# How To Count Past Infinity

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**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: http://iloverimini.mobi/user/numberphile

BOOKS related to these topics that I used:

“The Outer Limits of Reason” by Noson S. Yanofsky: amzn.com/0262019353

“Infinity and The Mind” by Rudy Rucker: amzn.com/0691121273

“Roads to Infinity” by John C. Stilwell: amzn.com/1568814666

“More Precisely: The Math You Need to Do Philosophy” by Eric Steinhart: amzn.com/1551119099

“Satan, Cantor and Infinity: Mind-Boggling Puzzles” by Raymond M. Smullyan: amzn.com/0486470369

classic book that helps introduce concept of axioms: “Introduction to the Foundations of Mathematics” by Raymond L. Wilder: amzn.com/0486488209

Hugh Woodin speaking about infinity at the World Science Festival: iloverimini.mobi/video/KDCJZ81PwVM/video.html?t=29m45s

Names of large (finite) numbers: en.wikipedia.org/wiki/Names_of_large_numbers

Geoglyphs:

The biggest number: goo.gl/maps/7GWcpnzo7iG2

Fovant badges: en.wikipedia.org/wiki/Fovant_Badges

Battalion Park: en.wikipedia.org/wiki/Battalion_Park

A mile of pi [VIDEO]: iloverimini.mobi/user/watch?v=0r3cEKZiLmg

Wikipedia’s great visualization of ordinals out to omega^omega: en.wikipedia.org/wiki/File:Omega-exp-omega-labeled.svg

as seen on: en.wikipedia.org/wiki/Ordinal_number

this is also a good page about ordinals: math.wikia.com/wiki/Ordinal_Number

also: cut-the-knot.org/WhatIs/Infinity/Ordinals.shtml

and: en.wikipedia.org/wiki/Order_type and en.wikipedia.org/wiki/Well-order

Axioms:

en.wikipedia.org/wiki/Axiom

reddit.com/r/askscience/comments/30xokb/have_there_been_axioms_that_later_have_been/

philosophy.stackexchange.com/questions/5922/what-is-the-difference-between-dogma-and-an-axiom

cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms1.pdf

cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms2.pdf

THE UNREASONABLE EFFECTIVENSS OF MATHEMATICS IN THE NATURAL SCIENCES

[PDF]: maths.ed.ac.uk/~aar/papers/wigner.pdf

en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences

Large Cardinal game based on 2048: cantorontheshore.blogspot.it/2014/10/one-reinhardt-and-counting.html

Other good resources:

quibb.blogspot.com/2012/01/infinity-first-transfinite-cardinal.html

plato.stanford.edu/entries/set-theory/

cantorsattic.info/Cantor%27s_Attic

cantorontheshore.blogspot.co.at/2014/09/artemis-fowl-and-large-cardinals_22.html

isomorphism.es/post/10782081422/what-comes-after-infinity-transfinite-arithmetic-and-ord

lukepalmer.wordpress.com/2007/06/14/the-lesser-of-infinitely-many-evils/

MUSIC BY:

iloverimini.mobi/user/JakeChudnow

audionetwork.com - Science and Technology

Infinity plus 1

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

Vsauce : Inaccessible cardinal.

A guy talking about numbers more exciting than my teacher.

Do the lowest

17:30 well that de-escalated quickly

How to count past infinity.

Turn the infinity sideways, *9, 10, 11* ...

mom come pick me up i'm scared

You heard it here folks 40 is the biggest

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

Just say infinity and 1

It hurts my brain so much

Vsauce has a hot face, boi

Infinity and 1

Me: 40, 41

I’m smarter than vsause

Infinity and 1

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

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

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

Zero does have a value: zero.

me researching how you beat exodia

Crush: How much do you love me

Me:

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.

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.

I’m telling you

Soon he’s gonna say something that creates a black hole

Infinity is something beyond our universe.

Gbfvgn(fcsftjj,ninhb$egyj(j6rcscfnjjmffaswfgmjmfvxcaxdvgnhmfvsxqxscfnhmjmn fcscfhhmjnttgsc

40AET

Vsauce: how to count past infinity

Me: *iNfInItY aNd BeYoNd*

Nobody:

Absolutely Nobody

Vsauce: *hOw tO CoUNt PaSsEd InFiNiTy*

The way this guy hypes stuff is too much

It's rayo number

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?

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.

ez, infinity + 1

ΩоΩин

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

Infinity and a google and one

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

Rip math teachers

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

Is alif null odd or even

Me: watching the vid till end

My brain: i want to explode

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

Infinity one

Infinity two

Infinity three

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.

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.

@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.

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

@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.

@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.

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

To the infinity and beyond

Vsauce is the prince ea of science

and i thought 1st grade math was hard

The last number is...

That’s what I found

-siri

You count to infinity 1 to infinity 1000000000000000000000000

Infinity and one

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

Gabe Newell: *Wait what?*