                                                                        2:37 yeah, most people are thinking about the gd level right now..

                                                                                        • Gabe
                                                                                          Gabe  2 days back

                                                                                          Gabe Newell: *Wait what?*