# Largest number---What is it? **URL:** \ **Category:** Factual Questions\ **Created:** [June 17, 2000, 10:26pm UTC](https://boards.straightdope.com/t/largest-number-what-is-it/22725 "2000-06-17T22:26:29Z")\ **Posts on this page:** 16\ **Page:** 1
**Author:** ![insider](https://avatars.discourse-cdn.com/v4/letter/i/bbe5ce/32.png) [@insider](https://boards.straightdope.com/u/insider)\ **Post date:** [June 17, 2000, 10:26pm UTC](https://boards.straightdope.com/t/largest-number-what-is-it/22725/1 "2000-06-17T22:26:29Z")
I understand that the larget number is called a googooplex. Is this correct? It seems like you cannot have the largest number ever because all you have to do is to add a 1 to it to make it greater. Can someone straighten me out here? Thanks ---
**Author:** ![astro](https://avatars.discourse-cdn.com/v4/letter/a/9dc877/32.png) [@astro](https://boards.straightdope.com/u/astro)\ **Post date:** [June 17, 2000, 10:49pm UTC](https://boards.straightdope.com/t/largest-number-what-is-it/22725/2 "2000-06-17T22:49:44Z")
Googooplex… bah! The largest number known to man is a “gazillion” as immortalized in the movie “Forest Gump”. A gazillion is infinitely large and you cannot add any more numbers to this number… well because it’s just the biggest there is and there’s no more room for any more! ---
**Author:** ![handy](https://avatars.discourse-cdn.com/v4/letter/h/b5a626/32.png) [@handy](https://boards.straightdope.com/u/handy)\ **Post date:** [June 17, 2000, 10:56pm UTC](https://boards.straightdope.com/t/largest-number-what-is-it/22725/3 "2000-06-17T22:56:07Z")
'The highest lexicographically accepted named number in the system of successive powers of ten is the centillion, first recorded in 1852. It is the hundredth power of a million, or 1 followed by 600 zeros. The number 10 to the 10 to the 0 is designated a googol. The term was suggested by the nine-year old nephew of Dr Edward Kasner (USA). Ten raised to the power of a googol is described as a googolplex. Some conception of the magnitude of such numbers can be gained when it is said that the number of electrons in some models of the observable Universe does not exceed 10 to the 87. The highest named number outside the decimal notation is the Buddhist asankhyeya, which is equal to 10 to the 14 to the 0 and mentioned in Jain works of c. 100 B.C. The highest number ever used in a mathematical proof is a bounding value published in 1977 and known as Graham’s number. It concerns bichromatic hypercubes and is inexpressible without the special ‘arrow’ notation, devised by Knuth in 1976, extended to 64 layers." ---
**Author:** ![omni-not](https://avatars.discourse-cdn.com/v4/letter/o/8dc957/32.png) [@omni-not](https://boards.straightdope.com/u/omni-not)\ **Post date:** [June 17, 2000, 10:56pm UTC](https://boards.straightdope.com/t/largest-number-what-is-it/22725/4 "2000-06-17T22:56:31Z")
According to my 1996 edition of Guiness Book of World Records, “the largest lexicographically accepted named number in the system of successive powers of 10 is the centillion, first recorded in 1852. It is the hundredth power of a million, or 1 followed by 600 zeros.” You do the math.🙂 ---
**Author:** ![omni-not](https://avatars.discourse-cdn.com/v4/letter/o/8dc957/32.png) [@omni-not](https://boards.straightdope.com/u/omni-not)\ **Post date:** [June 17, 2000, 10:57pm UTC](https://boards.straightdope.com/t/largest-number-what-is-it/22725/5 "2000-06-17T22:57:55Z")
Eh. What handy said…😃 ---
**Author:** ![RM\_Mentock](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@RM\_Mentock](https://boards.straightdope.com/u/RM_Mentock)\ **Post date:** [June 17, 2000, 11:29pm UTC](https://boards.straightdope.com/t/largest-number-what-is-it/22725/6 "2000-06-17T23:29:57Z")
> [@](#): > > **handy wrote:** > The number 10 to the 10 to the 0 is designated a googol. I know that’s not a typo, since you used the notation twice. But I don’t think I’ve ever seen it before. How does it work? A googol is 10^100, right? ---
**Author:** ![manhattan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/manhattan/32/7_2.png) [@manhattan](https://boards.straightdope.com/u/manhattan)\ **Post date:** [June 18, 2000, 12:02am UTC](https://boards.straightdope.com/t/largest-number-what-is-it/22725/7 "2000-06-18T00:02:37Z")
**SDStaff Dex** on [Google and Googleplex](http://www.straightdope.com/mailbag/mgoogol.html). ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [June 18, 2000, 3:39am UTC](https://boards.straightdope.com/t/largest-number-what-is-it/22725/8 "2000-06-18T03:39:04Z")
> [@](#): > > inexpressible without the special ‘arrow’ notation, devised by Knuth in 1976, extended to 64 layers. You knew this was coming, but you had to make us ask, didn’t you? OK, I’ll ask. What’s the “special arrow notation” and how do you extend it to 64 layers? ---
**Author:** ![my85car](https://avatars.discourse-cdn.com/v4/letter/m/ed8c4c/32.png) [@my85car](https://boards.straightdope.com/u/my85car)\ **Post date:** [June 18, 2000, 3:48am UTC](https://boards.straightdope.com/t/largest-number-what-is-it/22725/9 "2000-06-18T03:48:57Z")
What’s the biggest number? REALLY, REALLY, REALLY, REALLY, REALLY, REALLY, BIG !!! :D:D:D:D:D:D ---
**Author:** ![Derleth](https://avatars.discourse-cdn.com/v4/letter/d/b9e5f3/32.png) [@Derleth](https://boards.straightdope.com/u/Derleth)\ **Post date:** [June 18, 2000, 4:10am UTC](https://boards.straightdope.com/t/largest-number-what-is-it/22725/10 "2000-06-18T04:10:24Z")
Seems an interesting question. To really answer it, one must accept the fact that numbers are infinite, while any notation system is finite, at least in practice. You can always add a few zeros, but eventually you run out of things to write on and with. Anyway, I’m glad that nobody has said ‘infinity’. That is not really a number in our sense of the word, but is a concept as many sets of numbers extend to infinity and some sets converge at infinity (For example, try adding .5 to .25 to .125 to … dividing the next number by 2, getting a set that will reach 1 after an infinite number of iterations. Neat, eh? An important concept in calculus.) Graham’s number is here: [http://public.logica.com/~stepneys/cyc/g/graham.htm](http://public.logica.com/~stepneys/cyc/g/graham.htm) and it is _very_ large. ---
**Author:** ![John\_Kentzel-Griffin](https://avatars.discourse-cdn.com/v4/letter/j/ccd318/32.png) [@John\_Kentzel-Griffin](https://boards.straightdope.com/u/John_Kentzel-Griffin)\ **Post date:** [June 18, 2000, 3:34pm UTC](https://boards.straightdope.com/t/largest-number-what-is-it/22725/11 "2000-06-18T15:34:15Z")
> [@](#): > > **Derleth** said: > Anyway, I’m glad that nobody has said ‘infinity’. That is not really a number in our sense of the word, but is a concept … I was just about to say infinity. How can you say infinity is not a number? Numbers are just what we define them to be and what we define them to be depends upon the situation. Is 1/2 a number? How about -1. These are not “counting” numbers, but they are numbers that are necessary in some situations and meaningless in others. The same applies to infinity or infinities. ---
**Author:** ![GasDr](https://avatars.discourse-cdn.com/v4/letter/g/ba9def/32.png) [@GasDr](https://boards.straightdope.com/u/GasDr)\ **Post date:** [June 18, 2000, 5:38pm UTC](https://boards.straightdope.com/t/largest-number-what-is-it/22725/12 "2000-06-18T17:38:08Z")
It seems that I once read in Guiness B.O.W.R. that the highest number was a ‘megaston’ which was described as a number so large that it had no physical meaning. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [June 18, 2000, 8:16pm UTC](https://boards.straightdope.com/t/largest-number-what-is-it/22725/13 "2000-06-18T20:16:36Z")
I think that what RM Mentock meant to say, is that he’s never seen that notation used in a way that makes any sense. Where I come from, 10 to the 10 to the 0 is either 10 or 1, depending on the order of operations you use for exponentiation, because anything (other than possibly 0 or the transfinites) to the 0 is 1. Graham’s number and arrow notation: First, we define arrow notation (I’m using the ^ symbol here, because I don’t have an “up arrow” key). 2^2 is defined as two to the two. 2^^2 is two to the (2^2), 2^^^2 = 2 to the (2^^2), etc. I think it can be seen that this generates some pretty big numbers, pretty quickly-- 2^2 = 4, 2^^2 = 16, 2^^^2 = 65536, and 2^^^^2 wouldn’t even fit on this page. Now for the fun part, layering. First, we take 2^^2 as our first layer. Then, we take the number that results from that, and use that number in our second layer, so our second layer is 2^^^^^^^^^^^^^^^^2. Then, we take that number, and put that number of arrows in the third layer. Continue this process for 64 layers, and what you finally get out of the end is Graham’s number. Now for the ironic part: Why Graham used this number. There’s a certain quantity in 4-dimensional topology (sorry, don’t remember what it’s called) that was known to be finite, but nobody knew the value, or even an upper bound on it. Graham proved that that quantity must be less than or equal to the above-mentioned monstrosity. It is widely believed, however, although not proven, that the actual value of that quantity is six. Most of the information herein comes from an old Scientific American article, but I’m going from memory here. I’m afraid that I can’t give a date for it, other than “sometime after 1970”. ---
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [June 19, 2000, 4:52am UTC](https://boards.straightdope.com/t/largest-number-what-is-it/22725/14 "2000-06-19T04:52:25Z")
Here’s a fun game that might interest some of you. I played it with two people, but any number would work. You all think up some finite number, and then take turns saying what yours was. (No fair changing.) Whoever thought up the highest number wins. I would always win the first couple times I played someone. A typical example: THEM: 100 Trillion. ME: 10[sup]200[/sup]. I win. Want to play again? THEM: Sure. You go first this time. ME: Okay. ((1,000,000!)!)! THEM: Ah, you got me. I only had 10[sup]1,000,000[/sup]. Pretty soon, they get the idea that you just come up with a number that’s so big that nobody would have any idea what it is. For instance, n raised to the n a million times, where n is a million with a million factorial signs after it. When both people are doing things like this, you pretty much have to call it draw. ---
**Author:** ![RM\_Mentock](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@RM\_Mentock](https://boards.straightdope.com/u/RM_Mentock)\ **Post date:** [June 19, 2000, 4:39pm UTC](https://boards.straightdope.com/t/largest-number-what-is-it/22725/15 "2000-06-19T16:39:50Z")
> [@](#): > > **Chronos wrote:** > I think that what RM Mentock meant to say, is that he’s never seen that notation used in a way that makes any sense. Where I come from, 10 to the 10 to the 0 is either 10 or 1, depending on the order of operations you use for exponentiation, because anything (other than possibly 0 or the transfinites) to the 0 is 1. Well, I have seen that notation used in a way that makes sense, but not in a way so that the answer came out to be a googol. > [@](#): > > Graham’s number and arrow notation: > First, we define arrow notation (I’m using the ^ symbol here, because I don’t have an “up arrow” key). 2^2 is defined as two to the two. 2^^2 is two to the (2^2), 2^^^2 = 2 to the (2^^2), etc. I think it can be seen that this generates some pretty big numbers, pretty quickly-- 2^2 = 4, 2^^2 = 16, 2^^^2 = 65536 2^^2 = 2^^^2 = 4. Arrow notation is a generalization of exponentiation: mxn means n copies of m added together. m^n means n copies of m multiplied together: mxmxmx…xm. m^^n means n copies of m^m^m^…^m, and m^^^n means n copies of m^^m^^m^^…^^m. So, 2^^2 = 2^2 = 4, and 2^^^2 = 2^^2 = 2^2 = 4, but 3^^^3 = 3^^3^^3 = 3^^(3^3^3) = 3^^(7625597484987), or 3 to the exponent 3 to the exponent 3…with over 7 trillion threes. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [June 19, 2000, 6:27pm UTC](https://boards.straightdope.com/t/largest-number-what-is-it/22725/16 "2000-06-19T18:27:52Z")
I stand corrected, RM. The point is, though, that you take a method that takes a reasonably small number and turns it into an unbelievably large number extremely quickly, and repeat an insane number of times. And Achernar, I don’t think that there’s any way any sane person is going to top Graham’s Number in your game, without invoking Graham’s number itself. Examples: G[sup]G[/sup] G^^G Arrow notation, repeated for G layers For that matter, I’m not sure any sane person would even contemplate those numbers. It gets to the point where you have to define their size in terms of the logarithm of the logarithm of the number of logarithms you have to take. 🙂