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ZACHS MARCH 12, 2012

One of the first questions that kids often ask is What is the biggest number? Thisquestion is an important step in transitioning to a world of abstract concepts. Theanswer is of course that numbers are generally considered endless, but there gets tobe a point were numbers become so big that there really is no point in having them,they have no real importance outside of the fact that yes technically they do exist. Tomake a list like this I could simply write down a massive number for the first number,and then write +1, +2, +3 and so on for the rest of the list. Instead I chose to take out 10numbers that do have some effect on the world and place them in ascending order,giving a brief explanation as to what they are and how they have some relevance onthe world, albeit very small relevance, especially when compared to the size of thenumber itself.

10 10^80

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10 Enormous Numbers

Ten to the eightieth power a 1 with 80 zeros after it is quite massive but somewhattangible at least from a relatively concrete point of view. This is the estimated numberof fundamental particles in the known universe, and with fundamental particles werenot talking about microscopic particles, were talking about much smaller things likeQuarks and Leptons subatomic particles. The name for this number in U.S. andModern British is One Hundred Quinquavigintillion I would write out phonetically howto pronounce that but I dont have a clue. The concept of the amount of such smallthings and how many of them make up the entire universe may seem overwhelming,but it is the smallest and easiest to understand of the numbers on this list.

9 One Googol

The word googol, with a slightly different spelling, has become a frequently used verbin modern times, thanks to a highly popular search engine. The number has aninteresting history which you can find by simply googling it. The term was coined byMilton Sirotta in 1938 when he was 9 years old. Although this is a relatively abstractnumber, only existing for the fact that it technically exists, but it does come upoccasionally in other uses.

Mental Calculator Alexis Lemaire set a world record for calculating the 13th root of a100 digit number, the 13th root of 8,192 is 2, or 2 times itself thirteen times, 100 digitnumbers are googols, one of the numbers that Lemaire had calculated would haveread (3 googol, 893 Duotrigintillion, ext, ext.) Another use is from about 1 to 1.5 googolyears after the big bang, the most massive black holes will have exploded. These willbe the last recognizable structure of our universe to disintegrate, and once it does theuniverse will enter its 5th and final era known as the Dark Era the end of theuniverse based on certain scientific models.

8 8.5 x 10^185

A Plank length is extremely small, approximately 1.616199 x 10-35 meters, or in longform 0.00000000000000000000000000000616199 meters. There are about a googol ofthem in a 1 inch cube. Plank length and Plank volumes are important in quantumphysics branches like string theory evidently sizes this small allow the extradimensions to be detected, at least in some theories. How do all these small thingsapply to the third smallest number of this list? There are approximately 8.5 x 10^185plank volumes in the universe. This number is both massive and its practical purposerelatively non-existent, however it is still simple compared to the rest of the numberson this list.

7 2^43,112,609 1

The third largest number on this list, the number of all the plank volumes in theuniverse, consists of 185 digits. This number here consists of almost 13 million digits.The significance of this number is that it is currently the largest known prime number.It was discovered in August of 2008 by the Great Internet Messene Prime Search(GIMPS). From here on the numbers become much more difficult to render.

6 Googolplex

A lot of people have heard this word as well, fans of the Back to the Future movies mayremember Dr. Emit L. Brown muttering the line shes one in a million, one in a billion,one in a googolplex. But what is a googolplex? Remember how long a googol is? A onewith a hundred zeros after it, a googolplex is a 1 with a googol zeros after it. How big isthis number? If the entire universe was filled with paper and all that those papers hadwritten on them were zeros at a size 10 font, it would only be about half the zerosrequired to write out this number in the long form. Even writing the number inscientific notation is not very practical, for a number this large it requires yet anothertype of notation, something called a power tower. For example our first number 10^80is the first part of a power tower, as the power tower grows the next number would beplaced as a superscript above and to the right of the 80. These are not always possibleto write in digital text, so we have to use yet another short hand, the same methodused on a graphing calculator, the symbol ^. So item 10 on this list can be renderedas so 10^80, or ten to the eightieth. Now with this form of notation we can more easilywrite out the googolplex, which is 10^10^100, or ten to the tenth to the one hundredth.We will also be using these towers for the next few numbers so I hope youre okay withconceptualizing them.

5 Skewes numbers

Skewes Number is the upper bounds to the math problem that: (x) > Li(x), a simplelooking enough equation, however Li is a much more complicated equation in its ownright. Essentially Skewes number proves that a number x exists that violates thisrule, assuming that Reimanns hypothesis is true then that number x is less than10^10^10^36, (most numbers are) the first of Skewes Numbers, much bigger than agoogolplex, noted because of the extra tower. There is also an even large Skewenumber, without assuming Reimanns hypothesis, x is less then 10^10^10^963.

4 Poincare Recurrence Time

This is very complicated stuff, but the core concept is relatively simple: given enoughtime, anything is possible Poincare recurrence time is the amount of time that itwould take for the entire universe to return to a state that is relatively the same as towhat it is today, caused by random quantum fluctuations, or in more simplified terms,History will repeat itself. The high estimate of how long this will take is10^10^10^10^10^1.1 years.

3 Grahams Number

This number is massive in the 1980s it was listed in the Guinness book of worldrecords as the most massive finite number ever used in a serious mathematical proof.It was created Ron Graham, as the upper bounds to a problem in Ramsey Theoryinvolving multicolored hyper cubes. The number is so big even a power tower would betoo cumbersome to represent the number. The only way to easily represent thenumber is to use Knuths Up-Arrow Notation and its own equation. Lets go throughthis piece by piece.

First Knuths Up-Arrow Notation is a method of writing very large numbers, it would bemuch too complicated to explain exactly how the arrows work here, but you canvisualize it this way. 33 translates to 33 or 27, 33 translates to 3^3^3 or7,625,597,484,987. Now if you were to add another arrow to the number 33, thenthe power tower would be over 7.5 trillion levels. This alone is much much bigger thanthe Poincare Recurrence time, and you can add an infinite amount of arrows and eacharrow makes the number that much more powerful.

The representation of Grahams number is: G=f64(4), where f(n)=3^n3. The best way tolook at this is in layers. The first layer is 33, which is already a number too massiveto represent in most other forms. The next layer has that many arrows between 3s.Then take that answer and put that many arrows into the next layer between 3s, andthis goes on for 64 layers. If youre interested the last ten digits of Grahams Numberare 2464195387, no one, not even Graham himself knows what the first digit is.

Infinity

2Most people know of this number and it is used in hyperbole all the time kind of likethe number one zillion but its more complicated then most people realize, and if youthought the numbers that came before this one were strange, this one is evenstranger, and a controversial number too. According to the rules of infinity, there are aninfinite number of odd numbers and even numbers in infinity even though there canonly be half as many odd numbers as total numbers. Infinity plus one equals infinity,infinity minus one equals infinity, infinity plus infinity equals infinity, infinity divided inhalf is still infinity, but infinity minus infinity is not exactly understood, infinity dividedby infinity would probably be 1.

Scientists estimate 1080 subatomic particles in our known universe, but that is theknown universe, or the observable universe. A lot of scientists, however, believe thatthe universe is infinite, or if they dont believe this is the case they still accept it as apossibility. If this is the case then by mathematics alone there must be another Earthout there where every atom happens to be in the exact same location in relation toevery other atom on Earth as it is in our own. The chances of two carbon copy Earthsare extremely small, however in an infinite universe it not only can occur but it has tooccur, and not only that, there has to be an infinite amount of carbon copy Earths outthere if the universe does in fact go one forever.

Not all people believe in infinity however, Israeli Mathematics Professor DoronZeilberger, stated that he feels numbers do not go on forever and there is a number solarge that when you add 1 to it you will go back to zero, however this number is muchhigher then anything humans can comprehend, and that number may never be foundor proven, this belief is the main pillar in a mathematical philosophy known asUltrafinitism.

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1 +1 Infinity + 1

Sorry, had to do it.

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Annonymus 2 years agoInfinity is not a number...

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Exiled Phoenix a year ago> Annonymusif there are an infinite amount of numbers... then...?

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JoeyP a year ago> Exiled PhoenixBut infinity is not a specific number. One can only say "approachinginfinity" because no matter what number you have; add one and it isbigger.

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Exiled Phoenix a year ago> JoeyPLegitimate point.

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Ruz 8 months ago> JoeyPNice one!

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Ian a year ago> JoeyPActually Graham's number in some ways may be equal toinfinity and a number I like to call googolplexian (a number with agoogolplex zeros) is basically equal to infinity simply becausethey can never be reached. They are in a way all equal. If youdivided a second in relation to a planck and went on "forever"you simply could not reach any of the 3 no matter how long youwent. Now hypothetically speaking if you went on for Graham'snumber planck seconds then sure you have reached it. Thething is that's just not possible to go on that long (time andspace would probably stop existing by then) or you would justkeep going and going and you would never get that far becauseyou have more to go. It's just that BIG. Also if you tried toimagine Graham's number in your mind and didn't die from it andwent on long enough your head would literally collapse into ablack hole and this is not a joke there is math behind it just lookit up. It's like the debt ceiling only with number's. It is so biggoing any bigger just doesn't matter because that number in thefirst place cant be reached by anything.

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Lewis Jones 10 months ago> IanHowever googolplexian is not equal to Grahams number. Andthey aren't infinity or infinite numbers. Because if you add 1 onto googolplexian, its bigger. And so on. So although it may notbe possible to reach to those numbers, they are still there

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ruz 8 months ago> IanI think this is not right - you can write googolplex andgoogolplexplex(what you call 'googolplexian') - you just needlots of time!

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Mike 3 months ago> ruzIf you mean in long form then uh no, unless you find anotheruniverse to do it in. You see, our current universe will have longdescended into darkness before you'd have gotten the merestspeck of those numbers written out.

Lewis Jones 9 months ago> Exiled Phoenix

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An infinite amount of numbers means the amount of numbers isunlimited/numbers go on forever

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Ryanlauph 2 years agoThis article is so badly written it's unreadable.You need an editor.

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Michael Jackson a year agoYep .. Close to how many records I sold

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riosrock12 2 years agothis is zillion:100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000,00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001

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Ruz 8 months ago> riosrock12I disagree with you. A zillion is not a number!

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Mike 2 years agoYou *seriously* underestimated the amount of space to write down a Googolplex. Ifyou assume 10^80 elementary particles in the observable universe and wrote a zeroon each particle, you'd need another 10^20 (100 quintillion to be precise) universeseach the size of of our observable universe to write the number down in long form.Remember, each time the exponent number increases by 1 (i.e. 10^80 to 10^81) itmultiples the whole number by a factor of 10. Just saying..

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Stefan 3 years agoLoved the list!Only infinity is not a number.Infinity+1= UndefinedInfinity-Infinity=Undefined One has to use limits to define these "equations"

Lim n+1 = Infinityn->Inf.

Just for those who are interested 7

another annonymus a year ago> Stefaninfinity - infinity = 0infinity / infinity = 1infinity * infinity = infinityinfinity + infinity = infinity

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infinity + infinity = infinityinfinity ^ infinity = infinity20 / 0 = 2020^0 = 20

just my opinion on famous maths problem like zero and infinity

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Anon 9 months ago> another annonymusYou can't use operations like addition and multiplication with infinitybecause infinity is not a number; it is a concept. You also can't divideby zero because there is no number you can multiply 0 by to get 20. Goahead and try it. Also, 20^0 is clearly not 0, it is 1. Any number, except0, to the power of 0 is 1.

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DMFW 6 months ago> AnonAnd what's a number if not a concept? Just because infinitydoesn't behave like other numbers doesn't make it "not anumber". Zero doesn't behave like other numbers. Neither doesthe square root of minus 1 or pi (in different senses of course). Ifyou can do maths with it, it's a number. You can do maths withinfinity (of a kind). Cantor showed the way...

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rusty shackleford a month ago> DMFWInfinity is not a number. See my post above.

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Ruz 8 months ago> AnonTrue... but it is also a number.

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Pangloss a year ago> StefanInfinity +1 is defined, so is 1+infinity. You don't need limits to discuss infinity.There is an entire calculus of infinte numbers. That of course depends onwhich infinity you are talking about. It is obvious to see that there must be aninfinite number of infinite numbers.

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Utah Larry 3 years agoThere are three kinds of people, those who understand math and those who don't. AndI'm one of 'em.

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Infinitely anonymous 2 years agoinfinity is what you call an unending string of numbers

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riosrock12 2 years agoshould be top 12

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riosrock12 2 years agoalso wut about centillion?

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riosrock12 2 years agozomg it should be top 11! the 5th should be mourers number 4th zillion 3rd grahamsnumber 2nd infinity 1st +1 Infinity + 1

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Lewis Jones 10 months ago> riosrock12But infinite is not a number. See my other posts and understand why.

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Johnny 2 years agoYES IT IS INFINITY IZ A NUMBA

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Lewis Jones 10 months ago> JohnnyBut it is not. Is there any way of using 'infinity' in numerical forms? It is notpossible to use infinity in a mathematics equation as infinity is a word todescribe something thats never ending. If a plank of wood went on for infinitymiles then it would go on forever. It will go on for so many miles there isn't anumber for the amount of miles because there is no amount of miles. It goes onforever. If your playing mario and you have infinite lives that means you haveunlimited because lives would be there no matter what.

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dmfw 6 months ago> Lewis JonesThere are all sorts of subtle ways of using transfinite numbers whichCantor explored for the first time. It is possible to do maths with theseconcepts and whilst infinity (strictly there are many infinities, but formost purposes the first one will do) is not a normal number it is still anumber of a kind to which extensions of arithmetic apply...

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Lewis Jones 9 months ago> JohnnyYou've got to be kidding me...

rusty shacklefordf a month agoYes, infinity is not a number. A number is concrete, specific. You also have differenttypes of infinity, i.e. countably infinite and uncountably infinite. The set of naturalnumbers is countably infinite. However, the set of numbers in the interval (0,1) is

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numbers is countably infinite. However, the set of numbers in the interval (0,1) isuncountably infinite.

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Ruz 8 months agogoogolplex = 10^googolgoogolplexplex = 10^googolplexgoogolplexplexplex = 10^googolplexplex

etc... 1

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Lewis Jones 10 months agoInfinite is not a number. It is used as a word similar to forever. There are an infiniteamount of numbers so that also means numbers go on forever. That doesnt makeinfinite a number. If something moves for an infinite amount of time it means it will movefor ever. And that doesn't mean it will move for infinite hours or any other measure oftime because infinite isn't a number. Infinite could just mean forever in someperspective but it isn't just that I know. But infinite is not a number and can't be used ina complete and legit mathematics equation.

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Ruz 8 months ago> Lewis JonesWhy not? Why? Whats a number? Explain what is a number? Here:A finite number: Used to count ,add,measure,multiplication and more...A infinite number - infinity!!!!*Well infinity is used in limits,you need to learn.

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Lewis Jones 8 months ago> RuzImagine there is infinity particles in the world. You can write 1 numberon each particle. Specify the amount of particles you would need towrite down infinity in numerical form. (you can't say infinity)

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MrCake000 a year ago(Infinite+1)-(Infinite+1)

=(Infinite)-(Infinite)

= 0

As you see infinite is not a number and subrtacting two infinite is just as likesubtracting A-A and it is equal to nothing or Zero but as many peapole says infinite is anumber think you are subtracting 1-1 it will give zero so the answer is Zero SOSIMPLE

And whiy infinite minus infinite is 1 how the hack is that possible this would be just like1-1=1 it doesn't make sense lol

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jefjkjsdkfj 2 years agoyou're such a dumb-ass infinity plus one is still infinity and 0 and infinity are concepts.

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careytommy 3 years ago#3 was totally crazy!

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Tony 3 years agoNumber ten, shouldn't that be to the power of minus 80, if it is a sub atomic particle?

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krleblok94 3 years agoThe 1st on this list should be the number that is so large, that when you power zero tothat number, it gives a positive number.

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Lewis Jones 9 months ago> krleblok94Every positive number to the power of zero gives an answer of one. Do someresearch and come back.

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Ruz 8 months ago> Lewis JonesTrue.

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jack54 a year ago> krleblok94That would be every positive number... 1^0=1

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Ed 19 days agoThe article states, "in an infinite universe it not only can occur but it has to occur..."However, one can have an infinite number of whole numbers without including thenumbers 1 to a googolplex (a number larger than the number of atoms in the knownuniverse). After subtracting those numbers or starting the set at googolplex + 1, aninfinite number of whole numbers still remains, so infinity is not necessarily allinclusive. A particular case does not have to occur.

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rust a month agoWhat the hell is "ext, ext"? More than that, the author should go back to grade school(that he probably didn't finish) and learn basic GRAMMAR. I can't bear to readsupposedly scientific articles written by people who don't know the difference between"its" and "it's". By the way, not "33 or 27", but "3^3 or 27".

Check your work!

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Jamie Maddux 3 months agoHow many digets are in the legendary Graham's number

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horst 3 months agowhat about

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Paul Gardner 6 months agoAs others have said, Infinity is not a number. Period. Also, you forgot TREE(3) whichis FAR larger than Graham's number.

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