Biology

How many zeros among Google. Among the googolplex more zeros than the particles in the universe known to us

american mathematician Edward Kazner (1878 - 1955) In the first half of the 20th century, he proposed to callgugol. In 1938, Kazner walked around the park with his two nephews Milton and Edwin orphans and discussed large numbers with them. During the conversation, we were talking about the number from a hundred zeros, which had no own name. Nine-year-old Milton, offered to call this numbergugol. (googol).

In 1940, Kazner together with James Newman published a book "Mathematics and imagination" (Mathematics and the Imagination ), where and was first used this term. According to other data, he first wrote about Google in 1938 in the article " New Names in Mathematics"In January issue of the magazine Scripta Mathematica..

Term gugol. does not have a serious theoretical and practical value. Kazner suggested him in order to illustrate the difference between an unimaginably large number and infinity, and for this purpose the term is sometimes used in teaching mathematics.

Four dozen years after the death of Edward Kazner Termin googol Used for self-confederation now the world famous corporation Google .

Judge for yourself, is good, whether googol is convenient as a unit of measurement of the quantities that really exist within our boundaries Solar system:

the average distance from the Earth to the Sun (1.49598 · 10 11 m) is taken for the astronomical unit (A.E.) - an insignificant tiny on the scale of Gugol;
Pluto - dwarf Planet. The solar system, until recently, the classic planet is the most remote from the ground, it has an orbit diameter equal to 80 AE. (12 · 10 13 m);
quantity elementary particlesFrom which the atoms of the whole universe are consisting, physicists are assessed by a number that does not exceed 10 88.

For the needs of the microcosm - elementary particles of the atom nucleus - the unit of length (generated) serves angstrom (Å \u003d 10-10 m). Introduced in 1868 by Swedish physicist and astronomer Anders Angstrom. This unit of measurement is often used in physics, since

10 -10 m \u003d 0, 000 000 000 1 m

This is an approximate diameter of an electron orbit in an unexcited hydrogen atom. The same order has a nuclear grid step in most crystals.

But at such a scale, the numbers expressing even interstellar distances, far from one google. For example:

The diameter of our galaxy is considered to be equal to 10 5 light years, i.e. It is equal to a piece of 10 5 per distance passable in one year; In Angstroms, this is just

10 31 · Å;

the distance to the presumably existing very remote galaxies does not exceed

10 40 · Å.

Ancient thinkers called the universe space bounded by the visible star sphere of the final radius. The center of this sphere was considered the land, while Archimedes, Aristarh Samos Center of the Universe gave way to the Sun. So, if this universe is filled with sands, then, as the calculations performed by Archimensional in " Pesmite" ("Calculating grains "), it would take about 10 63 pieces of sand - the number that

10 37 = 10 000 000 000 000 000 000 000 000 000 000 000 000

once smaller google.

And yet, a variety of phenomena, even in earthly organic life, is so large that physical quantities were found, surpassed one google. I solve the problem of learning robots to perceive the voice and understanding of them of verbal teams, the researchers found out that the variations of the characteristics of human votes reach numbers

45 · 10 100 \u003d 45 googol.

Many and in the most mathematics of examples of gigantic numbers having a specific belonging.For example, a position entrythe most famous for September 2013 is a simple number,numbers Mersenna

2 57885161 - 1,

It would consist of more than 17 million digits.

By the way, Edward Kazner and his nephew Milton came up with a name for even more than googol - for the number of 10 to the extent of Google -

10 10 100 .

This number was called - googolplex. Let's smile - the number of zeros after the unit in decimal record Gugolplex exceeds the number of all the elementary particles of our universe.

History of the term

Gugol is greater than the number of particles in the part of the universe known to us, which, according to different estimates, has from 10 79 to 10 81, which also limits its application.

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Watch what is "Gugol" in other dictionaries:

Gugolplex (from English GOOGOLPLEX) The number depicted by a unit with Gogol Zulu, 1010100. or 1010,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 000 000 Like Gugol, ... ... Wikipedia

This is an article about the number. See also an article about eng. googol) number, in a decimal number system depicted by a unit with 100 zeros: 10100 \u003d 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 ... Wikipedia

- (from the English Gogolplex) number equal to ten to the extent of Gugol: 1010100 or 1010,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 000. Like Gugol, the term ... ... Wikipedia

Perhaps this article contains an original study. Add links to sources, otherwise it can be set to delete. Additional information can be on the discussion page. (May 13, 2011) ... Wikipedia

Gogol Mogol dessert, the main components of which whipped egg yolk with sugar. There are many variations of this drink: with the addition of wine, vanillin, roma, bread, honey, fruit and berry juices. Often used how to lea ... Wikipedia

Named names of degrees thousands in ascending order name Number American system European system thousand 10³ 10³ Million 106 106 billion 109 109 Billion 109 1012 Trillion 1012 ... Wikipedia

Books

Magic world. Fantastic novel and stories, Vladimir Sigismundovich Number. Roman "Magic of Cosmos". Ground magician together with fabulous heroes Vasilisa, Koschey, Mountain and a fabulous cat are struggling with the power seeking to capture the galaxy. Collection of stories from ...

There are numbers that are so incredibly incredibly great, that even in order to record them, the entire Universe will be required. But that's what is really driven by ... Some of these incomprehensible large numbers are extremely important for understanding the world.

When I say "the greatest number in the universe", in fact, I mean the biggest meaningful The number, the maximum possible number, which is useful in some way. There are many applicants for this title, but I immediately warn you: In fact, there is a risk that an attempt to understand all this will explode your brain. And besides, with a breath of mathematics, you will get little pleasure.

Gugol and Gugolplex

Edward Kasner

We could start with two, very likely the biggest numbers that you have ever heard, and these are really the two biggest numbers that have generally accepted definitions in english language. (There is a fairly accurate nomenclature applied to designate numbers such as big as you would like, but these two numbers will currently you will not find in dictionaries.) Google, since it has become world famous (albeit with errors, notes. In fact, it is Googol) in the form of Google, born in 1920 as a way to interest children in large numbers.

To this end, Edward Casner (in the photo), took two her nephews, Milton and Edwina Sirett, for a walk through New Jersey Palisades. He offered them to put forward any ideas, and then the nine-year-old Milton offered "Gugol". Where he took this word is unknown, but Casner decided that or the number in which the unit cost a hundred zeros will be called Google.

But the young Milton did not stop at this, he suggested an even greater number, the googolplex. This is the number, according to Milton, in which there are 1 in the first place, and then as much zeros as you could write before you get tired. Although this idea is charming, Casner decided that a more formal definition is necessary. As he explained in his book of 1940, the "mathematics and imagination" publication, the definition of Milton leaves the open risky possibility that a random jester can become a mathematician, superior to Albert Einstein simply because he has more endurance.

Thus, Casner decided that the googolplex would be equal, or 1, and then the google zerule. Otherwise, in the notation similar to those with whom we will deal with other numbers, we will say that the googolplex is. To show how hard it fascinates, Karl Sagan once remarked that it is physically impossible to write down all the gugolplex zeros, because it simply does not have enough space in the universe. If you fill the entire amount of dust observed by the universe with small particles of approximately 1.5 microns, the number of different methods for the location of these particles will be approximately equal to one googolplex.

Linguistically speaking, Gugol and the Gugolplex are probably the two greatest significant numbers (at least in English), but, as we now install, the ways of determining the "significance '' are infinitely a lot.

Real world

If we talk about the biggest number, there is a reasonable argument that it really means that you need to find the largest number with the real value in the world. We can start with the current human population, which is currently about 6920 million. World GDP in 2010, estimated about $ 61960 billion, but both of these numbers are insignificant compared with about 100 trillion cells that make up the human body. Of course, none of these numbers can be compared with the complete number of particles in the universe, which is usually considered to be approximately, and this number is so great that our language has no word appropriate to him.

We can play a little with measures of measures, making numbers more and more. So, the mass of the sun in tons will be less than in pounds. A wonderful way to do this is to use the plank units system, which are the lowest possible measures for which the laws of physics remain in force. For example, the age of the universe in the time of the bar is about. If we return to the first place of the Planck time after Big bang, I will see that the density of the universe was then. We get more and more, but we have not yet reached even Google.

The greatest number with any real application of the world - or, in this case Real use in the worlds - probably, is one of the latest estimates of the number of universes in the multiverse. This number is so great that the human brain will be literally unable to perceive all these different universes, since the brain is capable only about configurations. In fact, this number is probably the greatest number with any practical meaning if you do not take into account the idea of \u200b\u200bthe multiverse as a whole. However, there are still much greater numbers that are hiding there. But in order to find them, we must go to the area of \u200b\u200bclean mathematics, and there is no better beginning than simple numbers.

Simple numbers of Mersenna

Part of the difficulties is to come up with a good definition of what a "meaningful" number is. One way is to argue in terms of simple and constituent numbers. A simple number, like you, probably, remember from school mathematics - this is any natural number (notice. Not equal to one), which is divided only on and itself. So, and are simple numbers, and the components. This means that any composite number can ultimately be represented by its simple divisors. In a sense, the number is more important than, let's say, because there is no way to express it through the work smaller numbers.

Obviously, we can go a little further. For example, in fact, simply, which means that in the hypothetical world, where our knowledge of numbers are limited by the number, the mathematician can still express the number. But the next number is simple, and it means that it is the only way to express it - to know directly about its existence. This means that the most famous simple numbers play an important role, and, say, googol - which, ultimately, just a set of numbers and multiply between themselves - not. And since simple numbers are mostly random, there are no ways to predict that an incredibly large number will actually be simple. To this day, the opening of new simple numbers - This is a difficult matter.

Mathematics Ancient Greece They had the concept of simple numbers, at least in 500 BC, and 2000 years later, people still knew what numbers were just about 750. Thinkers of Euclidea seen the opportunity to simplify, but right up to the era of the revival of mathematics could not Really use it in practice. These numbers are known as the number of Mermenna, they are named after the French scientist XVII century Marina Meresenna. The idea is quite simple: the number of Mersenna is any number of species. For example, this is a simple number, the same is true for.

It is much faster and easier to determine the simple numbers of Meressenn than any other type of prime numbers, and computers work intensively in their search over the past six decades. Until 1952, the largest known one was the number - a number with numbers. In the same year, the computer calculated that the number is simple, and this number consists of numbers, which makes it much more than Google.

Computers have since been on the hunt, and at present the number of Mercedes is the biggest one, famous humanity. Detected in 2008, it is a number with almost millions of digits. This is the largest known number that cannot be expressed through any smaller numbers, and if you want to help find an even more Merceda, you (and your computer) can always join the search for http: //www.mersenne. ORG /.

Number of Skusza

Stanley Skusz

Let's turn to simple numbers again. As I said, they behave in root incorrectly, it means that there is no way to predict what the next simple number will be. Mathematics were forced to appeal to some rather fantastic measurements to come up with some way to predict future simple numbers even in a foggy way. The most successful of these attempts is likely to have a function that considers simple numbers that invented in late XVIII A century legendary mathematician Karl Friedrich Gauss.

I will get rid of you from a more complex mathematics - anyway, we have a lot in front - but the essence of the function is as follows: for any whole, you can estimate how many simple numbers smaller. For example, if, the function predicts that there must be simple numbers if there are simply numbers smaller, and if there are smaller numbers that are simple.

The location of the simple numbers is indeed irregular, and this is just an approach of the actual number of prime numbers. In fact, we know that there are simple numbers, smaller, simple numbers of smaller, and simple numbers of smaller. This is an excellent assessment, which is, but it is always only an assessment ... and, more specifically, an estimate from above.

In all known cases Before, a function that finds the number of prime numbers, slightly exaggerates the actual number of simple numbers smaller. Mathematics once thought that it would always be to infinity, that this would certainly applies to some unimaginably huge numbers, but in 1914, John Idenzor Littlewood proved that for some unknown, unimaginably huge number this function will start issuing Less number of prime numbers, and then it will switch between an estimate from above and estimate from the bottom of an infinite number of times.

The hunt was on the point of starting jumps, and here it appeared Stanley Skusz (see photo). In 1933, he proved that the upper border when the function approaching the number of prime numbers first gives a smaller value - this is the number. It is difficult to really understand even in the most abstract sense that it actually represents this number, and from this point of view it was the greatest number ever used in serious mathematical proof. Since then, mathematicians were able to reduce the upper limit to a relatively small number, but the initial number remains known as the number of Skusz.

So how much is the number that makes a dwarf even a mighty googolplex? In The Penguin Dictionary of Curious and Interesting Numbers, David Wells tells about one way, with which Mathematics Hardy managed to comprehend the size of the Skusza number:

"Hardy thought it was" the largest number ever served any specific goal in mathematics ", and suggested that if you play chess with all the particles of the universe as figures, one move would be in the permutation of two particles in places, And the game stopped when the same position would repeat the third time, the number of all possible parties would be approximately the number of Skusz.

And the latter before moving on: we talked about the smaller of two numbers of Skuse. There is another number of Skusza, which mathematician found in 1955. The first number was obtained on the grounds that the so-called Riemann hypothesis is true - this is a particularly complex hypothesis of mathematics, which remains unproved, is very useful when we are talking about simple numbers. Nevertheless, if Riemann's hypothesis is false, Skusz found that the starting point of jumps increases to.

The problem of magnitude

Before we turn to the number, next to which even the number of Skuse looks tiny, we need to talk a little about the scale, because otherwise we do not have the opportunity to appreciate where we are going to go. First, let's take a number - this is a tiny number, so small that people can really have an intuitive understanding of what it means. There are very few numbers that correspond to this description, since the numbers more than six cease to be separate numbers and become "somewhat ''," a lot '', etc.

Now let's take, i.e. . Although in reality we can not intuitively, as it was for the number, to understand what is, to imagine what is very easy. While everything goes well. But what happens if we go to? This is equal, or. We are very far from the ability to imagine this magnitude, like any other, very large - we lose the ability to comprehend certain parts somewhere around a million. (True, insanely a large amount of time would take to really count to a million of anything, but the fact is that we are still capable of perceiving this number.)

Nevertheless, although we cannot imagine, we are at least able to understand in general featuresWhat is 7600 billion, possibly comparing it with something like the US GDP. We switched from intuition to the presentation and to a simple understanding, but at least we still have some gap in understanding what a number is. This is about to change, as we move to another step up the stairs.

To do this, we need to proceed to the designation introduced by Donald Knut, known as the direction notation. In these notation can be written in the form. When we then turn to the number that we get will be equal. This is equal to where a total of triples. We are now significantly and truly surpassed all the other numbers that have already spoken. In the end, even in the biggest of them there were only three or four members in a number of indicators. For example, even a super-number of Skusza is "only" - even with amendment that the basis and the indicators are much larger than, it is still absolutely nothing compared to the size of the numerical tower with billion members.

Obviously, there is no way to comprehend so huge numbers ... and nevertheless, the process by which they are created can still be understood. We could not understand the real number, which is asked by the Tower of degrees in which billion triples, but we can mainly imagine such a tower with many members, and a really decent supercomputer will be able to store such towers in memory, even if he cannot calculate their actual meanings. .

It becomes more abstract, but it will be only worse. You might think that the tower of degrees, the length of which is equal to (moreover, in the previous version of this post I did this error), but it's easy. In other words, imagine that you have the opportunity to calculate the exact value of the power tower from the triple, which consists of elements, and then you took this value and created a new tower with so much in it, ... which gives.

Repeat this process with each subsequent number ( note. Starting right) until you do it, and then you finally get. This is a number that is simply incredibly large, but at least the steps of his reception seem to be understandable if everyone does very slowly. We can no longer understand the numbers or submit to the procedure, thanks to which it turns out, but at least we can understand the main algorithm, only at a fairly long term.

Now prepare the mind to really blow it up.

Graham number (sin)

Ronald Gram.

This is how you get the number of Graham, which takes place in the Guinness Book of Records as the largest number that ever used in mathematical proof. It is absolutely impossible to imagine how large it is, and just as hard to explain exactly what it is. In principle, the Graham number appears when they deal with hypercubs that are theoretical geometric shapes with more than three dimensions. Mathematician Ronald Graham (see photo) wanted to find out with what the smallest number of measurements certain properties of the hypercube will remain stable. (Sorry for such a vague explanation, but I am sure that we all need to get at least two scientific degrees in mathematics to make it more accurate.)

In any case, the Graham number is an estimate from above of this minimum measurement number. So how big is this upper border? Let's go back to the number, so great that the algorithm of his receipt we can understand rather vaguely. Now, instead of just jumping up another level before, we will assume a number in which there are arrows between the first and last three. Now we are far beyond even the slightest understanding of what is this number or even from what needs to be done to calculate it.

Now we repeat this process times ( note. At each next step, we write the number of arrows, equal numberobtained in the previous step).

These are the ladies and gentlemen, the number of Graham, which approximately about the order is above the point of human understanding. This number that is so greater than any number that you can imagine is much more than any infinity that you could ever hope to imagine - it is simply not amenable to even the most abstract description.

But here is a strange thing. Since the Graham number is mostly - it is just three, multiplied with each other, we know some of its properties without the actual calculation of it. We can not imagine the number of Graham with any familiar designations for us, even if we used the whole universe to record it, but I can call you right now the last twelve digits of Graham number :. And that's not all: we know at least the last figures of Graham.

Of course, it is worth remembering that this number is only the upper bound in the original Graham problem. It is possible that the actual number of measurements required to perform the desired property are much less. In fact, since the 1980s, it was considered, according to most of the specialists in this area, which actually the number of measurements is only six - the number is so small that we can understand it at an intuitive level. Since then, the lower border has been increased before, but there is still a very big chance that the decision of the Graham's task does not lie next to the number as big as the number of Graham.

To infinity

So there are numbers more than graham? There are, of course, to begin with the number of Graham. As for the meaningful number ... Well, there are some devilish complex areas of mathematics (in particular, areas known as combinatorics) and informatics in which there are even large numbers than the number of Graham. But we almost achieved the limit of what, as I can hope, will ever be able to reasonably explain. For those who are enough reckless enough to go even further, the literature is offered for additional reading at your own risk.

Well, now an amazing quote that is attributed to Douglas Rey ( note. Honestly, it sounds pretty funny):

"I see the clusters of vague numbers that are hiding there in the dark, behind a small spot of light, which gives a mind candle. They whisper with each other; Conduousing who knows about what. Perhaps they are not very fond of the capture of their smaller brothers by our minds. Or, perhaps, they simply lead a unambiguous numeric lifestyle, there beyond our understanding.

As a child, I was tormented by the question of which there is a largest number, and I got out of this stupid question of almost all in a row. Having learned the number Million, I asked if there was a number of more than a million. Billion? And more than a billion? Trillion? And more trillion? Finally, someone cleverly found, who explained to me that the question is stupid, as it is enough just to add to the largest number of one, and it turns out that it has never been the biggest, as there is a number even more.

And here, after many years, I decided to ask another question, namely: what is the largest number that has its own name? Fortunately, now there is an Internet and you can pose patient search engines that will not call my questions idiot ;-). Actually, I did it, and that's what I found out.

Number	Latin name	Russian console
1	Unus	An-
2	duo.	duo-
3	Tres.	three-
4	quattuor	quadry
5	QUINQUE	quint
6	Sex	sexti
7	septem.	septic
8	Octo.	octic
9	novem.	non-
10	Decem.	deci-

There are two numbers name systems - American and English.

The American system is pretty simple. All the names of large numbers are built like this: at the beginning there is a Latin sequence numerical, and at the end, suffix is \u200b\u200badded to it. The exception is the name "Million" which is the name of the number of a thousand (lat. mille) and magnifying suffix -illion (see table). So the numbers are trillion, quadrillion, quintillion, sextillion, septillion, octillion, nonillion and decillion. The American system is used in the USA, Canada, France and Russia. You can find out the number of zeros in the number written through the American system, it is possible by a simple formula 3 · X + 3 (where X is Latin numerical).

The English name system is most common in the world. She enjoyed, for example, in the UK and Spain, as well as in most former English and Spanish colonies. The names of the numbers in this system are built as follows: so: Sufifix -Ilion is added to the Latin number, the following number (1000 times more) is built on the principle - the same Latin numerical, but suffix - -lilliard. That is, after a trillion in the English system, trilliard goes, and only then the quadrillion followed by quadrilliore, etc. Thus, quadrillion in English and American systems are quite different numbers! You can find out the amount of zeros in the number recorded in the English system and the ending suffix-cylon, it is possible according to the formula 6 · X + 3 (where X is Latin numeral) and according to the formula 6 · x + 6 for the numbers ending on -ylard.

Of english system In Russian, only the number of billion (10 9) passed, which it would still be more correct to call as the Americans call him - Billion, since we received the American system. But who in our country does something according to the rules! ;-) By the way, sometimes in Russian use the word trilliard (you can make sure about it, running a search in Google or Yandex) and it means, apparently, 1000 trillion, i.e. quadrillion.

In addition to the numbers recorded with the help of Latin prefixes on the American or England system, the so-called non-systemic numbers are known, i.e. Numbers that have their own names without any Latin prefixes. There are several such numbers, but I will tell you more about them a little later.

Let's return to the record with Latin numerals. It would seem that they can be recorded to the numbers before concern, but it is not quite so. Now I will explain why. Let's see for a start called numbers from 1 to 10 33:

Name	Number
Unit	10 0
Ten	10 1
One hundred	10 2
One thousand	10 3
Million	10 6
Billion	10 9
Trillion	10 12
Quadrillion	10 15
Quintillion	10 18
Sextillion	10 21
Septillion	10 24
Octillion	10 27
Quintillion	10 30
Decillion	10 33

And now, the question arises, and what's next. What is there for Decillion? In principle, it is possible, of course, with the help of the combination of consoles to generate such monsters as: Andecilion, Duodeticillion, Treadsillion, Quarterdecillion, Quendecyllion, Semtecillion, Septecyllin, Oktodeticillion and New Smecillion, but it will already be composite names, and we were interested in our own names. numbers. Therefore, its own names on this system, in addition to the above, can still be obtained only three - Vigintillion (from Lat. viginti. - Twenty), Centillion (from Lat. centum. - One hundred) and Milleillion (from Lat. mille - one thousand). More than a thousand of their own names for numbers in the Romans was no longer (all numbers more than a thousand they had compounds). For example, a million (1,000,000) Romans called decies Centena Milia., that is, "ten hundred thousand". And now, in fact, Table:

Thus, according to a similar system, the number is greater than 10,3003, which would be their own, incompening name is impossible! Nevertheless, the number more than Milleillion is known - these are the most generic numbers. Let's tell you finally, about them.

Name	Number
Miriada	10 4
Gugol.	10 100
Asankhaya	10 140
Googolplex	10 10 100
The second number of Skusza	10 10 10 1000
Mega	2 (in the notation of Moser)
Megiston	10 (in the notation of Moser)
Moser	2 (in the notation of Moser)
Graham number	G 63 (in the Graham Notation)
Ostasks	G 100 (in Graham Notation)

The smallest such number is miriada (it is even in the Dala dictionary), which means hundreds of hundreds, that is - 10,000. The word is, however, it is outdated and practically not used, but it is curious that the word "Miriada" is widely used, which means not a certain number at all, but Countless, unpleasant set of something. It is believed that the word Miriad (eng. Myriad) came to european languages From ancient Egypt.

Gugol. (from the English. Googol) is a number of ten to a hundredth, that is, a unit with a hundred zeros. About "Google" for the first time wrote in 1938 in the article "New Names in Mathematics" in the January issue of Scripta Mathematica magazine American mathematician Edward Kasner (Edward Kasner). According to him, to call "Gugol" a large number suggested his nine-year-old nephew Milton Sirotta (Milton Sirotta). Well-known this number was due to the search engine named after him Google . Please note that "Google" is a trademark, and googol - a number.

In the famous Buddhist treatise, Jaina-Sutra, belonging to 100 g. BC, meets the number asankhaya (from whale. asianz - innumerable), equal to 10 140. It is believed that this number is equal to the number of space cycles required to gain nirvana.

Googolplex (eng. googolplex) - the number also invented by Castner with his nephew and meaning a unit with a google of zeros, that is 10 10 100. Here's how Kasner himself describes this "Opening":

Words of Wisdom Are Spoken by Children At Least Asiss AS by Scientists. The Name "Googol" Was Invented by A Child (Dr. Kasner "S Nine-Year-Old NEPHEW) Who Was Asked to Think Up a Name For a Very Big Number, Namely, 1 With a Hundred Zeros After IT. He Was Very CERTIAIN THIS THIS NUMBER WAS NOT INFINITE, AND THEREFORE EQUALLY CERTAIN THAT IT TIME THAT A NAME. AT THE SAME TIME THAT HE SUGGESTED "GOOGOL" HE GAVE A NAME FOR A STILL LARGER NUMBER: "GOOGOLPLEX." A GOOGOLPLEX IS MUCH LARGER THAN A Googol, But Is Still Finite, As The Inventor of the Name Was Quick to Point Out.

Mathematics and the Imagination (1940) by Kasner and James R. NEWMAN.

Even more than a googolplex number - the number of Skuse (Skewes "Number) was proposed by Skews in 1933 (Skewes. J. London Math. SOC. 8 , 277-283, 1933.) In case of proof of Riman's hypothesis concerning prime numbers. It means e.in degree e.in degree e.by degree 79, that is, E E E 79. Later, Riel (Te Riele, H. J. J. "On the Sign of the Difference P(x) -li (x). " Math. Comput. 48 , 323-328, 1987) reduced the number of Scyss to E E 27/4, which is approximately 8.185 · 10 370. It is clear that once the value of the number of Scyss depends on the number e., it is not a whole, so we will not consider it, otherwise I would have to recall other unprofitable numbers - the number of pi, the number E, the number of Avogadro, and the like.

But it should be noted that there is a second number of Skusza, which in mathematics is indicated as SK 2, which is even greater than the first number of Skuse (SK 1). The second number of SkuszaIt was introduced by J. Skews in the same article for the designation of the number, to which the Hypothesian of Riman is valid. SK 2 is 10 10 10 10 3, that is, 10 10 10 1000.

As you understand the more degrees, the harder it is to understand which of the numbers is more. For example, looking at the number of Skusz, without special calculations, it is almost impossible to understand which of these two numbers is more. Thus, for super-high numbers, it becomes inconvenient to use degrees. Moreover, you can come up with such numbers (and they are already invented), when the degrees are simply not climbed into the page. Yes, that on the page! They will not fit, even in a book, the size of the whole universe! In this case, the question arises how to record them. The problem, as you understand, are solvable, and mathematics have developed several principles for recording such numbers. True, every mathematician who asked this problem came up with his way of recording, which led to the existence of several not related to each other, methods for recording numbers - these are notations of Knuta, Conway, Steinhause, etc.

Consider the notation of the Hugo Roach (H. Steinhaus. Mathematical Snapshots., 3rd EDN. 1983), which is pretty simple. Stein House offered to record large numbers inside geometric figures - triangle, square and circle:

Steinhauses came up with two new super-high numbers. He called the number - Mega, and number - Megiston.

Mathematics Leo Moser finalized the notation of the wallhause, which was limited by the fact that if it was required to record numbers a lot more Megiston, difficulties and inconvenience occurred, since it had to draw a lot of circles one inside the other. Moser suggested not circles after squares, and pentagons, then hexagons and so on. He also offered a formal entry for these polygons so that the numbers can be recorded without drawing complex drawings. The notation of Moser looks like this:

Thus, according to the notation of Mosel, Steinhouse mega is recorded as 2, and Megstone as 10. In addition, Leo Moser proposed to call a polygon with the number of sides to mega-megaagon. And suggested the number "2 in the megagon", that is 2. This number became known as Moser (Moser "s Number) or just like moser.

But Moser is not the largest number. The largest number ever used in mathematical proof is the limit value known as graham number (Graham "S Number), first used in 1977 in the proof of one assessment in the Ramsey theory. It is associated with bichromatic hypercubs and cannot be expressed without a special 64-level system of special mathematical symbols introduced by the whip in 1976.

Unfortunately, the number recorded in the notation of the whip cannot be translated into a record on the Mosel system. Therefore, this system will have to explain. In principle, it also has nothing complicated. Donald Knut (yes, yes, this is the same whip that wrote the "Art of Programming" and created the TeX editor) invented the concept of a superpope, which offered to record the arrows directed upwards

In general, it looks like this:

I think everything is clear, so let us return to the number of Graham. Graham proposed the so-called G-numbers:

The number G 63 began to be called number Graham (It is often simple as G). This number is the largest number in the world in the world and entered even in the "Guinness Book of Records". A, here is that the number of Graham is greater than the number of Mosel.

P.S. To bring the great benefit to all mankind and become famous in the centuries, I decided to come up with and name the biggest number. This number will be called ostasks And it is equal to the number G 100. Remember it and when your children will ask what the world's largest number, tell them that this number is called ostasks.

Update (4.09.2003): Thank you all for the comments. It turned out that when writing text, I made several errors. I will try to fix now.

I made several mistakes at once, just mentioning the number of Avogadro. First, several people indicated me that in fact 6,022 · 10 23 - the most that neither is a natural number. And secondly, there is an opinion and it seems to me correct that the number of Avogadro is not at all the number in its own, the mathematical sense of the word, as it depends on the system of units. Now it is expressed in the "mole -1", but if it is expressed, for example, in a moles or something else, it will be expressed by a completely different number, but the number of Avogadro will not cease to be at all.
They turned my attention to the fact that the ancient Slavs also gave their names to the numbers and not well forget about them. So here is the list of older names numbers:
10 000 - Darkness
100 000 - Legion
1 000 000 - Leodr
10 000 000 - Raven or Van
100 000 000 - deck
What is interesting, the ancient Slavs also loved big numbers able to count to a billion. Moreover, such a score was called the "Small Account". In some manuscripts, the authors were also considered "the Great Account", reaching the number of 10 50. About the numbers more than 10 50 said: "And more than one to bear the human mind of understanding." The names used in the "Small Account" were transferred to the "Great Account", but with another meaning. So, darkness meant not 10,000, but a million, legion - darkness (million million); Leodr - Legion of Legions (10 to 24 degrees), then it was said - ten Leods, one hundred leodrov, ..., and, finally, one hundred thousand topics Leodrov (10 in 47); Leodr Leodrov (10 in 48) was called Raven and, finally, a deck (10 in 49).
The topic of the national names of the numbers can be expanded if you remember the Japanese name system of numbers, which is very different from the English and American system (Ieroglyphs I will not draw, if someone is interested, then they):
10 0 - Ichi
10 1 - Jyuu
10 2 - Hyaku
10 3 - SEN
10 4 - MAN
10 8 - OKU
10 12 - Chou
10 16 - KEI
10 20 - Gai
10 24 - JYO
10 28 - JYOU
10 32 - Kou
10 36 - Kan
10 40 - SEI
10 44 - SAI
10 48 - Goku
10 52 - Gougasya
10 56 - Asougi
10 60 - Nayuta
10 64 - FUKASHIGI
10 68 - Muryoutaisuu
As for the numbers of Hugo Steinhause (in Russia, his name was translated for some reason as Hugo Steinhause). botev He assures that the idea of \u200b\u200brecording super-high numbers in the form of numbers in circles, belongs not to Steinhouse, and Daniel Harmsu, who hesibly published this idea in the article "Raising the number". I also want to thank Evgeny Skarevsky, the author of the most interesting site entertaining mathematics in the Russian-speaking Internet - watermelon, for the information that Steinhauses came up with not only the number of mega and Megiston, but also offered another number medzonequal to (in his notation) "3 in a circle".
Now about the number miriada or Mirii. What about the origin of this number there are different opinions. Some believe that it originated in Egypt, others believe that it was born only in antique Greece. Be that as it may, in fact, I received Miriad's fame thanks to the Greeks. Miriada was the name for 10,000, and for numbers more than ten thousand names was not. However, in the note "Psammit" (i.e., the calculus of sand) Archimedes showed how to systematically build and call arbitrarily large numbers. In particular, placing the grains in the poppy grain 10,000 (Miriada), it finds that in the universe (the ball with a diameter of the diameter of the earth) would fit (in our symbols) not more than 10,63 grades. It is curious that modern calculations of the amounts of atoms in the visible universe lead to a number of 10,67 (in total in a myriad of times more). The names of the numbers Archimeda suggested such:
1 Miriad \u003d 10 4.
1 di-Miriada \u003d Miriada Miriad \u003d 10 8.
1 tri-myriad \u003d di-myriad di-myriad \u003d 10 16.
1 tetra-myriad \u003d three-myriad three-myriad \u003d 10 32.
etc.

If there are comments -

The famous search engine, as well as a company that created this system and many other products is named after the Gogol number - one of the largest numbers in an infinite multitude of natural numbers. However, the largest number is not even a googol, but a googolplex.

The number of the googolplex was first suggested by Edward Kazner in 1938, it represents a unit and an incredible number of zeros. The name happened from another number - googol - units with hundreds of zeros. Typically, the number of Google is written as 10 100, or 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

Guogolplex, in turn, is the number of ten to the extent of Google. Usually it is written in this way: 10 10 ^ 100, and it is very, very much zeros. They are so much that if you decide to calculate the number of zeros using individual particles in the universe, the particles would end earlier than zeros in the googolplex.

According to Karl Sagan, write this number is impossible, because for its writing it will take more space than exists in the visible universe.

How does the "brains" work - the transmission of messages from the brain to the brain via the Internet