Countless different numbers surrounds us every day. Surely many people at least once were interested, which number is considered the largest. The child can simply say that this is a million, but adults perfectly understand what other numbers follow and other numbers. For example, it is only possible to add a single one every time, and it will become more and more - it happens until infinity. But if you disassemble the numbers that have names, you can find out what is called the largest number in the world.
The appearance of the names of numbers: what methods are used?
Today there are 2 systems, according to which the numbers are given names - American and English. The first is quite simple, and the second is the most common worldwide. American allows you to give names to large numbers like this: first indicates the sequence numerical on Latin, and then there is an adding a suffix "Illion" (an exception here is a million, meaning a thousand). Americans, French, Canadians are used such a system, and it is also used in our country.
English is widely used in England and Spain. According to it, the numbers are referred to as so: the numeral on Latin "plunges" with the suffix "Illion", and to the subsequent (more thousand times) the number "plus" "Illyrad". For example, first goes a trillion, behind him "walks" by Trilliard, the quadrillion is kvadrillia, etc.
So, the same number in various systems can mean different, for example, the American Billion in the English system is referred to as a billion.
Intimated numbers
In addition to the numbers, which are recorded according to the well-known systems (given above), there are also generated. They possess their names in which Latin prefixes are not included.
You can start their consideration with a number called Miriadi. It is determined as hundreds of hundred (10,000). But in its assignment, this word does not apply, but is used as an instruction on countless. Even the Dala dictionary will kindly provide a definition of such a number.
The next after Miriad is a googol, denoting 10 to the degree of 100. For the first time, this name was used in 1938 - Mathematics from America E. Kasner, who noted that this name came up with his nephew.
In honor of Google, Google received its name (search engine). Then the 1st Central Committee with Google Zuli (1010100) is a googolplex - such a name has also come up with Kasner.
An even greater compared to the guggolplex is the number of Skusza (e to the degree of E79) proposed by Skews in the proof of Roman's hypothesis about the simple numbers (1933). There is another number of Skusza, but it applies when the hypothesis of the Romanman is unfair. Which one more is quite difficult to say, especially if it comes to big degrees. However, this number, despite its "greatness," can not be considered the most of all those possessed by their names.
And the leader among the largest numbers in the world is the number of Graham (G64). It was he who was used for the first time to conduct evidence in the field of mathematical science (1977).
When it comes to this number, then you need to know that without a special 64-level system created by the whip, do not do - the reason for the connection of the number G with bichromatic hypercubes. The whip was invented superpire, and in order to make it convenient to make her records, he suggested using the arrows up. So we learned how the largest number in the world is called. It is worth noting that this number G hit the pages of the famous book of records.
June 17th, 2015
"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
We continue our. Today we have numbers ...
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.
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 the 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:
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 at 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 of Asankhey (from KIT. asianz - innumerable), equal to 10 140. It is believed that this number is equal to the number of space cycles required to gain nirvana.
Gugolplex (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 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 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 SkuszaIt was introduced by J. Skews in the same article for the designation of the number for which Rimnane's hypothesis is not valid. SK2 is 1010. 10103 , that is, 1010 101000 .
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 the number is 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 offered the number "2 in the megagon", that is 2. This number became known as the Moser number (Moser "s Number) or simply as Moser.
But Moser is not the largest number. The largest number ever used in mathematical proof is the limit value known as the number of Graham (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:
- G1 \u003d 3..3, where the number of superpope arrows is 33.
- G2 \u003d ..3, where the number of superpope arrows is equal to G1.
- G3 \u003d ..3, where the number of superpope arrows is equal to G2.
- G63 \u003d ..3, where the number of superpope arrows is G62.
The number G63 became known as 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". And here
The question "What is the largest number in the world?", At least, incorrect. There are both various calculus systems - decimal, binary and hexadecimal and various categories of numbers - semisimple and simple, and the latter are divided into legal and illegal. In addition, there are numbers of Skusza (Skewes "Number), Steinhouse and other mathematicians, which is something in a joke, or seriously invent and post the public to the public such as" Megiston "or" Moser ".
What is the largest number in the world in the decimal system
From the decimal system, most of the "nonmamatics" are well known a million, a billion and a trillion. Moreover, if a million Russians are mainly associated with a dollar bribe, which can be carried in a suitcase, then where to sink a billion (not to mention the trillion) of North American monetary signs - most lacking fantasy. However, in the theory of large numbers there are such concepts as quadrillion (ten in the fifteenth degree - 1015), sextillion (1021) and octillion (1027).
In the English, the most widespread decimal system with a maximum number in the world is considered to be Decillion - 1033.
In 1938, due to the development of applied mathematics and the expansion of micro and macromir, Professor of Columbia University (USA), Edward Kasner (Edward Kasner) published on the pages of the Scripta Mathematica magazine the offer of his nine-year nephew to use in the decimal system A large number "Google" ("Googol") is ten to the hundredth (10100), which is expressed on paper as a unit with a hundred zeros. However, they did not stop at this and after a few years they proposed to introduce a new largest number in the world in the world - "Gugolplex" (Googolplex), which is ten, erected into a tenth and once again erected into a hundredth degree - (1010) 100, An expressed unit to which the Gogol zerule is attributed to the right. However, for most of even professional mathematicians and "googol", and "Gugolplex" are purely speculative interest, and it is unlikely to apply them in everyday practice.
Exotic numbers
What is the largest number in the world among prime numbers - those who can only share themselves and per unit. One of the first who recorded the largest simple number, equal to 2,147,483,647, was the great mathematician Leonard Euler. By January 2016, the expression calculated as 274 207 281 - 1 was recognized as the expression.
Have you ever thought how many zeros are in one million? This is a fairly simple question. What about a billion or trillion? Unit with nine zeros (10,000,000,000) - what is the name of the number?
Brief list of numbers and their quantitative designation
- Ten (1 zero).
- One hundred (2 zero).
- Thousand (3 zero).
- Ten thousands (4 scratch).
- One hundred thousand (5 zeros).
- Million (6 zeros).
- Billion (9 zeros).
- Trillion (12 zeros).
- Quadrillion (15 zeros).
- Quintillon (18 zeros).
- Sextillion (21 zero).
- Septylon (24 zero).
- Occlicon (27 zeros).
- Nonalon (30 zeros).
- Decalon (33 zero).
Grouping zeros.
10,000,000 - what is the name of which there are 9 zeros? This is a billion. For convenience, large numbers are accepted to group three sets separated from each other with a space or such punctuation marks as a comma or point.
This is done in order to make it easier to read and understand quantitative importance. For example, what is the name of the number of 100,000,000? In this form, it is necessary to say a little, calculate. And if you write 1,000,000,000, then immediately visually the task is facilitated, so it is necessary to consider not zeros, but the top of the zeros.
Numbers with a very large number of zeros
Million and billion are from the most popular (1,000,000,000). What is the number having a 100 zeros? This is a number googol, called so Milton Sirette. This is wildly a huge amount. Do you think that this number is big? Then how about googolplex, the units behind which googol zerule? This figure is so great that it makes sense to come up with difficult for her. In fact, there is no need for such giants, except to count the number of atoms in the infinite universe.
1 billion is a lot?
There are two measurement scales - short and long. Worldwide in the field of science and finance 1 billion is 1,000 million. This is a short scale. There is a number with 9 zeros.
There is also a long scale that is used in some European countries, including in France, and used to be used in the UK (until 1971), where the billion was 1 million million, that is, a unit and 12 zeros. This gradation is also called a long-term scale. A short scale is now the predominant in solving financial and scientific issues.
Some European languages \u200b\u200bsuch as Swedish, Danish, Portuguese, Spanish, Italian, Dutch, Norwegian, Polish, German, use a billion (or Billion) in this system. In Russian, a number of 9 zeros is also described for a short scale of thousands of millions, and a trillion is a million million. This avoids unnecessary confusion.
Conversational options
In Russian spoken speech after the events of 1917 - the Great October Revolution - and the period of hyperinflation in the early 1920s. 1 billion rubles called Limard. And in the dashing 1990s for a billion, a new slang "Watermelon" appeared, a million called "Lemon".
The word "billion" is now used internationally. This is a natural number that is depicted in the decimal system, like 10 9 (unit and 9 zeros). There is also another name - Billion, which is not used in Russia and the CIS countries.
Billion \u003d Billion?
Such a word as Billion is used to designate a billion only in those states in which the "short scale" is adopted as a basis. These are countries such as the Russian Federation, the United Kingdom of Great Britain and Northern Ireland, USA, Canada, Greece and Turkey. In other countries, the concept of Billion means the number 10 12, that is, one and 12 zeros. In countries with a "short scale", including in Russia, this figure corresponds to 1 trillion.
Such confusion appeared in France at a time when the formation of such science as an algebra took place. Initially, a billion had 12 zeros. However, everything changed after the emergence of the main arithmetic allowance (by Tranchan) in 1558), where a billion is an already number with 9 zeros (thousand million).
For several subsequent centuries, these two concepts were used on par with each other. In the middle of the 20th century, namely in 1948, France moved to a long scale of a system of numerical names. In this regard, a short scale, once borrowed from the French, is still different from the one they enjoy today.
Historically, the United Kingdom has used a long-term billion, but since 1974 official statistics of Great Britain used a short-term scale. Since the 1950s, the short-term scale was increasingly used in the field of technical writing and journalism, despite the fact that the long-term scale remained.
It is impossible to answer this question correctly, since the numeric number does not have an upper limit. So, to any number just enough to add a unit to get the number even greater. 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. For example, the numbers and have their own names "one" and "hundred", and the name of the number 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 at the same time, how big numbers came up with mathematics.
"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 that was between a million and Billion, did not have his own name and was called simply "thousand million", the "Thousand Billion" was called, - "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, it became known "Billion," - "Billiard", "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 a number 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" () and "millions of millions" ().
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 millions () began to be called "Billion", () - "Trillion", () - "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" |
| Million | ||
| Billion | ||
| Billion | ||
| Billiard | - | |
| Trillion | ||
| Trilliard | - | |
| Quadrillion | ||
| Quadrilliard | - | |
| Quintillion | ||
| Quintilliard | - | |
| Sextillion | ||
| Sextillard | - | |
| Septillion | ||
| Septilliard | - | |
| Octillion | ||
| Octallard | - | |
| Quintillion | ||
| Nonilliard | - | |
| Decillion | ||
| Decilliard. | - | |
| Vigintillion | ||
| Vigintilliard | - | |
| Centillion | ||
| Centillard | - | |
| Milleilla | ||
| Milleillado | - |
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 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, Million () The 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 in the "short scale" the maximum number that has its own name and is not composite of smaller numbers - this is "Milleilla" (). 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.
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. It is possible for example, to recall the number E, the number "pi", a dozen, the number of beasts, etc. However, since we are now interested in large numbers, then consider only those numbers with your own incompetent 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. So, "darkness" meant not ten thousand, and a thousand thousand () , "Legion" - darkness () ; "Leodr" - Legion Legion () , "Raven" - Leodr Leodrov (). "The deck" in the great Slavic account for some reason was not called "Crow Voronov" () , but only ten "crows", that is, (see Table).
| Name of the number | Meaning in "Small Account" | Meaning in "Great Account" | Designation |
| Dark | |||
| Legion | |||
| Leodr | |||
| Raven (Van) | |||
| Deck | |||
| Darkness Tom |  |
The number 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 on average moves and at each progress player makes a choice on average from options, which corresponds to (approximately equal) 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, meets the number "Asankhay" equal. It is believed that this number is equal to the number of space cycles required to gain nirvana.
Nine-year Milton Sirette entered the history of mathematics not only by what came up with the number of Guogol, but also in the fact that at the same time he was offered another number - "Gugolplex", which is equal 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, which later began to call the "first number of Skusza", is equal to the degree to the degree to the degree, that is. However, the "second number of Skusza" is even more.
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:
"In a triangle" means "",
"In the square" means "in triangles",
"In the circle" means "in squares".
Explaining this method of recording, Steinghause comes up with the number of "mega", equal in the circle and shows that it is equal in the "square" or triangles. To calculate it, it is necessary to be taken to the extent resulting in the extent to the degree, then the resulting number of the resulting number and so fart all the time to erect. For example, the calculator in MS Windows cannot count due to overflow even in two triangles. Approximately this huge number is.
Having determined the number "Mega", Steinhause offers readers independently evaluate another number - "Medzon", equal in the circle. In another publication of the book, Steinhauses, instead of a medical unit, it proposes to evaluate even more - "Megiston", equal 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 for large 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:
"Triangle" \u003d \u003d;
"In the square" \u003d \u003d "in triangles" \u003d;
"In a pentagon" \u003d \u003d "in squares" \u003d;
"In the fighting" \u003d \u003d "in fetters" \u003d.
Thus, according to the notation of Mosel, Steingerovsky "Mega" is recorded as, "Medzon" as, and "Megiston" as. In addition, Leo Moser suggested calling a polygon with the number of sides to Mega - Magagon. And offered the number « In Magagon, "that is. This number has become known as the Muser 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 -Momes 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 arrows directed upwards.
Conventional arithmetic operations - addition, multiplication and construction to the degree - naturally can be expanded into the sequence of hyperoperators as follows.
The multiplication of natural numbers can be determined through the re-produced operation of the addition ("folded copies of the number"):
For example,
The erection of the number can be defined as a repeated multiplication operation ("multiply copies of the number"), and in the knot designation, this entry looks like a single arrow pointing up:
For example,
Such a single upward arrow was used as a degree in Algol programming language.
For example,
Hereinafter, the calculation of the expression always goes to the right left, also the shooting operators of the whip (as well as the construction of the exercise to the degree) by definition have the right associativeness (in terms of the right to left). According to this definition,
This leads to quite large numbers, but the designation system does not end. The "Triple Arrogo" operator is used to record the re-erection of the operator "Double Arrogo" (also known as "Pentation"):
Then the "Four Arrogo" operator:
And so on. General rule Operator "-I Arrow ", in accordance with the right associativity, continues to the right to the serial series of operators « Arrogo ". Symbolically, this can be written as follows
For example:
The notation form is usually used to record with arrows.
Some numbers are so big that even the recording by the arrows of the whip becomes too cumbersome; In this case, the use of the Operator is preferable (and also to describe with a variable number of arrows), or equivalent to hyperoperators. But some numbers are so huge that even such a record is insufficient. For example, the number of Graham.
When using the shooting notation of the whip number of graves can be written as
Where the number of arrows in each layer starting from the top is determined by the number in the next layer, that is, where, where the upper index of the arrows shows the total number of arrows. In other words, it is calculated in step: in the first step, we calculate with four arrows between the top three, on the second - with the arrows between the top three, on the third - with the arrows between the top three, and so on; At the end, we calculate with the arrows between the top three.
This can be written how, where, where the upper index of U means iterations of functions.
If other numbers with the "names" can be selected the corresponding number of objects (for example, the number of stars in the visible part of the Universe is estimated in sextilones -, and the number of atoms from which the globe has the order of dodecalon), then Gugol is already "virtual", not to mention About the number of Graham. The scale of only the first member is so great that it is almost impossible to realize, although the record is above relatively simple for understanding. Although it is only a number of towers in this formula for, this number is a lot of more than the number of volumes of the plank (the lowest possible physical volume), which are contained in the observed universe (approximately). After the first member, we are waiting for another member of the rapidly growing sequence.