The largest number in the world title. The largest figure in the world

June 17th, 2015

“I see clusters of vague numbers that are hiding there, in the darkness, behind a small spot of light that the candle of the mind gives. They whisper to each other; conspiring who knows what. Perhaps they don't like us very much for capturing their little brothers with our minds. Or, perhaps, they simply lead an unambiguous numerical way of life, there, beyond our understanding ''.
Douglas Ray

We continue ours. Today we have numbers ...

Sooner or later, everyone is tormented by the question, what is the largest number. A child's question can be answered in a million. What's next? Trillion. And even further? In fact, the answer to the question of what are the largest numbers is simple. You just need to add one to the largest number, as it will no longer be the largest. This procedure can be continued indefinitely.

And if you ask the question: what is the largest number that exists, and what is its own name?

Now we will all find out ...

There are two systems for naming numbers - American and English.

The American system is pretty simple. All the names of large numbers are constructed as follows: at the beginning there is a Latin ordinal number, and at the end the suffix-million is added to it. An exception is the name "million" which is the name of the number one thousand (lat. mille) and the increasing suffix-million (see table). This is how the numbers are obtained - 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 a number written in the American system using the simple formula 3 x + 3 (where x is a Latin numeral).

The English naming system is the most common in the world. It is used, for example, in Great Britain and Spain, as well as in most of the former English and Spanish colonies. The names of numbers in this system are built like this: so: the suffix-million is added to the Latin numeral, the next number (1000 times larger) is built according to the principle - the same Latin numeral, but the suffix is -billion. That is, after a trillion in the English system, there is a trillion, and only then a quadrillion, followed by a quadrillion, etc. Thus, a quadrillion in the English and American systems are completely different numbers! You can find out the number of zeros in a number written in the English system and ending with the suffix-million by the formula 6 x + 3 (where x is a Latin numeral) and by the formula 6 x + 6 for numbers ending in -billion.

Only the number billion (10 9) passed from the English system to the Russian language, which would still be more correct to call it as the Americans call it - a billion, since it is the American system that has been adopted in our country. But who in our country does something according to the rules! ;-) By the way, sometimes the word trillion is also used in Russian (you can see for yourself by running a search in Google or Yandex) and it means, apparently, 1000 trillion, i.e. quadrillion.

In addition to numbers written using Latin prefixes according to the American or English system, so-called off-system numbers are also known, i.e. numbers that have their own names without any Latin prefixes. There are several such numbers, but I will talk about them in more detail a little later.

Let's go back to writing using Latin numerals. It would seem that they can write numbers to infinity, but this is not entirely true. Let me explain why. Let's see for a start how the numbers from 1 to 10 33 are called:

And so, now the question arises, what's next. What's behind the decillion? In principle, of course, it is possible, of course, by combining prefixes to generate such monsters as: andecillion, duodecillion, tredecillion, quattordecillion, quindecillion, sexdecillion, septemdecillion, octodecillion and novemdecillion, but these will already be compound names, but we were interested in numbers. Therefore, according to this system, in addition to the above, you can still get only three proper names - vigintillion (from lat.viginti- twenty), centillion (from lat.centum- one hundred) and a million (from lat.mille- one thousand). The Romans did not have more than a thousand of their own names for numbers (all numbers over a thousand were composite). For example, the Romans called a million (1,000,000)decies centena milia, that is, "ten hundred thousand". And now, in fact, the table:

Thus, according to a similar system, the numbers are greater than 10 3003 , which would have its own, non-compound name, it is impossible to get! But nevertheless, numbers more than a million million are known - these are the very off-system numbers. Let's finally tell you about them.

The smallest such number is a myriad (it is even in Dahl's dictionary), which means one hundred hundred, that is, 10,000 does not mean a definite number at all, but an uncountable, uncountable set of something. It is believed that the word myriad came into European languages from ancient Egypt.

There are different opinions about the origin of this number. Some believe that it originated in Egypt, while others believe that it was born only in Ancient Greece. Be that as it may in reality, but the myriad gained fame thanks to the Greeks. Myriad was the name for 10,000, but there were no names for numbers over ten thousand. However, in the note "Psammit" (ie the calculus of sand), Archimedes showed how one can systematically construct and name arbitrarily large numbers. In particular, placing 10,000 (myriad) grains of sand in a poppy seed, he finds that in the Universe (a sphere with a diameter of a myriad of the Earth's diameters) no more than 10 63 grains of sand. It is curious that modern calculations of the number of atoms in the visible Universe lead to the number 10 67 (just a myriad of times more). Archimedes suggested the following names for numbers:
1 myriad = 10 4.
1 d-myriad = myriad myriad = 10 8 .
1 three-myriad = di-myriad di-myriad = 10 16 .
1 tetra-myriad = three-myriad three-myriad = 10 32 .
etc.

Googol (from the English googol) is the number ten to the hundredth power, that is, one followed by one hundred zeros. Googol was first written about in 1938 in the article "New Names in Mathematics" in the January issue of Scripta Mathematica by the American mathematician Edward Kasner. According to him, his nine-year-old nephew Milton Sirotta suggested calling a large number "googol". This number became well-known thanks to the search engine named after him. Google... Note that "Google" is a trademark and googol is a number.

Edward Kasner.

On the Internet, you can often find it mentioned that - but it is not ...

In the famous Buddhist treatise Jaina Sutra dating back to 100 BC, the number asankheya (from Ch. asenci- uncountable) equal to 10 140. It is believed that this number is equal to the number of cosmic cycles required to attain nirvana.

Googolplex (eng. googolplex) is a number also invented by Kasner with his nephew and means one with a googol of zeros, that is, 10 10100 ... This is how Kasner himself describes this "discovery":

Words of wisdom are spoken by children at least as often 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 certain that this number was not infinite, and therefore equally certain that it had to have 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.

An even larger number than the googolplex, the Skewes "number, was proposed by Skewes in 1933 (Skewes. J. London Math. Soc. 8, 277-283, 1933.) in proving the Riemann conjecture concerning prime numbers. It means e to the extent e to the extent e to the 79th power, that is, ee e 79 ... Later, Riele (te Riele, H. J. J. "On the Sign of the Difference P(x) -Li (x). " Math. Comput. 48, 323-328, 1987) reduced Skuse's number to ee 27/4 , which is approximately equal to 8.185 · 10 370. It is clear that since the value of Skuse's number depends on the number e, then it is not an integer, therefore we will not consider it, otherwise we would have to recall other non-natural numbers - pi, e, etc.

But it should be noted that there is a second Skuse number, which in mathematics is denoted as Sk2, which is even greater than the first Skuse number (Sk1). Second Skewes number, was introduced by J. Skuse in the same article to denote a number for which the Riemann hypothesis is not valid. Sk2 is 1010 10103 , that is, 1010 101000 .

As you understand, the more there are in the number of degrees, the more difficult it is to understand which of the numbers is greater. For example, looking at the Skuse numbers, without special calculations, it is almost impossible to understand which of these two numbers is greater. Thus, it becomes inconvenient to use powers for very large numbers. Moreover, you can think of such numbers (and they have already been invented) when the degrees of degrees simply do not fit on the page. Yes, what a page! They will not fit, even in a book the size of the entire Universe! In this case, the question arises how to write them down. The problem, as you understand, is solvable, and mathematicians have developed several principles for writing such numbers. True, every mathematician who asked this problem came up with his own way of writing, which led to the existence of several unrelated ways to write numbers - these are the notations of Knuth, Conway, Steinhouse, etc.

Consider the notation of Hugo Steinhaus (H. Steinhaus. Mathematical Snapshots, 3rd edn. 1983), which is pretty simple. Stein House proposed to write large numbers inside geometric shapes - a triangle, a square and a circle:

Steinhaus came up with two new super-large numbers. He named the number Mega and the number Megiston.

The mathematician Leo Moser refined Stenhouse's notation, which was limited by the fact that if it was required to write numbers much larger than the megiston, difficulties and inconveniences arose, since many circles had to be drawn one inside the other. Moser suggested drawing not circles, but pentagons after the squares, then hexagons, and so on. He also proposed a formal notation for these polygons so that numbers could be written down without drawing complex drawings. Moser's notation looks like this:

Thus, according to Moser's notation, the Steinhouse mega is written as 2, and the megiston as 10. In addition, Leo Moser suggested calling a polygon with the number of sides equal to a mega - megaagon. And he proposed the number "2 in Megagon", that is 2. This number became known as the Moser's number (Moser's number) or simply as moser.

But Moser is not the largest number either. The largest number ever used in mathematical proof is a limiting quantity known as the Graham "s number, first used in 1977 to prove one estimate in Ramsey theory. It is associated with bichromatic hypercubes and cannot be expressed. without the special 64-level system of special mathematical symbols introduced by Knuth in 1976.

Unfortunately, the number written in Knuth's notation cannot be translated into the Moser system. Therefore, we will have to explain this system as well. In principle, there is nothing complicated about it either. Donald Knuth (yes, yes, this is the same Knuth who wrote "The Art of Programming" and created the TeX editor) invented the concept of superdegree, which he proposed to write down with arrows pointing up:

In general, it looks like this:

I think everything is clear, so let's go back to Graham's number. Graham proposed the so-called G-numbers:

G1 = 3..3, where the number of superdegree arrows is 33.

G2 = ..3, where the number of superdegree arrows is equal to G1.

G3 = ..3, where the number of superdegree arrows is equal to G2.

G63 = ..3, where the number of overdegree arrows is equal to G62.

The G63 number became known as the Graham number (it is often denoted simply as G). This number is the largest known number in the world and is even included in the Guinness Book of Records. But

Once in childhood, we learned to count to ten, then to a hundred, then to a thousand. So what's the biggest number you know? A thousand, a million, a billion, a trillion ... And then? Petallion, someone will say, will be wrong, because he confuses the prefix SI with a completely different concept.

In fact, the question is not as simple as it seems at first glance. First, we are talking about naming the names of the degrees of a thousand. And here, the first nuance that many know from American films - they call our billion a billion.

Further more, there are two types of scales - long and short. In our country, a short scale is used. On this scale, at each step, the mantisa increases by three orders of magnitude, i.e. multiply by a thousand - thousand 10 3, million 10 6, billion / billion 10 9, trillion (10 12). On a long scale, after a billion 10 9, there is a billion 10 12, and then the mantisa already increases by six orders of magnitude, and the next number, which is called a trillion, already denotes 10 18.

But back to our native scale. Want to know what's coming after the trillion? Please:

10 3 thousand
10 6 million
10 9 billion
10 12 trillion
10 15 quadrillion
10 18 quintillion
10 21 sextillion
10 24 septillion
10 27 octillion
10 30 nonillion
10 33 decillion
10 36 undecillion
10 39 dodecillion
10 42 tredecillion
10 45 quattuorddecillion
10 48 quindecillion
10 51 cedecillion
10 54 seventh decillion
10 57 duodevigintillion
10 60 undevigintillion
10 63 vigintillion
10 66 anvigintillion
10 69 duovigintillion
10 72 trevigintillion
10 75 quattorvigintillion
10 78 quinvigintillion
10 81 sexwigintillion
10 84 septemvigintillion
10 87 octovigintillion
10 90 novemvigintillion
10 93 trigintillion
10 96 antrigintillion

At this number, our short scale does not hold up, and in the future, the mantisa increases progressively.

10 100 googol
10 123 quadragintillion
10,153 quinquagintillion
10 183 sexagintillion
10 213 septuagintillion
10,243 octogintillion
10,273 nonagintillion
10,303 centillion
10,306 centunillion
10,309 centduollion
10 312 cent trillion
10,315 cents quadrillion
10 402 centretrigintillion
10 603 ducentillion
10,903 trecentillion
10 1203 quadringentillion
10 1503 quingentillion
10 1803 sescentillion
10 2103 septingentillion
10 2403 oxtingentillion
10 2703 nongentillion
10 3003 million
10 6003 duomillion
10 9003 tremillion
10 3000003 Million
10 6000003 duomiliamilillion
10 10 100 googolplex
10 3 × n + 3 zillion

Googol(from the English googol) - a number in decimal notation represented by one with 100 zeros:
10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
In 1938, the American mathematician Edward Kasner (1878-1955) walked in the park with his two nephews and discussed large numbers with them. During the conversation, they talked about a number with one hundred zeros, which did not have its own name. One of the nephews, nine-year-old Milton Sirotta, suggested calling the number "googol". In 1940, Edward Kasner, together with James Newman, wrote the popular science book "Mathematics and Imagination" ("New Names in Mathematics"), where he told the lovers of mathematics about the number of googols.
The term "googol" has no serious theoretical or practical meaning. Kasner proposed it in order to illustrate the difference between an unimaginably large number and infinity, and for this purpose the term is sometimes used in teaching mathematics.

Googolplex(from the English googolplex) - a number represented by one with a googol of zeros. Like googol, the term googolplex was coined by the American mathematician Edward Kasner and his nephew Milton Sirotta.
The number of googol is greater than the number of all particles in the known part of the universe, which ranges from 1079 to 1081. Thus, the number of googolplex, consisting of (googol + 1) digits, cannot be written in the classical "decimal" form, even if all matter in the known turn parts of the universe into paper and ink or into computer disk space.

Zillion(eng. zillion) is a common name for very large numbers.

This term does not have a strict mathematical definition. In 1996, Conway (eng. J. H. Conway) and Guy (eng. R. K. Guy) in their book eng. The Book of Numbers defined the nth power zillion as 10 3 × n + 3 for the short scale naming system.

Answering such a difficult question, what is the largest number in the world, first it should be noted that today there are 2 accepted ways of naming numbers - English and American. According to the English system, the suffixes -billion or -million are added to each large number in sequence, resulting in the number of million, billion, trillion, trillion, and so on. If we proceed from the American system, then according to it, the suffix-million must be added to each large number, as a result of which the numbers trillion, quadrillion and larger are formed. It should be noted here that the English number system is more widespread in the modern world, and the numbers available in it are quite sufficient for the normal functioning of all systems of our world.

Of course, the answer to the question about the largest number from a logical point of view cannot be unambiguous, because you only need to add one to each subsequent digit, then a new larger number is obtained, therefore, this process has no limit. However, oddly enough, the largest number in the world still exists and it is entered in the Guinness Book of Records.

Graham's number - the largest number in the world

It is this number that is recognized in the world as the largest in the Book of Records, while it is very difficult to explain what it is and how large it is. In a general sense, these are triples, multiplied among themselves, as a result of which a number is formed that is 64 orders of magnitude higher than the point of understanding of each person. As a result, we can only give the final 50 digits of Graham's number – 0322234872396701848518 64390591045756272 62464195387.

Googol's number

The history of the emergence of this number is not as complex as the above. So the American mathematician Edward Kasner, talking with his nephews about large numbers, could not answer the question of how to call numbers that have 100 zeros or more. The resourceful nephew proposed his name to such numbers - googol. It should be noted that this number does not have much practical value, however, it is sometimes used in mathematics to express infinity.

Googlex

This number was also invented by mathematician Edward Kasner and his nephew Milton Sirotta. In a general sense, it is the tenth power of a googol. Answering the question of many curious people, how many zeros are in Googleplex, it is worth noting that in the classical version this number cannot be represented, even if you write down all the paper on the planet with classical zeros.

Skuse's number

Another contender for the title of the highest number is the Skuse number, proved by John Littlewood in 1914. According to the evidence given, this number is approximately 8.185 × 10370.

Moser number

This method of naming very large numbers was invented by Hugo Steinhaus, who proposed to denote them by polygons. As a result of three performed mathematical operations, the number 2 is born in a mega-gon (a polygon with mega sides).

As you can see, a huge number of mathematicians have made efforts to find it - the largest number in the world. To what extent these attempts were crowned with success, of course, is not for us to judge, however, it should be noted that the real applicability of such numbers is questionable, because they do not lend themselves even to human understanding. In addition, there will always be that number that will be larger if you perform a very easy mathematical operation +1.

Once I read a tragic story, which tells about the Chukchi, whom polar explorers taught to count and write numbers. The magic of numbers amazed him so much that he decided to write down absolutely all the numbers in the world in a row, starting with one, in the notebook donated by the polar explorers. The Chukchi abandons all his affairs, stops communicating even with his own wife, no longer hunts for seals and seals, but writes everything and writes numbers in a notebook .... So a year goes by. In the end, the notebook ends and the Chukchi understands that he was able to write down only a small part of all the numbers. He cries bitterly and, in despair, burns down his scribbled notebook in order to start living the simple life of a fisherman again, no longer thinking about the mysterious infinity of numbers ...

We will not repeat the feat of this Chukchi and try to find the largest number, since any number only needs to add one to get an even larger number. Let us ask ourselves, albeit similar, but a different question: which of the numbers that have their own name is the largest?

Obviously, although the numbers themselves are infinite, they do not have so many proper names, since most of them are content with names made up of smaller numbers. So, for example, the numbers 1 and 100 have their own names "one" and "one hundred", and the name of the number 101 is already compound ("one hundred and one"). It is clear that in the finite set of numbers that humanity has awarded with its own name, there must be some largest number. But what is it called and what is it equal to? Let's try to figure it out and find, in the end, this is the largest number!

Number	Latin cardinal number	Russian prefix

"Short" and "long" scale

The history of the modern naming system for large numbers dates back to the middle of the 15th century, when in Italy they began to use the words "million" (literally - a large thousand) for a thousand squared, "bimillion" for a million squared and "trillion" for a million cubed. We know about this system thanks to the French mathematician Nicolas Chuquet (c. 1450 - c. 1500): in his treatise "Science of numbers" (Triparty en la science des nombres, 1484), he developed this idea, suggesting further use of Latin cardinal numbers (see table), adding them to the ending "-million". Thus, Schuquet's “bimillion” became a billion, “trillion” into a trillion, and a million to the fourth power became “quadrillion”.

In the Schuke system, the number 10 9, which was between a million and a billion, did not have its own name and was simply called “one thousand million”, similarly 10 15 was called “one thousand billion”, 10 21 - “one thousand trillion”, etc. It was not very convenient, and in 1549 the French writer and scientist Jacques Peletier du Mans (1517-1582) proposed to name such “intermediate” numbers using the same Latin prefixes, but the ending “-billion”. So, 10 9 began to be called “billion”, 10 15 - “billiard”, 10 21 - “trillion”, etc.

The Suke-Peletier system gradually became popular and began to be used throughout Europe. However, in the 17th century, an unexpected problem arose. It turned out that some scientists for some reason began to get confused and call the number 10 9 not “a billion” or “a thousand million”, but “a billion”. Soon, this mistake quickly spread, and a paradoxical situation arose - “billion” became simultaneously synonymous with “billion” (10 9) and “million million” (10 18).

This confusion lasted long enough and led to the fact that the United States created its own system of naming large numbers. According to the American system, the names of numbers are constructed in the same way as in the Schuke system - the Latin prefix and the ending “illion”. However, the magnitudes of these numbers are different. If in the Shuke system names with the ending "million" received numbers that were degrees of a million, then in the American system the ending "-million" received degrees of a thousand. That is, one thousand million (1000 3 = 10 9) began to be called “billion”, 1000 4 (10 12) - “trillion”, 1000 5 (10 15) - “quadrillion”, etc.

The old system of naming large numbers continued to be used in conservative Great Britain and began to be called "British" throughout the world, despite the fact that it was invented by the French Schuquet and Peletier. However, in the 1970s, Great Britain officially switched to the "American system", which led to the fact that it became somewhat strange to call one system American and the other British. As a result, the American system is now commonly referred to as the "short scale", and the British system, or the Schuke-Peletier system, as the "long scale."

In order not to get confused, let's summarize the intermediate result:

Number name	Short scale value	Long Scale Value

Billion

Billiard
Trillion
Trillion
Quadrillion
Quadrillion
Quintillion
Quintilliard
Sextillion
Sexbillion
Septillion
Septilliard
Octillion
Octilliard
Quintillion
Nonbillion
Decillion
Decilliard

The short naming scale is now used in the United States, United Kingdom, Canada, Ireland, Australia, Brazil and Puerto Rico. Russia, Denmark, Turkey and Bulgaria also use a short scale, except that the number 10 9 is not called “billion”, but “billion”. The long scale, however, continues to be used in most other countries at the present time.

It is curious that in our country the final transition to the short scale took place only in the second half of the 20th century. For example, even Yakov Isidorovich Perelman (1882-1942) in his "Entertaining arithmetic" mentions the parallel existence of two scales in the USSR. The short scale, according to Perelman, was used in everyday life and financial calculations, and the long scale was used in scientific books on astronomy and physics. However, now it is wrong to use the long scale in Russia, although the numbers there turn out to be large.

But back to looking for the largest number. After decillion, the names of numbers are obtained by combining prefixes. This is how numbers such as undecillion, duodecillion, tredecillion, quattordecillion, quindecillion, sexdecillion, septemdecillion, octodecillion, novemdecillion, etc. are obtained. However, these names are no longer interesting to us, since we agreed to find the largest number with our own non-composite name.

If we turn to Latin grammar, we find that the Romans had only three non-compound names for numbers more than ten: viginti - "twenty", centum - "one hundred" and mille - "thousand". For numbers greater than "a thousand", the Romans did not have their own names. For example, the Romans called a million (1,000,000) "decies centena milia", that is, "ten times a hundred thousand." According to Schücke's rule, these three remaining Latin numerals give us names for numbers like "vigintillion", "centillion" and "milleillion".

So, we found out that on the “short scale” the maximum number that has its own name and is not a composite of the smaller numbers is “million” (10 3003). If the "long scale" of naming numbers was adopted in Russia, then the largest number with its own name would be "milliard" (10 6003).

However, there are names for even larger numbers.

Numbers outside the system

Some numbers have their own name, without any connection with the naming system using Latin prefixes. And there are many such numbers. You can, for example, remember the number e, the number "pi", a dozen, the number of the beast, etc. However, since we are now interested in large numbers, we will consider only those numbers with their own non-composite name, which are more than a million.

Until the 17th century, Russia used its own system of naming numbers. Tens of thousands were called "darkness", hundreds of thousands - "legions", millions - "leodra", tens of millions - "crows", and hundreds of millions - "decks". This counting up to hundreds of millions was called the "little count", and in some manuscripts the authors also considered the "great count", in which the same names were used for large numbers, but with a different meaning. So, "darkness" meant not ten thousand, but a thousand thousand (10 6), "legion" - the darkness of those (10 12); "Leodr" - legion of legions (10 24), "raven" - leodr leodr (10 48). For some reason, the “deck” in the great Slavic account was called not “ravens of ravens” (10 96), but only ten “ravens”, that is, 10 49 (see table).

Number name	Meaning in "small count"	Value in the "grand score"	Designation



Raven (vran)

The number 10 100 also has its own name and was invented by a nine-year-old boy. And it was like this. In 1938, the American mathematician Edward Kasner (1878-1955) walked in the park with his two nephews and discussed large numbers with them. During the conversation, they talked about a number with one hundred zeros, which did not have its own name. One of the nephews, nine-year-old Milton Sirott, suggested calling the number "googol". In 1940, Edward Kasner, together with James Newman, wrote the popular science book "Mathematics and the Imagination", where he told math lovers about the number of googols. Google gained even more prominence in the late 1990s, thanks to the Google search engine named after it.

The name for an even larger number than googol originated in 1950 thanks to the father of computer science, Claude Elwood Shannon (1916-2001). In his article "Programming a Computer for Playing Chess," he tried to estimate the number of possible variants of a chess game. According to him, each game lasts on average 40 moves and on each move the player makes a choice on average out of 30 options, which corresponds to 900 40 (approximately equal to 10 118) options for the game. This work became widely known, and this number became known as the "Shannon number".

In the famous Buddhist treatise Jaina Sutra, dating back to 100 BC, the number "asankheya" is found equal to 10 140. It is believed that this number is equal to the number of cosmic cycles required to attain nirvana.

Nine-year-old Milton Sirotta went down in the history of mathematics not only for inventing the number of googol, but also for the fact that at the same time he proposed another number - googolplex, which is equal to 10 to the power of googol, that is, one with googol of zeros.

Two more numbers, larger than the googolplex, were proposed by the South African mathematician Stanley Skewes (1899-1988) when proving the Riemann hypothesis. The first number, which later became known as the "first Skuse number", is e to the extent e to the extent e to the 79th power, that is e e e 79 = 10 10 8.85.10 33. However, the "second Skewes number" is even larger and amounts to 10 10 10 1000.

Obviously, the more degrees there are 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 they, by the way, have already been invented), when the degrees of degrees simply do not fit on the page. Yes, what a page! They won't even fit into a book the size of the entire Universe! In this case, the question arises how to write such numbers. The problem, fortunately, is solvable, and mathematicians have developed several principles for writing such numbers. True, every mathematician who asked this problem came up with his own way of writing, which led to the existence of several unrelated ways to write large numbers - these are the notations of Knuth, Conway, Steinhaus, etc. We now have to deal with some of them.

Other notations

In 1938, the same year that nine-year-old Milton Sirotta invented the numbers googol and googolplex, a book about entertaining mathematics, Mathematical Kaleidoscope, written by Hugo Dionizy Steinhaus (1887-1972) was published in Poland. This book has become very popular, has gone through many editions and has been translated into many languages, including English and Russian. In it, Steinhaus, discussing large numbers, offers a simple way to write them, using three geometric shapes - a triangle, a square and a circle:

"N in a triangle "means" n n»,
« n squared "means" n v n triangles ",
« n in a circle "means" n v n squares ".

Explaining this way of writing, Steinhaus comes up with the number "mega" equal to 2 in a circle and shows that it is equal to 256 in a "square" or 256 in 256 triangles. To calculate it, you need to raise 256 to the power of 256, raise the resulting number 3.2.10 616 to the power of 3.2.10 616, then raise the resulting number to the power of the resulting number, and so on, raise the total to the power of 256 times. For example, a calculator in MS Windows cannot calculate because of overflow 256 even in two triangles. Approximately this huge number is 10 10 2.10 619.

Having determined the number "mega", Steinhaus invites readers to independently estimate another number - "mezons", equal to 3 in a circle. In another edition of the book, Steinhaus, instead of Medzon, proposes to estimate an even higher number - "megiston", equal to 10 in a circle. Following Steinhaus, I will also recommend readers to temporarily break away from this text and try to write these numbers themselves using ordinary degrees in order to feel their gigantic magnitude.

However, there are names for b O higher numbers. So, the Canadian mathematician Leo Moser (Leo Moser, 1921-1970) modified the Steinhaus notation, which was limited by the fact that if it was required to write down the numbers many large megistones, then difficulties and inconveniences would arise, since many circles would have to be drawn one inside another. Moser suggested drawing not circles, but pentagons after the squares, then hexagons, and so on. He also proposed a formal notation for these polygons so that numbers could be written down without drawing complex drawings. Moser's notation looks like this:

« n triangle "= n n = n;
« n squared "= n = « n v n triangles "= nn;
« n in a pentagon "= n = « n v n squares "= nn;
« n v k + 1-gon "= n[k+1] = " n v n k-gons "= n[k]n.

Thus, according to Moser's notation, the Steinhaus “mega” is written as 2, the “mezon” as 3, and the “megiston” as 10. In addition, Leo Moser suggested calling a polygon with the number of sides equal to mega - “mega-gon”. And he proposed the number "2 in mega", that is, 2. This number became known as Moser's number or simply as "Moser".

But even the Moser is not the largest number. So, the largest number ever used in a mathematical proof is the "Graham number". This number was first used by the American mathematician Ronald Graham in 1977 when proving one estimate in Ramsey theory, namely, when calculating the dimensions of certain n-dimensional bichromatic hypercubes. But Graham's number gained fame only after the story about him in Martin Gardner's book "From Penrose Mosaics to Reliable Ciphers", published in 1989.

To explain how large the Graham number is, we have to explain another way of writing large numbers, introduced by Donald Knuth in 1976. American professor Donald Knuth came up with the concept of superdegree, which he proposed to write down with arrows pointing up:

I think everything is clear, so let's go back to Graham's number. Ronald Graham proposed the so-called G-numbers:

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

And finally

Having written this article, I can't help but be tempted to come up with my own number. Let this number be called " stasplex"And will be equal to the number G 100. Memorize it, and when your children ask what is the largest number in the world, tell them that this number is called stasplex.

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And if you ask the question: what is the largest number that exists, and what is its own name?

Now we will all find out ...

There are two systems for naming numbers - American and English.

Googol(from the English googol) is the number ten to the hundredth power, that is, one with one hundred zeros. Googol was first written about in 1938 in the article "New Names in Mathematics" in the January issue of Scripta Mathematica by the American mathematician Edward Kasner. According to him, his nine-year-old nephew Milton Sirotta suggested calling a large number "googol". This number became well-known thanks to the search engine named after him. Google... Note that "Google" is a trademark and googol is a number.

Edward Kasner.

On the Internet, you can often find it mentioned that - but it is not ...

In the famous Buddhist treatise of the Jaina Sutra, dating back to 100 BC, there is a number asankheya(from whale. asenci- uncountable) equal to 10 140. It is believed that this number is equal to the number of cosmic cycles required to attain nirvana.

Googolplex(eng. googolplex) is a number also invented by Kasner with his nephew and means one with a googol of zeros, that is, 10 10100 ... This is how Kasner himself describes this "discovery":

Words of wisdom are spoken by children at least as often 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 certain that this number was not infinite, and therefore equally certain that it had to have 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 - Skewes number (Skewes "number) was proposed by Skewes in 1933 (Skewes. J. London Math. Soc. 8, 277-283, 1933.) in proving the Riemann conjecture concerning prime numbers. It means e to the extent e to the extent e to the 79th power, that is, ee e 79 ... Later, Riele (te Riele, H. J. J. "On the Sign of the Difference P(x) -Li (x). " Math. Comput. 48, 323-328, 1987) reduced Skuse's number to ee 27/4 , which is approximately equal to 8.185 · 10 370. It is clear that since the value of Skuse's number depends on the number e, then it is not an integer, therefore we will not consider it, otherwise we would have to recall other non-natural numbers - pi, e, etc.

Steinhaus came up with two new super-large numbers. He called the number - Mega and the number is Megiston.

But Moser is not the largest number either. The largest number ever used in mathematical proof is a limiting value known as Graham's number(Graham "s number), first used in 1977 to prove one estimate in Ramsey's theory, it is associated with bichromatic hypercubes and cannot be expressed without the special 64-level system of special mathematical symbols introduced by Knuth in 1976.

In general, it looks like this:

I think everything is clear, so let's go back to Graham's number. Graham proposed the so-called G-numbers:

The number G63 became known as Graham number(it is often denoted simply as G). This number is the largest known number in the world and is even included in the Guinness Book of Records. Ah, here's that Graham's number is greater than Moser's.

P.S. In order to bring great benefit to all mankind and become famous for centuries, I decided to come up with and name the largest number myself. This number will be called stasplex and it is equal to the number G100. Memorize it, and when your children ask what is the largest number in the world, tell them that this number is called stasplex

So there are numbers greater than Graham's number? There is, of course, there is Graham's number for starters.... As for the significant number ... well, there are some devilishly complex areas of mathematics (in particular, the area known as combinatorics) and computer science, in which numbers even larger than Graham's number occur. But we have almost reached the limit of what can be reasonably and intelligibly explained.

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