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Diseases and pests

The largest natural number in the world. I am writing about what clings

John Sommer

Place zeros after any digit, or multiply with tens raised to any higher power. It will not seem a little. A lot will show. But the bare tapes are still not very impressive. The piling zeros in the humanities cause not so much surprise as a slight yawn. In any case, to any largest number in the world that you can imagine, you can always add one more ... And the number will come out even more.

And yet, are there words in Russian or any other language for very large numbers? Those who more than a million, billion, trillion, billion? And in general, how much is a billion?

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

In the American system numbers are called as follows: the Latin numeral + - illion (suffix) is taken. Thus, the numbers are obtained:

Trillion - 1,000,000,000,000 (12 zeros)

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

Quintillion - 1 and 18 zeros

Sextillion - 1 and 21 zero

Septillion - 1 and 24 zeros

octillion - 1 and 27 zeros

Nonillion - 1 and 30 zeros

Decillion - 1 and 33 zeros

The formula is simple: 3 x + 3 (x is a Latin numeral)

In theory, there should also be anilion numbers (unus in Latin- one) and duolion (duo - two), but, in my opinion, such names are not used at all.

English number naming system more widespread.

Here, too, a Latin numeral is taken and the suffix-million is added to it. However, the name of the next number, which is 1000 times larger than the previous one, is formed using the same Latin number and the suffix - illiard. I mean:

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

Trillion - 1 and 24 zeros (in the American system - septillion)

Quadrillion - 1 and 27 zeros

Quadrillion - 1 and 30 zeros

Quintillion - 1 and 33 zeros

Queenilliard - 1 and 36 zeros

Sextillion - 1 and 39 zeros

Sexbillion - 1 and 42 zeros

The formulas for counting the number of zeros are as follows:

For numbers ending in - illion - 6 x + 3

For numbers ending in - illiard - 6 x + 6

As you can see, confusion is possible. But let's not be afraid!

In Russia adopted American system names of numbers. From the English system, we borrowed the name of the number "billion" - 1,000,000,000 = 10 9

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

Using the Latin names of numbers and the American system, we will call the numbers:

- vigintillion- 1 and 63 zeros

- centillion- 1 and 303 zeros

- million- one and 3003 zeros! Whoa ...

But this, it turns out, is not all. There are also non-systemic numbers.

And the first one is probably myriad- one hundred hundred = 10,000

Googol(it is in honor of him that the famous search system) - one and one hundred zeros

In one of the Buddhist treatises, the number asankheya- one and one hundred forty zeros!

Number name googolplex(as well as googol) was invented by the English mathematician Edward Kasner and his nine-year-old nephew - the unit s - mother dear! - googol zeros !!!

But that's not all ...

The mathematician Skuse named Skuse's number after himself. It means e to the extent e to the extent e to the 79th power, that is, e e e 79

And then a great difficulty arose. You can come up with names for numbers. But how to write them down? The number of degrees of degrees of degrees is already such that it simply does not disappear on the page! :)

And then some mathematicians began to write numbers in geometric shapes Oh. And the first, they say, this method of recording was invented by the outstanding writer and thinker Daniil Ivanovich Kharms.

And yet, what is the BIGGEST NUMBER IN THE WORLD? - It is called STASPLEX and is equal to G 100,

where G is the Graham number, the most big number ever used in mathematical proofs.

This number - a stasplex - was invented by a wonderful person, our compatriot Stas Kozlovsky, to LJ which I am addressing you :) - ctac

Many are interested in questions about how they are called large numbers and which number is the largest in the world. We will deal with these interesting questions in this article.

History

Southern and Eastern Slavic peoples to write numbers, alphabetical numbering was used, and only those letters that are in Greek alphabet... A special “titlo” icon was placed above the letter that denoted the number. Numerical values letters increased in the same order in which the letters followed in the Greek alphabet (in the Slavic alphabet, the order of the letters was slightly different). In Russia, Slavic numbering was preserved until the end of the 17th century, and under Peter I they switched to “Arabic numbering,” which we still use today.

The names of the numbers also changed. So, until the 15th century, the number “twenty” was designated as “two ten” (two dozen), and then it was reduced for a faster pronunciation. Until the 15th century, the number 40 was called “fourty”, then it was supplanted by the word “forty”, originally denoting a bag containing 40 squirrel or sable skins. The name “million” appeared in Italy in 1500. It was formed by adding a magnifying suffix to the number millet (thousand). Later, this name came to the Russian language.

In the old (XVIII century) "Arithmetic" by Magnitsky, a table of the names of numbers is given, brought to "quadrillion" (10 ^ 24, according to the system after 6 digits). Perelman Ya.I. in the book "Entertaining arithmetic" the names of large numbers of that time are given, somewhat different from those of today: septillion (10 ^ 42), octalion (10 ^ 48), nonalion (10 ^ 54), decallion (10 ^ 60), endecalion (10 ^ 66), dodecalion (10 ^ 72) and it is written that "there are no further names."

Methods for constructing names of large numbers

There are 2 main ways of naming large numbers:

American system which is used in the USA, Russia, France, Canada, Italy, Turkey, Greece, Brazil. The names of large numbers are built quite simply: first there is a Latin ordinal number, and the suffix “-million” is added to it at the end. Exceptions are the number “million”, which is the name of the number thousand (mille) and the augmenting suffix “-million”. The number of zeros in a number written in the American system can be found by the formula: 3x + 3, where x is a Latin ordinal
English system most widespread in the world, it is used in Germany, Spain, Hungary, Poland, Czech Republic, Denmark, Sweden, Finland, Portugal. The names of numbers according to this system are built as follows: the suffix "-million" is added to the Latin numeral, next number(1000 times larger) - the same Latin numeral, but the suffix “-billion” is added. The number of zeros in the number, which is written by English system and ends with the suffix “-million”, you can find out by the formula: 6x + 3, where x is a Latin ordinal number. The number of zeros in numbers ending with the suffix “-billion” can be found by the formula: 6x + 6, where x is a Latin ordinal number.

Only the word billion passed from the English system to the Russian language, which is nevertheless more correct to call it as the Americans call it - billion (since the American system of naming numbers is used in Russian).

In addition to numbers that are written in the American or English system using Latin prefixes, off-system numbers are known that have their own names without Latin prefixes.

Proper names for large numbers

Number		Latin numeral	Name	Practical value
10 1	10		ten	Number of fingers on 2 hands
10 2	100		hundred	About half the number of all states on Earth
10 3	1000		thousand	Approximate number of days in 3 years
10 6	1000 000	unus (I)	million	5 times the number of drops per 10 liter. bucket of water
10 9	1000 000 000	duo (II)	billion (billion)	Approximate population of India
10 12	1000 000 000 000	tres (III)	trillion
10 15	1000 000 000 000 000	quattor (IV)	quadrillion	1/30 parsec length in meters
10 18		quinque (V)	quintillion	1/18 of the number of grains from the legendary chess inventor award
10 21		sex (VI)	sextillion	1/6 the mass of the planet Earth in tons
10 24		septem (VII)	septillion	The number of molecules in 37.2 liters of air
10 27		octo (VIII)	octillion	Half the mass of Jupiter in kilograms
10 30		novem (IX)	quintillion	1/5 of all microorganisms on the planet
10 33		decem (X)	decillion	Half the mass of the Sun in grams

Vigintillion (from Lat.viginti - twenty) - 10 63
Centillion (from Lat.centum - one hundred) - 10 303
Million (from Latin mille - thousand) - 10 3003

For numbers over a thousand, the Romans did not have their own names (all the names of numbers were further compound).

Compound names for large numbers

In addition to proper names, for numbers greater than 10 33, compound names can be obtained by combining prefixes.

Compound names for large numbers

Number	Latin numeral	Name	Practical value
10 36	undecim (XI)	andecillion
10 39	duodecim (XII)	duodecillion
10 42	tredecim (XIII)	tredecillion	1/100 of the number of air molecules on Earth
10 45	quattuordecim (XIV)	quattordecillion
10 48	quindecim (XV)	quindecillion
10 51	sedecim (XVI)	sexdecillion
10 54	septendecim (XVII)	septemdecillion
10 57		octodecillion	So many elementary particles in the sun
10 60		novemdecillion
10 63	viginti (XX)	vigintillion
10 66	unus et viginti (XXI)	anvigintillion
10 69	duo et viginti (XXII)	duovigintillion
10 72	tres et viginti (XXIII)	trevigintillion
10 75		quattorvigintillion
10 78		quinvigintillion
10 81		sexvigintillion	So many elementary particles in the universe
10 84		septemwigintillion
10 87		octovigintillion
10 90		novemvigintillion
10 93	triginta (XXX)	trigintillion
10 96		antrigintillion

10 123 - quadragintillion
10 153 - quinquagintillion
10 183 - sexagintillion
10 213 - septuagintillion
10 243 - octogintillion
10 273 - nonagintillion
10,303 - centillion

Further names can be obtained directly or reverse order Latin numerals (as correct, it is not known):

10 306 - antcentillion or centunillion
10 309 - duocentillion or centduollion
10 312 - trecentillion or centtrillion
10 315 - quattorcentillion or centquadrillion
10 402 - tretrigintacentillion or centtretrigintillion

The second spelling is more consistent with the construction of numerals in Latin and avoids ambiguities (for example, in the number trecentillion, which, according to the first spelling, is 10 903 and 10 312).

10 603 - ducentillion
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 15003 - quinquemillion
10 308760 -on
10 3000003 - Million
10 6000003 - duomiliamilillion

Myriad- 10 000. The name is outdated and practically not used. However, the word “myriads” is widely used, which does not mean a certain number, but an innumerable, uncountable set of something.

Googol ( English . googol) — 10 100. This number was first written by the American mathematician Edward Kasner in 1938 in the journal Scripta Mathematica in the article “New Names in Mathematics”. According to him, his 9-year-old nephew Milton Sirotta suggested the name so. This number became common knowledge thanks to the Google search engine named after him.

Asankheya(from Chinese asenci - uncountable) - 10 1 4 0. This number is found in the famous Buddhist treatise Jaina Sutra (100 BC). It is believed that this number is equal to the number space cycles necessary to attain nirvana.

Googolplex ( English . Googolplex) — 10 ^ 10 ^ 100. This number was also invented by Edward Kasner and his nephew, it means one with a googol of zeros.

Skuse's number (Skewes' number, Sk 1) means e to the e to the e to 79, that is, e ^ e ^ e ^ 79. This number was proposed by Skewes in 1933 (Skewes. J. London Math. Soc. 8, 277-283, 1933.) in the proof of the Riemann conjecture concerning prime numbers. Later, Riel (te Riele, HJJ "On the Sign of the Difference P (x) -Li (x)." Math. Comput. 48, 323-328, 1987) reduced the Skuse number to e ^ e ^ 27/4, which is approximately 8.185 10 ^ 370. However, this number is not an integer, so it is not included in the table of large numbers.

Skewes' second number (Sk2) is equal to 10 ^ 10 ^ 10 ^ 10 ^ 3, that is, 10 ^ 10 ^ 10 ^ 1000. This number was introduced by J. Skuse in the same article to denote the number up to which the Riemann hypothesis is valid.

For very large numbers, it is inconvenient to use powers, so there are several ways to write numbers - notation by Knuth, Conway, Steinhouse, etc.

Hugo Steinhouse proposed to write large numbers inside geometric shapes (triangle, square and circle).

The mathematician Leo Moser refined Steinhouse's notation, suggesting that after the squares, draw not circles, but pentagons, then hexagons, etc. Moser also proposed a formal notation for these polygons so that numbers could be written down without drawing complex drawings.

Steinhouse came up with two new super-large numbers: Mega and Megiston. In Moser's notation, they are written as follows: Mega – 2, Megiston- 10. Leo Moser also proposed to call a polygon with the number of sides equal to mega - megagon, and also proposed the number “2 in Megagon” - 2. The last number is known as Moser's number or just like Moser.

There are numbers greater than Moser. The largest number used in mathematical proof is number Graham(Graham's number). It was first used in 1977 to prove one estimate in Ramsey's theory. This number is associated with bichromatic hypercubes and cannot be expressed without a special 64-level system of special mathematical symbols introduced by Knuth in 1976. Donald Knuth (who wrote The Art of Programming and created the TeX editor) came up with the concept of superdegree, which he proposed to write down with arrows pointing up:

V general view

Graham suggested G-numbers:

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

As a child, I was tormented by the question of what is the largest number, and I tormented 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? 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 was never the largest, since there are even more numbers.

And now, many years later, I decided to ask another question, namely: what is the largest number that has its own name? Fortunately, now there is an Internet and they can be puzzled by patient search engines that will not call my questions idiotic ;-). Actually, this is what I did, and this is what I found out as a result.

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

There are two systems for naming numbers - 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 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 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 using 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 one 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:

Name	Number
Unit	10 0
Ten	10 1
Hundred	10 2
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's next. What's behind the decillion? In principle, it is possible, of course, by combining prefixes to generate such monsters as: andecilion, 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 those indicated above, you can still get only three - vigintillion (from lat. viginti- twenty), centillion (from lat. centum- one hundred) and a million (from lat. mille- 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, a million (1,000,000) Romans called decies centena milia, that is, "ten hundred thousand". And now, in fact, the table:

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

Name	Number
Myriad	10 4
Googol	10 100
Asankheya	10 140
Googolplex	10 10 100
Second Skewes number	10 10 10 1000
Mega	2 (in Moser notation)
Megiston	10 (in Moser notation)
Moser	2 (in Moser notation)
Graham's number	G 63 (in Graham notation)
Stasplex	G 100 (in Graham notation)

The smallest such number is myriad(it is even in Dahl's dictionary), which means a hundred hundred, that is, 10,000 a certain number, but a countless, uncountable set of something. It is believed that the word myriad came into 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. 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... Please note that "Google" is trademark and googol is a number.

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 10 100. 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 a 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, e e e 79. Later, Riele (te Riele, H. J. J. "On the Sign of the Difference NS(x) -Li (x). " Math. Comput. 48 , 323-328, 1987) reduced the Skewes number to e e 27/4, which is approximately 8.185 10 370. It is clear that since the value of the Skuse number depends on the number e, then it is not an integer, therefore we will not consider it, otherwise we would have to remember other non-natural numbers - pi, e, Avogadro's number, etc.

But it should be noted that there is a second Skuse number, which in mathematics is denoted as Sk 2, which is even greater than the first Skuse number (Sk 1). Second Skewes 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 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 called the 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 required to write numbers much larger than the megiston, difficulties and inconveniences arose, since many circles had to be drawn inside one 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:

Thus, according to Moser's notation, the Steinhaus 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 Moser's number (Moser "s number) or simply as moser.

But the moser is not the largest number either. The largest number ever used in a mathematical proof is limit value known as Graham's number(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 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 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:

The number G 63 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. 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 G 100. Remember 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 I made several mistakes while writing the text. I'll try to fix it now.

I made several mistakes at once by simply mentioning Avogadro's number. Firstly, several people pointed out to me that in fact 6,022 10 23 is the most that neither is natural number... And secondly, there is an opinion, and it seems to me correct, that Avogadro's number is not at all a number 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 you express it, for example, in moles or something else, then it will be expressed in a completely different number, but this will not stop being Avogadro's number at all.
10,000 - darkness
100,000 - legion
1,000,000 - leodr
10,000,000 - a raven or a lie
100,000,000 - deck
Interestingly, the ancient Slavs also loved large numbers and knew how to count up to a billion. Moreover, they called such an account "small account". In some manuscripts, the authors considered and " great score", reaching the number 10 50. About numbers greater than 10 50 it was said:" And the human mind cannot understand more than this. " meant no longer 10,000, but a million, legion - the darkness of those (a million million); leodr - legion of legions (10 to 24 degrees), then it was said - ten leodr, one hundred leodr, ..., and, finally, one hundred thousand themes legion leodr (10 in 47); leodr leodr (10 in 48) was called a raven and, finally, a deck (10 in 49).
Theme national names numbers can be expanded if we recall the Japanese system of naming numbers forgotten by me, which is very different from the English and American systems (I will not draw hieroglyphs, if someone is interested, they are):
10 0 - ichi
10 1 - jyuu
10 2 - hyaku
10 3 - sen
10 4 - man
10 8 - oku
10 12 - chou
10 16 - kei
10 20 - gai
10 24 - jyo
10 28 - jyou
10 32 - kou
10 36 - kan
10 40 - sei
10 44 - sai
10 48 - goku
10 52 - gougasya
10 56 - asougi
10 60 - nayuta
10 64 - fukashigi
10 68 - muryoutaisuu
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 Steinhaus, but to Daniil Kharms, who published this idea for nothing 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-language Internet - Watermelon, for the information that Steinhaus came up with not only the mega and megiston numbers, but also suggested another number mezzon, equal (in its notation) "3 in a circle".
Now about the number myriad or myrioi. 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 Earth's 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 10 67 (just a myriad of times more). Archimedes suggested the following names for numbers:
1 myriad = 10 4.
1 d-myriad = myriad of myriads = 10 8.
1 three-myriad = di-myriad of di-myriads = 10 16.
1 tetra-myriad = three-myriad three-myriad = 10 32.
etc.

If there are any comments -

“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, out there, beyond our understanding ''.
Douglas Ray

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 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 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 according to the English and American systems is 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 by the formula 6 x + 6 for numbers ending in -billion.

From the English system, only the number billion (10 9) passed into 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.

And so, now the question arises, what's next. What's behind the decillion? In principle, it is possible, of course, by combining prefixes to generate such monsters as: andecilion, 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 those indicated above, you can still get only three - vigintillion (from lat.viginti- twenty), centillion (from lat.centum- one hundred) and a million (from lat.mille- 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, a million (1,000,000) Romans calleddecies 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! Nevertheless, numbers over 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 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 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 NS(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 the Skuse number depends on the number e, then it is not an integer, therefore we will not consider it, otherwise we would have to remember 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 .

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

But the 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 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 notation cannot be translated into the Moser system. Therefore, we will have to explain this system as well. 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 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:

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. 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. Remember 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, for starters there is a Graham number... 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.

Countless different numbers surround us every day. Surely many people wondered at least once what number is considered the largest. You can simply tell a child that this is a million, but adults are well aware that other numbers follow a million. For example, it is only necessary to add one to the number each time, and it will become more and more - this happens ad infinitum. But if you take apart the numbers that have names, you can find out what the largest number in the world is called.

The emergence of the names of numbers: what methods are used?

Today there are 2 systems according to which numbers are given names - American and English. The first is fairly simple, while the second is the most common around the world. American allows you to give names to large numbers like this: first, the ordinal in Latin is indicated, and then the suffix "illion" is added (the exception here is a million, meaning a thousand). This system is used by Americans, French, Canadians, and it is also used in our country.

English is widely used in England and Spain. According to it, the numbers are named as follows: the numeral in Latin is "plus" with the suffix "illion", and the next (a thousand times larger) number is "plus" "illiard". For example, first comes a trillion, followed by a trillion, followed by a quadrillion, and so on.

So, the same number in different systems can mean different things, for example, the American billion in the English system is called a billion.

Off-system numbers

In addition to the numbers that are written by known systems(above), there are also non-systemic ones. They have their own names, which do not include Latin prefixes.

You can start considering them with a number called a myriad. It is defined as one hundred hundreds (10000). But for its intended purpose, this word is not used, but is used as an indication of an innumerable number. Even Dahl's dictionary will kindly provide a definition of such a number.

The next after the myriad is googol, denoting 10 to the power of 100. This name was first used in 1938 - by a mathematician from America E. Kasner, who noted that this name was invented by his nephew.

Google (search engine) got its name in honor of googol. Then 1-tsa with a googol of zeros (1010100) is a googolplex - this name was also invented by Kasner.

Even larger in comparison with the googolplex is the Skuse number (e to the e to the e79), proposed by Skuse in the proof of the Rimmann conjecture on primes (1933). There is one more Skuse number, but it is applied when the Rimmann hypothesis is not valid. Which of them is more, it is rather difficult to say, especially when it comes to large degrees... However, this number, despite its "enormity", cannot be considered the most-most of all those that have their own names.

And the leader among the largest numbers in the world is the Graham number (G64). It was he who was used for the first time to carry out proofs in the field of mathematical science (1977).

When it comes about such a number, then you need to know that you cannot do without a special 64-level system created by Knut - the reason for this is the connection of the number G with bichromatic hypercubes. The whip invented a superdegree, and in order to make it convenient to take her notes, he suggested using the up arrows. So we learned the name of the largest number in the world. It is worth noting that this G number got on the pages of the famous Book of Records.