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The largest number is called. The biggest digit in the world

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.

From the English system, only the number of billion (10 9) passed from the English system, which would still be more correctly called 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 of Miriad (Eng. Myriad) came to European languages \u200b\u200bfrom 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.
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 Sklylyevsky, the author of the most interesting site on 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 -

"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.
Douglas Ray

Each early or later torments the question, and what the largest number. On the question of the child can be answered by a million. What's next? Trillion. And even further? In fact, the answer to the question is what the largest numbers are simple. To the large number, it is simply worth adding a unit, as it will not be the largest. This procedure can be continued to infinity.

And if you wonder: what is the largest number, and what is his own name?

Now we will find out ...

There are two numbers name systems - American and English.

From the English system, only the number of billion (10 9) passed from the English system, which would still be more correctly called 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 the search in Google or Yandex) and it means, apparently, 1000 trillion, i.e. quadrillion.

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 calleddecies 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 own, the inexpensive name is not possible! Nevertheless, the number more than Milleillion is known - these are the most generic numbers. Let's tell you finally, about them.

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 is widely used There is not a certain number at all, but countless, the incredible set of something. It is believed that the Word of Miriad (Eng. Myriad) came to European languages \u200b\u200bfrom ancient Egypt.

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 grains in the poppy seeds of 10,000 (Miriad), he finds that in the universe (the ball with a diameter of the diameter of the earth) would fit (in our designations) not more than 1063 peschin. It is curious that modern counting of the number of atoms in the visible universe leads to67 (In total, Miriad times more). The names of the numbers Archimeda suggested such:
1 Miriad \u003d 10 4.
1 di-Miriada \u003d Miriad Miriad \u003d 108 .
1 tri-myriad \u003d di-myriad di-myriad \u003d 1016 .
1 tetra-myriad \u003d three-myriad three-myriad \u003d 1032 .
etc.

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.

Edward Kasner (Edward Kasner).

On the Internet, you can often meet the mention that - but it is not so ...

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 google zeros, that is 10 10100 . 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 greater than the googolplex number - number of Skusza (Skewes "Number) was proposed by Skusom in 1933 (Skewes. J. London Math. SOC. 8, 277-283, 1933.) In the proof of Riman's hypothesis concerning prime numbers. It means e.in degree e.in degree e.to degree 79, that is, EE 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 Skuse to EE 27/4 that 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 remember other insignificant numbers - the number Pi, the number E, and the like.

But it should be noted that there is a second number of Skuse, which in mathematics is indicated as SK2, which is even more than the first number of Skusz (SK1). The second number of Skusza, J. Skews were introduced in the same article to designate the number for which Riman's hypothesis is not valid. SK2 is 1010. 10103 , that is, 1010 101000 .

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

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.

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 G63 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 G100. Remember it and when your children will ask what the world's largest number, tell them that this number is called ostasks

So there are numbers more than graham? There are, of course, to start there are 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 reached the limit of what can be reasonably and understood.

John Sommer.

Put after any digit of zeros or prolonged with dozens, raised to an arbitrarily degree. It will not seem little. It seems a lot. But bare records, nevertheless, are not too impressive. The praying zeros of humanities are not so much surprise as light yawn. In any case, to any large number in the world that you can imagine, you can always add another unit ... and the number will be released even more.

Nevertheless, is there a word in Russian or any other language to designate very large numbers? Those who are more than a million, billion, trillion, billion? And in general, Billion is how much?

It turns out that there are two numbers name systems. But not the Arab, Egyptian, or any other ancient civilizations, but is American and English.

In the American system Numbers are called like this: Latin numerical + - Illyon (suffix) is taken. Thus, the numbers are obtained:

Trillion - 1 000 000 000 000 (12 zeros)

Quadrillion - 1,000,000,000,000,000 (15 zeros)

Quintillion - 1 and 18 zeros

Sextillion - 1 and 21 zero

Septillion - 1 and 24 zero

octillion - 1 and 27 zeros

Nonillion - 1 and 30 zeros

Decillion - 1 and 33 zero

Formula is simple: 3 · x + 3 (x - Latin numeral)

In theory, there should be more Anilion numbers (Unus in Latin - one) and duolaion (Duo - two), but, in my opinion, such names are not used at all.

English Names System Numbers Distributed to a greater extent.

Here, the Latin numerical is taken and suffix is \u200b\u200badded to it. However, the name of the next number, which is more than the previous one 1,000 times, is formed using the same Latin number and suffix - Illiard. I mean:

Trillion - 1 and 21 zero (in the American system - Sextillion!)

Trilliard - 1 and 24 zero (in the American system - Septillion)

Quadrillion - 1 and 27 zeros

Quadrillard - 1 and 30 zeros

Quintillion - 1 and 33 zero

Quinilliard - 1 and 36 zeros

Sextillion - 1 and 39 zeros

Sextillard - 1 and 42 zero

Formulas for counting the number of zeros, are:

For numbers ending on - Illion - 6 · X + 3

For numbers ending in - Illiard - 6 · X + 6

As you can see, confusion is possible. But not reassured!

Russia adopted an American number of numbers. From the English system, we borrowed the name of the number "billion" - 1 000 000 000 \u003d 10 9

And where is the "cherished" billion? - Why is Billion - this is a billion! American. And we, although we use the American system, and "Billion" took from English.

Using the Latin names of the numbers and the American system called numbers:

- Vigintillion - 1 and 63 zero

- Centillion - 1 and 303 zero

- Milleilla - Unit and 3003 zero! Oh-go ...

But this, it turns out, not all. There are still numbers are intimidated.

And the first of them, probably, miriada - hundred hundred \u003d 10 000

Gugol. (It is in honor of him known a well-known search engine) - one and a hundred zeros

In one of the Buddhist treatises called the number asankhaya - One and hundred forty zeros!

Name of the number googolplex (like Gugol) invented English Mathematician Edward Casner and his nine nephew - a unit with - Mom dear! - Gogol Zulu !!!

But this is not all ...

Mathematics Skusz called in honor of himself the number of Skusza. It means e.in degree e.in degree e.to degree 79, that is, E E E 79

And then there was a great difficulty. You can come up with the names. But how to record them? The number of degrees degrees is already such that it is simply not cleaned to the page! :)

And then some mathematics began to record numbers in geometric shapes. And first, they say, such a way of recording came up with an outstanding writer and thinker Daniel Ivanovich Harms.

And, nevertheless, what is the largest number in the world? - It is called the forex and equal to G 100,

where G is the number of Graham, the largest number ever used in mathematical evidence.

This number is the forex - invented a wonderful person, our compatriot Stas Kozlovsky, To the lighh which I am you and address :) - ctac

Once I read one tragic story, where it is narrated by Chukche, whom the polar explosives have learned to count and record numbers. The magic of the numbers was so struck him that he decided to record a notebook in the notebook presented by the polarists absolutely all in the world in a row, starting from the unit. Chukcha throws all his affairs, stops communicating even with his own wife, does not hunt more on Nerpen and seals, and everything writes and writes numbers in the notebook .... So goes for a year. In the end, the notebook ends and Chukcha understands that he was able to write only a small part of all numbers. He bitterly crying and burns his written notebook in despair to start living a simple life of a fisherman, without thinking more about the mysterious infinity of the numbers ...

We will not repeat the feat of this Chukchi and try to find the largest number, as any number is enough just to add a unit to get the number even more. I will define although it looks like, but another question: which of the numbers that have their own name, the greatest?

It is obvious that although the numbers themselves are infinite, their own names are not so much, since most of them are content with the names composed of smaller numbers. So, for example, the numbers 1 and 100 have their own names "one" and "hundred", and the name of the number 101 is already composite ("one hundred one"). It is clear that in the final set of numbers, which humanity awarded his own name, should be some greatest number. But what is it called and what is it equal? Let's try to figure it out and find it in the end, this is the largest number!

Number	Latin quantitative numeral	Russian console

"Short" and "Long" scale

The history of the modern system of the name of large numbers is beginning from the middle of the XV century, when in Italy began to use the words "million" (literally - a large one thousand) for thousands in square, "Bimillion" for a million in a square and trimillion for a million in Cuba. About this system, we know thanks to the French Mathematics of Nicolas Chuke (Nicolas Chuquet, Ok. 1450 - approx. 1500): In its treatise, "TRIPARTY EN LA SCIENCE DES NOMBRESS, 1484) he developed this idea, offering to use Latin Quantitatively numerical (see table) by adding them to the end of "-Lion". Thus, Bimillion has turned into Billion, Trimillion in trillion, and a million in the fourth degree became a "quadrillion".

In the Schuke system, the number 10 9, which was between a million and Billion, did not have its own name and was simply called "Thousand Millions", the same way 10 15 was called "Thousand Billion", 10 21 - "Thousand Trillion", etc. It was not very convenient, and in 1549, the French writer and scientist Jacques Pelette (Jacques Peletier Du Mans, 1517-1582) proposed to form such "intermediate" numbers with the same Latin prefixes, but the end of the "Stalliard". So, 10 9 became known as the "billion", 10 15 - "Billiard", 10 21 - "Trilliards", etc.

The Schuke-Pelette Schuke gradually became popular and they began to use all over Europe. However, an unexpected problem arose in the XVII century. It turned out that some scientists for some reason began to be confused and called the number 10 9 not "billion" or "thousand of millions", but "Billion". Soon, this error quickly spread, and a paradoxical situation arose - "Billion" became simultaneously synonymous with the "billion" (10 9) and "Million Millions" (10 18).

This confusion continued long enough and led to the fact that in the United States created their system names of large numbers. According to the American Names System, the numbers are built in the same way as in the Schuke system - the Latin prefix and the end of Illion. However, the values \u200b\u200bof these numbers differ. If the names of the name "Illion" received the numbers that were degrees of a million in the ILION system, then in the American system, the end of the "-Illion" received a degree of thousands. That is, a thousand million (1000 3 \u003d 10 9) began to be called "Billion", 1000 4 (10 12) - "Trillion", 1000 5 (10 15) - "quadrillion", etc.

The old language of the name of large numbers continued to be used in a conservative Britain and began to be called "British" throughout the world, despite the fact that she was invented by the French shyke and Pelet. However, in the 1970s, the United Kingdom officially switched to the "American system", which led to the fact that calling one American system, and another British became somehow strange. As a result, now the American system is usually called a "short scale", and the British system or the Schuke-Pelette system is a "long scale".

In order not to get confused, we will summarize the result:

Name of the number	Value by "short scale"	Value for a "long scale"

Billion

Billiard
Trillion
Trilliard
Quadrillion
Quadrilliard
Quintillion
Quintilliard
Sextillion
Sextillard
Septillion
Septilliard
Octillion
Octallard
Quintillion
Nonilliard
Decillion
Decilliard.

A short name scale is used now in the USA, Great Britain, Canada, Ireland, Australia, Brazil and Puerto Rico. In Russia, Denmark, Turkey and Bulgaria, a short scale is also used, except that the number 10 9 is not called "Billion", but a "billion". The long scale is currently continuing to be used in most other countries.

It is curious that in our country the final transition to a short scale occurred only in the second half of the 20th century. So, for example, Jacob Isidovich Perelman (1882-1942) in its "entertaining arithmetic" mentions parallel existence in the USSR of two scales. The short scale, according to Perelman, was used in everyday use and financial calculations, and long - in scientific books on astronomy and physics. However, now use the long scale in Russia is incorrect, although the numbers there are and large.

But back to the search for the largest number. After decillion, the names of numbers are obtained by combining consoles. Thus, such numbers are as undercillion, duodeticillion, treadsillion, quotoroidicillion, quindecillion, semotecyllium, septemberion, octopesillion, newcillion, etc. are obtained. However, these names are no longer interesting for us, since we agreed to find the largest number with our own incompatible name.

If we turn to Latin grammar, it was discovered that there were only three numbers for numbers for numbers more than ten at the Romans: Viginti - "Twenty", Centum - "Hundred" and Mille - "Thousand". For numbers more than the "thousand", the own names of the Romans did not exist. For example, a million (1,000,000) Romans called "Decies Centena Milia", that is, "ten times on hundred thousand". According to the rules, these three remaining Latin numerals give us such names for the numbers as "Vigintillion", "Centillion" and Milleillan.

So, we found out that by the "short scale" the maximum number that has its own name and is not a composite of smaller numbers - this is "Milleilla" (10 3003). If the "long scale" of the names of numbers would be adopted in Russia, then Milleirliard would be the largest number with their own name (10 6003).

However, there are names for even large numbers.

Numbers outside the system

Some numbers have their own name, without any connection with the name system with Latin prefixes. And there are a lot of such numbers. Can, for example, remember the number e., the number "PI", dozen, the number of beasts, etc. However, since we are now interested in large numbers, we will consider only those numbers with our own inconsimal name that are more than a million.

Until the XVII century, its own numbers name system was used in Russia. Tens of thousands were called "darkness", hundreds of thousands - "Legions", Millions - "Lodrats", tens of millions - "crowns", and hundreds of millions - "decks". This score to hundreds of millions was called a "small account", and in some manuscripts, the authors were also considered "the Grand Account", which used the same names for large numbers, but with another meaning. Thus, the "darkness" meant not ten thousand, and a thousand thousand (10 6), "Legion" to the darkness of those (10 12); Leodr - Legion Legions (10 24), "Raven" - Leodr Leodrov (10 48). "The deck" for some reason was not called "Raven Voronov" (10 96) for some reason, but only ten "crows", that is, 10 49 (see Table).

Name of the number	Meaning in "Small Account"	Meaning in "Great Account"	Designation



Raven (Van)

The number 10 100 also has its own name and invented his nine-year-old boy. And it was so. In 1938, American mathematician Edward Kasner (Edward Kasner, 1878-1955) walked around the park with his two nephews and discussed large numbers with them. During the conversation, we were talking about the number from a hundred zeros, which had no own name. One of the nephews, a nine-year-old Milton Sirett, offered to call this number "Google" (GOOGOL). In 1940, Edward Casner in conjunction with James Newman wrote a scientific and popular book "Mathematics and imagination", where he told Mathematics lovers about the number Gugol. Hugol received even wider fame in the late 1990s, thanks to the Google search engine named after him.

The name for an even more than Google, originated in 1950 due to the father of informatics Claud Shannon (Claude Elwood Shannon, 1916-2001). In his article "Programming a computer for playing chess", he tried to assess the number of possible chess game options. According to him, each game lasts an average of 40 moves and at every time the player makes a choice on average of 30 options, which corresponds to 900 40 (approximately 10,118) game options. This work has become widely known, and this number began to be called "Shannon's number".

In the famous Buddhist treatise, Jaina Sutra, belonging to 100 BC, occurs, is found by the number "Asankhey" equal to 10 140. It is believed that this number is equal to the number of space cycles required to gain nirvana.

Nine-year-old Milton Sirette entered the history of mathematics not only by what came up with the number of Google, but also in the fact that at the same time he suggested another number - "Gugolplex", which is equal to 10 to the degree of "Google", that is, a unit with google zerule.

Two more numbers, large than the googolplex, were proposed by South African Mathematics Stanley Skusom (Stanley Skewes, 1899-1988) in the proof of Riemann's hypothesis. The first number that later began to call the "first number of Skuse", equal e. in degree e. in degree e. in degree 79, that is e. e. e. 79 \u003d 10 10 8,85.10 33. However, the "second number of Skusza" is even more and amounts to 10 10 10 1000.

Obviously, the more degrees in degrees, the more difficult it is to write numbers and understand their meaning when reading. Moreover, it is possible to come up with such numbers (and, by the way, have already been invented), when the degrees are simply not placed on the page. Yes, that on the page! They will not fit even in the book size with the whole universe! In this case, the question arises as such numbers to record. The problem, fortunately, is solvable, and mathematics have developed several principles for recording such numbers. True, every mathematician who wondered by this problem came up with his way of recording, which led to the existence of several non-other ways to write large numbers - these are notations of whip, Konveya, Steinhause, etc. With some of them we have to deal with some of them.

Other notations

In 1938, in the same year, when Nine-year-old Milton Sirette came up with the number of Gugol and the Gugolplex, a book about entertaining mathematics "Mathematical Kaleidoscope" was published in Poland, written by Hugo Steinhaus (Hugo Dionizy Steinhaus, 1887-1972). This book has become very popular, withstood many publications and has been translated into many languages, including English and Russian. In it, Steinghauses, discussing large numbers, offers an easy way to write their, using three geometric shapes - triangle, square and circle:

"N. In a triangle "means" n N.»,
« n. in a square "means" n. in n. triangles ",
« n. In the circle, "means" n. in n. Squares.

Explaining this method of recording, Steinhause comes up with the number "mega", equal to 2 in a circle and shows that it is equal to 256 in the "square" or 256 in 256 triangles. To calculate it, it is necessary to 256 to the degree 256, the resulting number 3.2.10 616 is erected into a ratio of 3.2.10 616, then the resulting number of the resulting number and so it is to raise a distance of 256 times. For example, the calculator in MS Windows cannot count due to overflow 256 even in two triangles. Approximately this huge number is 10 10 2.10 619.

Having determined the number of "mega", Steinhause offers readers independently evaluate another number - "Medzon", equal to 3 in a circle. In another edition of the book, Steinhauses, instead of a medical unit, it proposes to evaluate even more - Megiston, equal to 10 in the circle. Following the Steinhause, I will also recommend readers for a while to tear yourself away from this text and try to write these numbers yourself with the help of ordinary degrees to feel their gigantic value.

However, there are names and for b aboutenough numbers. So, Canadian mathematician Leo Moser (Leo Moser, 1921-1970) finalized the notation of the Stengaus, which was limited by the fact that if it were necessary to record numbers a lot of big Megiston, then there would be difficulties and inconvenience, as it would have to draw a lot of circles one inside 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:

« n. triangle "\u003d n N. = n.;
« n. squared "\u003d n. = « n. in n. Triangles "\u003d n. N.;
« n. in pentagon "\u003d n. = « n. in n. squares "\u003d n. N.;
« n. in k +.1-carbon "\u003d n.[k.+1] \u003d " n. in n. k."Grounds" \u003d n.[k.] N..

Thus, according to the notation of Mosel, Steingerovsky "Mega" is recorded as 2, "Mazzon" as 3, and "Megiston" as 10. In addition, Leo Moser proposed to call a polygon with the number of parties to Mega-Magagon. And he suggested the number "2 in Magagon", that is 2. This number became known as the number of Moser or simply as "Moser".

But even "Moser" is not the largest number. So, the largest number ever used in mathematical evidence is the "Graham". For the first time, this number was used by the American mathematician Ronald Gram (Ronald Graham) in 1977 in the proof of one assessment in the Ramsey theory, namely, when calculating the dimension of certain n.- Meritative bichromatic hypercubes. Family the sameness of Graham received only after the story about him in the book of Martin Gardner "from Mosaik Penrose to reliable ciphers in 1989.

To explain how great Graham number will have to explain another way to record large numbers introduced by Donald Knut in 1976. American professor Donald Knut invented the concept of a superpope, which offered to record the arrows directed upwards:

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

Here is the number G 64 and is called the Graham number (it is often simple as G). This number is the largest number known in the world used in mathematical proof, and even listed in the Guinness Book of Records.

And finally

Having written this article, I can not help but resist the temptation and do not come up with my number. Let this number be called " ostasks"And it will be 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.

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Many are interested in questions about how large numbers are called and what number is the largest in the world. With these interesting questions and we will understand this article.

History

Southern and Eastern Slavic nations for recording numbers used alphabetical numbering, and only those letters that are in the Greek alphabet. Above the letter that marked the figure, put a special "Title" icon. The numerical values \u200b\u200bof letters increased in the same way, in what order letters followed in the Greek alphabet (in the Slavic alphabet, the order of letters was a little different). In Russia, Slavic numbering has been preserved until the end of the 17th century, and under Peter I switched to "Arab numbering" we use and now.

The names of the numbers also changed. So, up to the 15th century, the number Twenty was designated as "two ten" (two dozen), and then decreased for a faster pronunciation. The number 40 to the 15th century was called "Fourth", then it was displaced by the word "forty", denoting the original bag, which en deems 40 squirrels or sobular skins. The name "Million" appeared in Italy in 1500. It was formed by adding a magnifying suffix to the Mille (thousand). Later, this name came to Russian.

In the old (XVIII century), the "arithmetic" of Magnitsky, the table of the names of the numbers brought to the "quadrillion" (10 ^ 24, by system through 6 digits). Perelman Ya.I. In the book "Entertaining arithmetic", the names of large numbers of the time are given, somewhat different from today: septylon (10 ^ 42), Occlicon (10 ^ 48), nonalone (10 ^ 54), decalon (10 ^ 60), Endecalon (10 ^ 66), Dodecalon (10 ^ 72) and it is written that "then the names are not available."

Ways to build big numbers

There are 2 main ways of large numbers:

American systemwhich is used in the USA, Russia, France, Canada, Italy, Turkey, Greece, Brazil. The names of large numbers are built quite simply: first there is a Latin order numerical, and the suffix "-lion" is added to it. Exceptions are the number "Million", which is the name of the number of a thousand (Mille) and the magnifying suffix "-LI10". The number of zeros among which is recorded on the American system can be found in the formula: 3x + 3, where x - Latin sequence numerical
English system The most common in the world is used in Germany, Spain, Hungary, Poland, the Czech Republic, Denmark, Sweden, Finland, Portugal. The names of the numbers on this system are structured as follows: the "-Lion" suffix is \u200b\u200badded to the Latin numerical, the following number (1000 times more) is the same latin numerical, but suffix "-lilliard" is added. The number of zeros among which is recorded in the English system and ends with the suffix "-lion", can be found in the formula: 6x + 3, where x - Latin sequence is numerical. The number of zeros in the numbers ending with the suffix "-lilliard" can be found in the formula: 6x + 6, where x - Latin sequence is numerical.

From the English system to the Russian language, only the word billion, which is still more correct to call as the Americans call it - Billion (since the American Nizhny Name System is used in Russian).

In addition to the numbers that are recorded in the American or English system with the help of Latin prefixes, some-system numbers that have their own names without Latin prefixes are known.

Own names of large numbers

Number		Latin numerical	Name	Practical value
10 1	10		ten	The number of fingers on 2 hands
10 2	100		one hundred	Approximately half of the number of all states on Earth
10 3	1000		one thousand	Approximate number of days in 3 years
10 6	1000 000	unus (I)	million	5 times more than the number of drops in a 10-liter. Water buckets
10 9	1000 000 000	dUO (II)	billion (Billion)	Approximate population of India
10 12	1000 000 000 000	tRES (III)	trillion
10 15	1000 000 000 000 000	quattor (IV)	quadrillion	1/30 Parsek length in meters
10 18		qUINQUE (V)	quintillion	1/18 grains from the legendary award inventor chess
10 21		sex (VI)	sextillion	1/6 masses of the planet Earth in tons
10 24		sEPTEM (VII)	septillion	Number of molecules in 37.2 l air
10 27		oCTO (VIII)	octillion	Half of the mass of Jupiter in kilograms
10 30		novem (IX)	quintillion	1/5 of the number of all microorganisms on the planet
10 33		decem (X)	decillion	Half of the mass of the Sun in grams

Vigintillion (from lat. Viginti - twenty) - 10 63
Centillion (from lat. Centum - hundred) - 10 303
Milleilla (from Lat. Mille - one thousand) - 10 3003

For numbers, more than a thousand in the Romans of their own names were no (all the names of numbers were further composite).

Composite names of large numbers

In addition to its own names, for numbers more than 10 33, you can get composite names by combining consoles.

Composite names of large numbers

Number	Latin numerical	Name	Practical value
10 36	undecim (xi)	andesillion
10 39	duodecim (XII)	doodecillion
10 42	tredecim (XIII)	treadcillion	1/100 on the number of air molecules on earth
10 45	qUATTUORDECIM (XIV)	kvattordecillion
10 48	qUINDECIM (XV)	quendecyllion
10 51	sedecim (XVI)	sexotilion
10 54	septendecim (XVII)	sepemdiscillion
10 57		oktodecillion	So many elementary particles in the sun
10 60		novmetsillion
10 63	viginti (XX)	vigintillion
10 66	uNUS ET VIGINTI (XXI)	anvigintillion
10 69	duo et Viginti (XXII)	duviygintillion
10 72	tres et Viginti (XXIII)	tremgintillion
10 75		kvattorvigintillion
10 78		queenvigintillion
10 81		sexVigintillion	So many elementary particles in the universe
10 84		septemvigintillion
10 87		octovigintillion
10 90		nov'vvigintillion
10 93	triginta (XXX)	trigintillion
10 96		annigintillion.

10 123 - Quadchantillion
10 153 - Quecilwagintillion
10 183 - Sexagintillion
10 213 - Septuagintillion
10 243 - Oktogintillion
10 273 - Nonagintillion
10 303 - Centillion

Further names can be obtained by direct or reverse Latin numerical order (as proper, it is not known):

10 306 - Angentillion or Centunillion
10 309 - Duocenteillion or centindollion
10 312 - Tirettyllion or Centrillion
10 315 - Quartercertillion or Cenkvadrillion
10 402 - Ferrigintantyaltyillion or Centraletrigintillion

The second version of writing more corresponds to the construction of numeral in Latin and avoids ambiguities (for example, among the number of Tientymalillion, which is 1,093 and 10 312, and 10 312).

10 603 - Dutentillion
10 903 - Tientyllion
10 1203 - Quadringentillion
10 1503 - Quingventillion
10 1803 - Sedsertillion
10 2103 - Septingsentillion
10 2403 - Oaktingtillion
10 2703 - Nonhentillion
10 3003 - Milleillion
10 6003 - Domillalion
10 9003 - Tremlillion
10 15003 - QUINKVEMILION
10 308760 - DucenduomylanionenTeemecillion
10 3000003 - Miliamilialion
10 6000003 - DomoilyamiliaIillion

Miriada - 10 000. The name is obsolete and practically not used. However, the word "Miriada" is widely used, which means not a certain number, but countless, uncountable many of something.

Gugol (english . googol) — 10 100. For the first time, American mathematician Edward Kasner (Edward Kasner) wrote about this number in 1938 in the Journal of Scripta Mathematica in the article "New Names in Mathematics". According to him, to call so the number suggested his 9-year-old nephew Milton Sirotta (Milton Sirotta). This number has become well known for the Google search engine called in honor of him.

Asankhaya(from whale. Asianzi - innumerable) - 10 1 4 0. This number is found in the famous Buddhist treatise Jaina-Sutra (100 g. BC). It is believed that this number is equal to the number of space cycles required to gain nirvana.

Gugolplex (english . Googolplex) — 10 ^ 10 ^ 100. This number also came up with Edward Casner with his nephew, means it is a unit with a google zerule.

Number of Skusza (Skewes' Number,SK 1) means e to the degree E into the degree E to the degree 79, that is, E ^ E ^ E ^ 79. This number was suggested by Skews in 1933 (Skewes. J. London Math. Soc. 8, 277-283, 1933.) In the proof of Riman's hypothesis relating to prime numbers. Later, Riele (Te Riele, HJJ "On the Sign of the Difference P (X) -LI (X)." Math. Comput. 48, 323-328, 1987) reduced the number of skuse to E ^ E ^ 27/4, That approximately equal to 8.185 · 10 ^ 370. However, this number is not a whole, so it is not included in the table of large numbers.

Second number of Skuse (SK2) Equally 10 ^ 10 ^ 10 ^ 10 ^ 3, that is, 10 ^ 10 ^ 10 ^ 1000. This number was introduced by J. Skews in the same article for the designation of the number, to which the Hypothesis of Riman is valid.

For super-high numbers, it is inconvenient to use degrees, therefore there are several ways to write numbers - the notation of the whip, Konveya, Steinhaus, etc.

Hugo Steinhause offered to record large numbers inside the geometric figures (triangle, square and circle).

Mathematics Leo Moser finalized the notation of Steinhaus, offering after squares not circles, but pentagons, then hexagons, etc. Moser also offered a formal entry for these polygons, so that the numbers can be recorded without drawing complex drawings.

Steinhauses came up with two new super-high numbers: Mega and Megiston. In the notation of Moor, they are recorded like this: Mega – 2, Megiston - 10. Leo Moser also offered to call a polygon with the number of parties equal to Mega - magagonand also offered the number "2 in the megagon" - 2. The last number is known as moser's number (Moser's Number) or just as Moser.

There are numbers, more Moser. The largest number that was used in mathematical proof is number Graham (Graham's Number). It was first used in 1977 in proof of one assessment in the Ramsey theory. This number 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. Donald Knut (who wrote the "Programming Art" and created the TeX editor) invented the concept of a superpope, which offered to record the arrows directed upwards:

In general

Graham offered G-numbers:

The number G 63 is called the Graham number, often indicated by G. This number is the largest known number in the world and is listed in the "Guinness Book of Records".

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