The largest number and its name. What are the largest numbers in the world called?

As a child, I was tormented by the question, what is the most big number, and I plagued almost everyone with this stupid question. Having learned the number one million, I asked if there was a number greater than a million. Billion? And more than a billion? Trillion? And more than a trillion? Finally, there was someone smart who explained to me that the question is stupid, since it is enough just to add one to the largest number, and it turns out that it has never been the largest, since there are even larger numbers.

And now, 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 puzzle them with patient search engines that will not call my questions idiotic ;-). Actually, this is what I did, and here's what I found out as a result.

Number	Latin name	Russian prefix
1	unus	en-
2	duo	duo-
3	tres	three-
4	quattuor	quadri-
5	quinque	quinti-
6	sex	sexty
7	September	septi-
8	octo	octi-
9	novem	noni-
10	decem	deci-

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

The American system is built quite simply. All names of large numbers are built like this: at the beginning there is a Latin ordinal number, and at the end the suffix -million is added to it. The exception is the name "million" which is the name of the number one thousand (lat. mille) and the magnifying suffix -million (see table). So 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: like this: a 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 comes a trillion, and only then a quadrillion, followed by a quadrillion, and so on. Thus, a quadrillion according to 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 using the formula 6 x + 3 (where x is a Latin numeral) and using the formula 6 x + 6 for numbers ending in -billion.

Only the number billion (10 9) passed from the English system into the Russian language, which, nevertheless, would be more correct to call it the way the Americans call it - a billion, since we have adopted the American system. But who in our country does something according to the rules! ;-) By the way, sometimes the word trilliard 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 in the American or English system, the 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. Now I will explain why. First, let's see how the numbers from 1 to 10 33 are called:

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 so, now the question arises, what next. What is a decillion? In principle, 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, and we were interested in our own names 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. percent- one hundred) and a million (from lat. mille- one thousand). The Romans did not have more than a thousand proper names for numbers (all numbers over a thousand were composite). For example, a million (1,000,000) Romans called centena milia i.e. ten hundred thousand. And now, actually, the table:

Thus, according to a similar system, numbers greater than 10 3003, which would have its own, non-compound name, cannot be obtained! But nevertheless, numbers greater than a million are known - these are the same off-system numbers. Finally, let's talk about them.

Name	Number
myriad	10 4
googol	10 100
Asankheyya	10 140
Googolplex	10 10 100
Skuse's second number	10 10 10 1000
Mega	2 (in Moser notation)
Megiston	10 (in Moser notation)
Moser	2 (in Moser notation)
Graham number	G 63 (in Graham's notation)
Stasplex	G 100 (in Graham's notation)

The smallest such number is myriad(it is even in Dahl's dictionary), which means a hundred hundreds, that is, 10,000. True, this word is outdated and is practically not used, but it is curious that the word "myriads" is widely used, which does not mean at all certain number, but an uncountable, uncountable set of something. It is believed that the word myriad (English myriad) came to European languages from ancient Egypt.

googol(from the English googol) is the number ten to the hundredth power, that is, one with one hundred zeros. The "googol" was first written about in 1938 in the article "New Names in Mathematics" in the January issue of the journal 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 trademark, and googol is a number.

In the famous Buddhist treatise Jaina Sutra, dating back to 100 BC, there is a number asankhiya(from Chinese asentzi- incalculable), equal to 10 140. It is believed that this number is equal to the number of cosmic cycles required to gain nirvana.

Googolplex(English) googolplex) - a number also invented by Kasner with his nephew and meaning one with a googol of zeros, that is, 10 10 100. Here 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 the refore 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 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 power of 79, that is, e e 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 the Skewes number to e e 27/4 , which is approximately equal to 8.185 10 370 . It is clear that since the value of the Skewes number depends on the number e, then it is not an integer, so we will not consider it, otherwise we would have to recall other non-natural numbers - the number pi, the number e, the Avogadro number, etc.

But it should be noted that there is a second Skewes number, which in mathematics is denoted as Sk 2 , which is even larger than the first Skewes number (Sk 1). Skuse's second number, was introduced by J. Skuse in the same article to denote the number up to which the Riemann hypothesis is valid. Sk 2 is equal to 10 10 10 10 3 , that is 10 10 10 1000 .

As you understand, the more degrees there are, the more difficult it is to understand which of the numbers is greater. For example, looking at the Skewes numbers, without special calculations, it is almost impossible to understand which of these two numbers is larger. Thus, for superlarge numbers, it becomes inconvenient to use powers. Moreover, you can come up with 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 won't even fit into 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 Stenhaus (H. Steinhaus. Mathematical Snapshots, 3rd edn. 1983), which is quite simple. Steinhouse suggested recording big numbers inside geometric shapes- triangle, square and circle:

Steinhouse came up with two new super-large numbers. He named a number Mega, and the number is Megiston.

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

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

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

Unfortunately, the number written in the Knuth notation cannot be translated into the Moser notation. Therefore, this system will also have to be explained. In principle, there is nothing complicated in it either. Donald Knuth (yes, yes, this is the same Knuth who wrote The Art of Programming and created the TeX editor) came up with the concept of superpower, which he proposed to write with arrows pointing up:

AT general view it looks like this:

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

The number G 63 began to be called Graham number(it is often denoted simply as G). This number is the largest known number in the world and is even listed in the Guinness Book of Records. And, here, that the Graham number is greater than the Moser number.

P.S. In order to bring great benefit to all mankind and become famous for centuries, I decided to invent and name the largest number myself. This number will be called stasplex and it is 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.

Update (4.09.2003): Thanks everyone for the comments. It turned out that when writing the text, I made several mistakes. I'll try to fix it now.

I made several mistakes at once, just mentioning Avogadro's number. First, several people pointed out to me that 6.022 10 23 is actually the most natural number. And secondly, there is an opinion, and it seems to me true, that Avogadro's number is not a number at all in the proper, mathematical sense of the word, since it depends on the system of units. Now it is expressed in "mol -1", but if it is expressed, for example, in moles or something else, then it will be expressed in a completely different figure, but it will not cease to be Avogadro's number at all.
10 000 - darkness
100,000 - legion
1,000,000 - leodre
10,000,000 - Raven or Raven
100 000 000 - deck
Interestingly, the ancient Slavs also loved large numbers, they knew how to count up to a billion. Moreover, they called such an account a “small account”. In some manuscripts, the authors also considered the "great count", which reached the number 10 50 . About numbers greater than 10 50 it was said: "And more than this to bear the human mind to understand." The names used in the "small account" were transferred to the "great account", but with a different meaning. So, darkness meant no longer 10,000, but a million, legion - the darkness of those (million millions); leodrus - a legion of legions (10 to 24 degrees), then it was said - ten leodres, a hundred leodres, ..., and, finally, a hundred thousand legions of leodres (10 to 47); leodr leodr (10 to 48) was called a raven and, finally, a deck (10 to 49).
The topic of national names of numbers can be expanded if we recall the Japanese system of naming numbers that I forgot, which is very different from the English and American systems (I will not draw hieroglyphs, if anyone is interested, then they are):
100-ichi
10 1 - jyuu
10 2 - hyaku
103-sen
104 - man
108-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
1044 - sai
1048 - goku
10 52 - gougasya
10 56 - asougi
10 60 - nayuta
1064 - fukashigi
10 68 - murioutaisuu
Regarding the numbers of Hugo Steinhaus (in Russia, for some reason, his name was translated as Hugo Steinhaus). botev assures that the idea of writing super-large numbers in the form of numbers in circles does not belong to Steinhouse, but to Daniil Kharms, who, long before him, published this idea in the article "Raising the Number". I also want to thank Evgeny Sklyarevsky, the author of the most interesting site on entertaining mathematics on the Russian-speaking Internet - Arbuz, for the information that Steinhouse came up with not only the numbers mega and megiston, but also proposed another number mezzanine, which is (in his notation) "circled 3".
Now for the number myriad or myrioi. As for the origin of this number, there are different opinions. Some believe that it originated in Egypt, while others believe that it was born only in Ancient Greece. Be that as it may, in fact, the myriad gained fame precisely thanks to the Greeks. Myriad was the name for 10,000, and there were no names for numbers over ten thousand. However, in the note "Psammit" (i.e., the calculus of sand), Archimedes showed how one can systematically build 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 Earth diameters) no more than 10 63 grains of sand would fit (in our notation). It is curious that modern calculations of the number of atoms in the visible universe lead to the number 10 67 (only a myriad of times more). The names of the numbers Archimedes suggested are as follows:
1 myriad = 10 4 .
1 di-myriad = myriad myriad = 10 8 .
1 tri-myriad = di-myriad di-myriad = 10 16 .
1 tetra-myriad = three-myriad three-myriad = 10 32 .
etc.

If there are comments -

Once in childhood, we learned to count to ten, then to a hundred, then to a thousand. So what is 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 SI prefix 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 powers of a thousand. And here, the first nuance that many people know from American films is that 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. In this scale, at each step, the mantis increases by three orders of magnitude, i.e. multiply by a thousand - a thousand 10 3, a million 10 6, a billion / billion 10 9, a trillion (10 12). In the long scale, after a billion 10 9 comes a billion 10 12, and in the future the mantisa already increases by six orders of magnitude, and the next number, which is called a trillion, already means 10 18.

But back to our native scale. Want to know what comes after a 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 quattuordecillion
10 48 quindecillion
10 51 sedecillion
10 54 septdecillion
10 57 duodevigintillion
10 60 undevigintillion
10 63 vigintillion
10 66 anvigintillion
10 69 duovigintillion
10 72 trevigintillion
10 75 quattorvigintillion
10 78 quinvintillion
10 81 sexwigintillion
10 84 septemvigintillion
10 87 octovigintillion
10 90 novemvigintillion
10 93 trigintillion
10 96 antirigintillion

On this number, our short scale does not stand up, and in the future, the mantissa 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 centtrillion
10 315 centquadrillion
10 402 centtretrigintillion
10,603 decentillion
10 903 trecentillion
10 1203 quadringentillion
10 1503 quingentillion
10 1803 sescentillion
10 2103 septingentillion
10 2403 octingentillion
10 2703 nongentillion
10 3003 million
10 6003 duomillion
10 9003 tremillion
10 3000003 miamimiliaillion
10 6000003 duomyamimiliaillion
10 10 100 googolplex
10 3×n+3 zillion

googol(from the English googol) - a number, in the decimal number system, represented by a unit 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 (Edward Kasner, 1878-1955) was walking in the park with his two nephews and discussing large numbers with them. During the conversation, we talked about a number with one hundred zeros, which did not have its own name. One of his nephews, nine-year-old Milton Sirotta, suggested calling this number "googol". In 1940, Edward Kasner, together with James Newman, wrote the popular science book "Mathematics and Imagination" ("New Names in Mathematics"), where he taught mathematics lovers about the googol number.
The term "googol" does not have a serious theoretical and practical value. Kasner proposed it to illustrate the difference between an unimaginably large number and infinity, and for this purpose the term is sometimes used in the teaching of mathematics.

Googolplex(from the English googolplex) - a number represented by a unit with a googol of zeros. Like googol, the term googolplex was coined by American mathematician Edward Kasner and his nephew Milton Sirotta.
The number of googols is greater than the number of all particles in the part of the universe known to us, which ranges from 1079 to 1081. 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 (English J. H. Conway) and Guy (English R. K. Guy) in their book English. The Book of Numbers defined a zillion of the nth power as 10 3×n+3 for the short scale number naming system.

Sometimes people who are not related to mathematics wonder: what is the largest number? On the one hand, the answer is obvious - infinity. The bores will even clarify that "plus infinity" or "+∞" in the notation of mathematicians. But this answer will not convince the most corrosive, especially since this is not a natural number, but a mathematical abstraction. But having well understood the issue, they can open up an interesting problem.

Indeed, there is no size limit in this case, but there is a limit to human imagination. Each number has a name: ten, one hundred, billion, sextillion, and so on. But where does the fantasy of people end?

Not to be confused with a Google Corporation trademark, although they share a common origin. This number is written as 10100, that is, one followed by a tail of one hundred zeros. It is difficult to imagine it, but it was actively used in mathematics.

It's funny what his child came up with - the nephew of the mathematician Edward Kasner. In 1938, my uncle entertained younger relatives with arguments about very large numbers. To the indignation of the child, it turned out that wonderful number does not have a name, and he gave his own version. Later, my uncle inserted it into one of his books, and the term stuck.

Theoretically, a googol is a natural number, because it can be used for counting. That's just hardly anyone has the patience to count to its end. Therefore, only theoretically.

As for the name of the company Google, then a common mistake crept in. The first investor and one of the co-founders was in a hurry when he wrote the check, and missed the letter “O”, but in order to cash it, the company had to be registered under this spelling.

Googolplex

This number is a derivative of the googol, but significantly larger than it. The prefix "plex" means raising ten to the power of the base number, so guloplex is 10 to the power of 10 to the power of 100, or 101000.

The resulting number exceeds the number of particles in the observable universe, which is estimated at about 1080 degrees. But this did not stop scientists from increasing the number simply by adding the prefix "plex" to it: googolplexplex, googolplexplexplex, and so on. And for especially perverted mathematicians, they invented an option to increase without endless repetition of the prefix "plex" - they simply put Greek numbers in front of it: tetra (four), penta (five) and so on, up to deca (ten). The last option sounds like a googoldekaplex and means a tenfold cumulative repetition of the procedure for raising the number 10 to the power of its base. The main thing is not to imagine the result. You still won’t be able to realize it, but it’s easy to get a trauma to the psyche.

48th Mersen number

Main characters: Cooper, his computer and a new prime number

Relatively recently, about a year ago, it was possible to discover the next, 48th Mersen number. On the this moment it is the largest prime number in the world. Recall that prime numbers are those that are only divisible without a remainder by 1 and themselves. The simplest examples are 3, 5, 7, 11, 13, 17 and so on. The problem is that the further into the wilds, the less often such numbers occur. But the more valuable is the discovery of each next one. For example, a new prime number consists of 17,425,170 digits if it is represented in the form of a decimal number system familiar to us. The previous one had about 12 million characters.

It was discovered by the American mathematician Curtis Cooper, who for the third time delighted the mathematical community with such a record. Just to check his result and prove that this number is really prime, it took 39 days of his personal computer.

This is how Graham's number is written in Knuth's arrow notation. How to decipher it, it's hard to say without having a complete higher education in theoretical mathematics. It is also impossible to write it down in the decimal form we are accustomed to: the observable Universe is simply not able to contain it. Fencing degree for degree, as in the case of googolplexes, is also not an option.

Good formula, but incomprehensible

So why do we need this seemingly useless number? Firstly, for the curious, it was placed in the Guinness Book of Records, and this is already a lot. Secondly, it was used to solve a problem that is part of the Ramsey problem, which is also incomprehensible, but sounds serious. Thirdly, this number is recognized as the largest ever used in mathematics, and not in comic proofs or intellectual games, but for solving a very specific mathematical problem.

Attention! The following information is dangerous for you mental health! By reading it, you accept responsibility for all the consequences!

For those who want to test their mind and meditate on the Graham number, we can try to explain it (but only try).

Imagine 33. It's pretty easy - you get 3*3*3=27. What if we now raise three to this number? It turns out 3 3 to the 3rd power, or 3 27. In decimal notation, this is equal to 7,625,597,484,987. A lot, but for now it can be understood.

In Knuth's arrow notation, this number can be displayed somewhat more simply - 33. But if you add only one arrow, it will turn out to be more difficult: 33, which means 33 to the power of 33 or in power notation. If expanded to decimal notation, we get 7,625,597,484,987 7,625,597,484,987 . Are you still able to follow the thought?

Next step: 33= 33 33 . That is, you need to calculate this wild number from the previous action and raise it to the same power.

And 33 is just the first of the 64 members of Graham's number. To get the second one, you need to calculate the result of this furious formula, and substitute the appropriate number of arrows into the 3(...)3 scheme. And so on, 63 more times.

I wonder if anyone besides him and a dozen other supermathematicians will be able to get at least to the middle of the sequence and not go crazy at the same time?

Did you understand something? We are not. But what a thrill!

Why are the largest numbers needed? It is difficult for the layman to understand and realize this. But a few specialists with their help are able to present new technological toys to the inhabitants: phones, computers, tablets. The townsfolk are also not able to understand how they work, but they are happy to use them for their own entertainment. And everyone is happy: the townsfolk get their toys, "supernerds" - the opportunity to play their mind games for a long time.

10 to 3003 degrees

The debate about which is the most big figure in the world are ongoing. Different calculus systems offer different variants and people do not know what to believe, and what kind of figure to consider the largest.

This question has interested scientists since the time of the Roman Empire. The biggest snag lies in the definition of what is a "number" and what is a "number". At one time people long time considered the largest number decillion, that is, 10 to the 33rd power. But, after scientists began to actively study the American and English metric systems, it was found that the largest number in the world is 10 to the power of 3003 - a million. Men in Everyday life consider that the largest number is a trillion. Moreover, this is quite formal, because after a trillion, names are simply not given, because the account starts too complicated. However, purely theoretically, the number of zeros can be added indefinitely. Therefore, to imagine even a purely visual trillion and what follows it is almost impossible.

in roman numerals

On the other hand, the definition of "number" in the understanding of mathematicians is a little different. A number is a sign that is universally accepted and is used to indicate a quantity expressed in numerical terms. The second concept of "number" means the expression of quantitative characteristics in a convenient form through the use of numbers. It follows that numbers are made up of digits. It is also important that the figure has sign properties. They are conditioned, recognizable, unchangeable. Numbers also have sign properties, but they follow from the fact that numbers are made up of digits. From this we can conclude that a trillion is not a figure at all, but a number. Then what is the biggest number in the world if it's not a trillion, which is a number?

The important thing is that numbers are used as constituent numbers, but not only that. The figure, however, is the same number if we are talking about some things, counting them from zero to nine. Such a system of signs applies not only to the Arabic numerals familiar to us, but also to the Roman I, V, X, L, C, D, M. These are Roman numerals. On the other hand, V I I I is a Roman number. In Arabic reckoning, it corresponds to the number eight.

in Arabic numerals

Thus, it turns out that counting units from zero to nine are considered numbers, and everything else is numbers. Hence the conclusion that the largest number in the world is nine. 9 is a sign, and a number is a simple quantitative abstraction. A trillion is a number, and not a number, and therefore cannot be the largest number in the world. A trillion can be called the largest number in the world, and then purely nominally, since numbers can be counted to infinity. The number of digits is strictly limited - from 0 to 9.

It should also be remembered that numbers and numbers different systems the calculus does not match, as we have seen from the examples with Arabic and Roman numbers and numerals. This is because numbers and numbers are simple concepts that a person himself invents. Therefore, the number of one system of calculation can easily be the number of another and vice versa.

Thus, the largest number is uncountable, because it can be continued to be added indefinitely from digits. As for the numbers themselves, in the generally accepted system, 9 is considered the largest number.

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. It is simply worth adding one to the largest number, as it will no longer be the largest. This procedure can be continued indefinitely. Those. it turns out there is no largest number in the world? Is it infinity?

But if you ask yourself: what is the largest number that exists, and what is its own name? Now we all know...

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

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: like this: a 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 comes a trillion, and only then a quadrillion, followed by a quadrillion, and so on. Thus, a quadrillion according to the English and American systems is quite different numbers! You can find out the number of zeros in a number written in the English system and ending with the suffix -million using the formula 6 x + 3 (where x is a Latin numeral) and using the formula 6 x + 6 for numbers ending in -billion.

Only the number billion (10 9) passed from the English system into the Russian language, which, nevertheless, would be more correct to call it the way the Americans call it - a billion, since we have adopted the American system. 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.

The smallest such number is a myriad (it is even in Dahl's dictionary), which means a hundred hundreds, that is, 10,000. True, this word is outdated and is practically not used, but it is curious that the word "myriad" is widely used, which does not mean a certain number at all, but an uncountable, uncountable set of something. It is believed that the word myriad (English myriad) came to 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 fact, the myriad gained fame precisely thanks to the Greeks. Myriad was the name for 10,000, and there were no names for numbers over ten thousand. However, in the note "Psammit" (i.e., the calculus of sand), Archimedes showed how one can systematically build 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 Earth diameters) no more than 1063 grains of sand would fit (in our notation). It is curious that modern calculations of the number of atoms in the visible universe lead to the number 1067 (only a myriad times more). The names of the numbers Archimedes suggested are as follows:
1 myriad = 104.
1 di-myriad = myriad myriad = 108.
1 tri-myriad = di-myriad di-myriad = 1016.
1 tetra-myriad = three-myriad three-myriad = 1032.
etc.

Googol (from the English googol) is the number ten to the hundredth power, that is, one with one hundred zeros. The "googol" was first written about in 1938 in the article "New Names in Mathematics" in the January issue of the journal 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 Google search engine named after him. Note that "Google" is a trademark and googol is a number.

Edward Kasner.

On the Internet, you can often find mention that Google is the largest number in the world, but this is not so ...

In the well-known Buddhist treatise Jaina Sutra, dating back to 100 BC, the number Asankheya (from the Chinese. asentzi- incalculable), equal to 10 140. It is believed that this number is equal to the number of cosmic cycles necessary to gain nirvana.

Googolplex (English) googolplex) - a number also invented by Kasner with his nephew and meaning one with a googol of zeros, that is, 10 10100. Here 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. 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 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 power of 79, i.e. eee79. 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 ee27/4, which is approximately equal to 8.185 10370. It is clear that since the value of the Skewes number depends on the number e, then it is not an integer, so we will not consider it, otherwise we would have to recall other non-natural numbers - the number pi, the number e, etc.

But it should be noted that there is a second Skewes number, which in mathematics is denoted as Sk2, which is even larger than the first Skewes number (Sk1). The second Skuse number was introduced by J. Skuse in the same article to denote a number for which the Riemann hypothesis is not valid. Sk2 is 101010103, which is 1010101000 .

Consider the notation of Hugo Stenhaus (H. Steinhaus. Mathematical Snapshots, 3rd edn. 1983), which is quite simple. Steinhouse suggested writing large numbers inside geometric shapes - a triangle, a square and a circle:

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

- n[k+1] = "n in n k-gons" = n[k]n.

But the moser is not the largest number. The largest number ever used in a mathematical proof is the limiting value known as Graham's number, first used in 1977 in the proof of 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.

In general, it looks like this:

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

The number G63 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 listed in the Guinness Book of Records.

So there are numbers bigger than Graham's number? There are, of course, for starters there is a Graham number + 1. As for significant number… well, there are some fiendishly difficult areas of mathematics (in particular, the area known as combinatorics) and computer science, in which there are numbers even larger than Graham's number. But we have almost reached the limit of what can be rationally and clearly explained.

sources http://ctac.livejournal.com/23807.html
http://www.uznayvse.ru/interesting-facts/samoe-bolshoe-chislo.html
http://www.vokrugsveta.ru/quiz/310/

https://masterok.livejournal.com/4481720.html