And their number is greater. What is the largest number

Sooner or later, everyone is tormented by the question, what is the largest number. There are a million answers to a child's question. What's next? Trillion. And even further? In fact, the answer to the question of what are the largest numbers is simple. Just add one to the largest number, and it will no longer be the largest. This procedure can be continued indefinitely. Those. It turns out there is not the largest number in the world? Is this infinity?

But if you ask the question: what is the largest number that exists, and what is its proper name? Now we will find out everything...

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

The American system is built quite simply. All names of large numbers are constructed like this: 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 thousand (lat. mille) and the magnifying suffix -illion (see table). This is how we get the numbers 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 according to 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 former English and Spanish colonies. The names of numbers in this system are built like this: like this: 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 - 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 are completely different numbers! You can find out the number of zeros in a number written according to 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 would still be more correct to be called as the Americans call it - billion, since we have adopted the American system. But who in our country does anything according to the rules! 😉 By the way, sometimes the word trillion is used in Russian (you can see this for yourself by running a search in Google or Yandex) and, apparently, it means 1000 trillion, i.e. quadrillion.

In addition to numbers written using Latin prefixes according to the American or English system, so-called non-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 tell you more about them a little later.

Let's return to writing using Latin numerals. It would seem that they can write down numbers to infinity, but this is not entirely true. Now I will explain why. Let's first see what the numbers from 1 to 10 33 are called:

And now the question arises, what next. What's behind the decillion? In principle, it is, of course, possible, 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 those indicated above, you can still get only three proper names - vigintillion (from Lat. viginti- twenty), centillion (from lat. centum- one hundred) and million (from lat. mille- thousand). The Romans did not have more than a thousand proper 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, actually, the table:

Thus, according to such a system, it is impossible to obtain numbers greater than 10 3003, which would have its own, non-compound name! But nevertheless, numbers greater than a million are known - these are the same non-systemic numbers. Let's finally talk about them.

The smallest such number is a myriad (it is even in Dahl’s dictionary), which means a hundred hundreds, that is, 10,000. This word, however, is outdated and practically not used, but it is curious that the word “myriads” is widely used, which does not mean a definite number at all, but an uncountable, uncountable multitude 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 fact, the myriad gained fame precisely thanks to the Greeks. Myriad was the name for 10,000, but there were no names for numbers greater than ten thousand. However, in his note “Psammit” (i.e., calculus of sand), Archimedes showed how to 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 ball with a diameter of a myriad of the diameters of the Earth) no more than 1063 grains of sand could fit (in our notation). It is curious that modern calculations of the number of atoms in the visible Universe lead to the number 1067 (in total a myriad of times more). Archimedes suggested the following names for the numbers:
1 myriad = 104.
1 di-myriad = myriad of myriads = 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 followed by 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, it was his nine-year-old nephew Milton Sirotta who suggested calling the large number a “googol”. This number became generally known thanks to the Google search engine named after it. Please note that "Google" is a brand name 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 true...

In the famous Buddhist treatise Jaina Sutra, dating back to 100 BC, the number asankheya (from Chinese. asenzi- innumerable), equal to 10,140. It is believed that this number is equal to the number of cosmic cycles necessary to achieve nirvana.

Googolplex (English) googolplex) - a number also invented by Kasner and his nephew and meaning 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. J. London Math. Soc. 8, 277-283, 1933.) in the proof of the Riemann hypothesis concerning prime numbers. It means e to a degree e to a degree e to the power of 79, that is eee79. Later, te Riele, H. J. J. "On the Sign of the Difference P(x)-Li(x)." Math. Comput. 48, 323-328, 1987) reduced the Skuse number to ee27/4, which is approximately 8.185 10370. It is clear that since the value of the Skuse number depends on the number e, then it is not an integer, so we will not consider it, otherwise we would have to remember other non-natural numbers - the number pi, the number 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). The second Skuse number was introduced by J. Skuse in the same article to designate a number for which the Riemann hypothesis does not hold. Sk2 is equal to 101010103, that is, 1010101000.

As you understand, the more degrees there are, the more difficult it is to understand which number is greater. For example, looking at Skewes numbers, without special calculations, it is almost impossible to understand which of these two numbers is larger. Thus, for super-large 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, that's on the page! They won’t fit even into a book the size of the entire Universe! In this case, the question arises of 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 wondered about this problem came up with his own way of writing, which led to the existence of several, unrelated to each other, methods for writing numbers - these are the notations of Knuth, Conway, Steinhouse, etc.

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

Steinhouse came up with two new superlarge numbers. He named the number - Mega, and the number - Megiston.

Mathematician Leo Moser refined Stenhouse's notation, which was limited by the fact that if it was necessary to write down numbers much larger than a megiston, difficulties and inconveniences arose, since many circles had to be drawn one inside the other. Moser suggested that after the squares, draw not circles, 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 pictures. Moser notation looks like this:

• • n[k+1] = "n V n k-gons" = n[k]n.

Thus, according to Moser's notation, Steinhouse's mega is written as 2, and megiston as 10. In addition, Leo Moser proposed 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 Moser’s number or simply as Moser.

But Moser is not the largest number. The largest number ever used in a mathematical proof is the limiting quantity known as Graham's number, first used in 1977 in the proof of an 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, a number written in Knuth's notation cannot be converted into notation in the Moser system. Therefore, we will have to explain this system too. 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) came up with the concept of superpower, which he proposed to write with arrows pointing upward:

In general it looks like this:

I think everything is clear, so let’s return to Graham’s number. Graham proposed so-called G-numbers:

The G63 number came to be called the Graham number (it is often designated simply as G). This number is the largest known number in the world and is even listed in the Guinness Book of Records.

So are there numbers greater than Graham's number? There is, of course, for starters there is the Graham number + 1. As for the significant number... well, there are some fiendishly complex areas of mathematics (specifically the area known as combinatorics) and computer science in which numbers even larger than the Graham number occur. 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

As a child, I was tormented by the question of what the largest number exists, 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? How about more than a billion? Trillion? How about more than a trillion? Finally, there was someone smart who explained to me that the question was 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 larger numbers.

And so, many years later, I decided to ask myself another question, namely: What is the largest number that has its own name? Fortunately, now there is the Internet and you can puzzle patient search engines with it, which will not call my questions idiotic ;-). Actually, that’s what I did, and this is what I found out as a result.

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

The American system is built quite simply. All names of large numbers are constructed like this: 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 thousand (lat. mille) and the magnifying suffix -illion (see table). This is how we get the numbers 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 according to 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 former English and Spanish colonies. The names of numbers in this system are built like this: like this: 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 - 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 are completely different numbers! You can find out the number of zeros in a number written according to 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 would still be more correct to be called as the Americans call it - billion, since we have adopted the American system. But who in our country does anything according to the rules! ;-) By the way, sometimes the word trillion is used in Russian (you can see this 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 non-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 tell you more about them a little later.

Let's return to writing using Latin numerals. It would seem that they can write down numbers to infinity, but this is not entirely true. Now I will explain why. Let's first see what the numbers from 1 to 10 33 are called:

And now the question arises, what next. What's behind the decillion? In principle, it is, of course, possible, 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 those indicated above, you can still get only three proper names - vigintillion (from Lat. viginti- twenty), centillion (from lat. centum- one hundred) and million (from lat. mille- thousand). The Romans did not have more than a thousand proper 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, actually, the table:

Thus, according to such a system, it is impossible to obtain numbers greater than 10 3003, which would have its own, non-compound name! But nevertheless, numbers greater than a million are known - these are the same non-systemic numbers. Let's finally talk about them.

The smallest such number is myriad(it is even in Dahl’s dictionary), which means a hundred hundreds, that is, 10,000. This word, however, is outdated and practically not used, but it is curious that the word “myriads” is widely used, which does not mean a specific number at all, but countless, uncountable multitudes of something. It is believed that the word myriad came into European languages ​​from ancient Egypt.

Google(from the English googol) is the number ten to the hundredth power, that is, one followed by 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, it was his nine-year-old nephew Milton Sirotta who suggested calling the large number a “googol”. This number became generally known thanks to the search engine named after it. Google. Please note that "Google" is a brand name and googol is a number.

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

Googolplex(English) googolplex) - a number also invented by Kasner and his nephew and meaning 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 the googolplex, the Skewes number, was proposed by Skewes in 1933. J. London Math. Soc. 8 , 277-283, 1933.) in proving the Riemann hypothesis concerning prime numbers. It means e to a degree e to a degree e to the power of 79, that is, e e e 79. Later, te Riele, H. J. J. "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 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, so 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 degrees there are, the more difficult it is to understand which number is greater. For example, looking at Skewes numbers, without special calculations, it is almost impossible to understand which of these two numbers is larger. Thus, for super-large 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, that's on the page! They won’t fit even into a book the size of the entire Universe! In this case, the question arises of 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 wondered about this problem came up with his own way of writing, which led to the existence of several, unrelated to each other, methods for writing numbers - these are the notations of Knuth, Conway, Steinhouse, etc.

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

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

Mathematician Leo Moser refined Stenhouse's notation, which was limited by the fact that if it was necessary to write down numbers much larger than a megiston, difficulties and inconveniences arose, since many circles had to be drawn one inside the other. Moser suggested that after the squares, draw not circles, 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 pictures. 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 proposed 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 Moser’s number or simply as Moser.

But Moser is not the largest number. The largest number ever used in mathematical proof is the limit 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, a number written in Knuth's notation cannot be converted into notation in the Moser system. Therefore, we will have to explain this system too. 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) came up with the concept of superpower, which he proposed to write with arrows pointing upward:

In general it looks like this:

I think everything is clear, so let’s return to Graham’s number. Graham proposed so-called G-numbers:

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

P.S. In order to bring great benefit to all humanity and become famous throughout the 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): Thank you all for the comments. It turned out that I made several mistakes when writing the text. I'll try to fix it now.

1. I made several mistakes just by mentioning Avogadro's number. First, several people pointed out to me that 6.022 10 23 is, in fact, the most natural number. And secondly, there is an opinion, and it seems correct to me, 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 as a completely different number, but this will not cease to be Avogadro’s number at all.
2. 10,000 - darkness
   100,000 - legion
   1,000,000 - leodr
   10,000,000 - raven or corvid
   100,000,000 - deck
   Interestingly, the ancient Slavs also loved large numbers and were able to count to a billion. Moreover, they called such an account a “small account.” In some manuscripts, the authors also considered the “great count”, reaching the number 10 50. About numbers greater than 10 50 it was said: “And more than this cannot be understood by the human mind.” The names used in the “small count” were transferred to the “great count”, but with a different meaning. So, darkness no longer meant 10,000, but a million, legion - the darkness of those (a million millions); leodre - legion of legions (10 to the 24th degree), then it was said - ten leodres, one hundred leodres, ..., and finally, one hundred thousand those legion of leodres (10 to 47); leodr leodrov (10 in 48) was called a raven and, finally, a deck (10 in 49).
3. The topic of national names of numbers can be expanded if we remember about the Japanese system of naming numbers that I had forgotten, which is very different from the English and American systems (I won’t draw hieroglyphs, if anyone 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
4. 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 superlarge numbers in the form of numbers in circles belongs not to Steinhouse, but to Daniil Kharms, who long before him published this idea in the article “Raising a Number.” I also want to thank Evgeniy Sklyarevsky, the author of the most interesting site on entertaining mathematics on the Russian-language Internet - Arbuza, for the information that Steinhouse came up with not only the numbers mega and megiston, but also suggested another number medical zone, equal (in his notation) to "3 in a circle".
5. Now about the number myriad or mirioi. 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, but there were no names for numbers greater than ten thousand. However, in his note “Psammit” (i.e., calculus of sand), Archimedes showed how to 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 ball with a diameter of a myriad of the diameters of the Earth) no more than 10 63 grains of sand could 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 (in total a myriad of times more). Archimedes suggested the following names for the numbers:
   1 myriad = 10 4 .
   1 di-myriad = myriad of myriads = 10 8 .
   1 tri-myriad = di-myriad di-myriad = 10 16 .
   1 tetra-myriad = three-myriad three-myriad = 10 32 .
   etc.

If you have any comments -

Have you ever thought how many zeros there are in one million? This is a pretty simple question. What about a billion or a trillion? One followed by nine zeros (1000000000) - what is the name of the number?

A short list of numbers and their quantitative designation

• Ten (1 zero).
• One hundred (2 zeros).
• One thousand (3 zeros).
• Ten thousand (4 zeros).
• One hundred thousand (5 zeros).
• Million (6 zeros).
• Billion (9 zeros).
• Trillion (12 zeros).
• Quadrillion (15 zeros).
• Quintilion (18 zeros).
• Sextillion (21 zeros).
• Septillion (24 zeros).
• Octalion (27 zeros).
• Nonalion (30 zeros).
• Decalion (33 zeros).

Grouping of zeros

1000000000 - what is the name of a number that has 9 zeros? This is a billion. For convenience, large numbers are usually grouped into sets of three, separated from each other by a space or punctuation marks such as a comma or period.

This is done to make the quantitative value easier to read and understand. For example, what is the name of the number 1000000000? In this form, it’s worth straining a little and doing the math. And if you write 1,000,000,000, then the task immediately becomes visually easier, since you need to count not zeros, but triples of zeros.

Numbers with a lot of zeros

The most popular are million and billion (1000000000). What is the name of a number that has 100 zeros? This is a Googol number, so called by Milton Sirotta. This is a wildly huge amount. Do you think this number is large? Then what about a googolplex, a one followed by a googol of zeros? This figure is so large that it is difficult to come up with a meaning for it. In fact, there is no need for such giants, except to count the number of atoms in the infinite Universe.

Is 1 billion a lot?

There are two measurement scales - short and long. Around the world in science and finance, 1 billion is 1,000 million. This is on a short scale. According to it, this is a number with 9 zeros.

There is also a long scale that is used in some European countries, including France, and was formerly used in the UK (until 1971), where a billion was 1 million million, that is, a one followed by 12 zeros. This gradation is also called the long-term scale. The short scale is now predominant when deciding financial and scientific issues.

Some European languages, such as Swedish, Danish, Portuguese, Spanish, Italian, Dutch, Norwegian, Polish, German, use billion (or billion) in this system. In Russian, a number with 9 zeros is also described for the short scale of a thousand million, and a trillion is a million million. This avoids unnecessary confusion.

Conversational options

In Russian colloquial speech after the events of 1917 - the Great October Revolution - and the period of hyperinflation in the early 1920s. 1 billion rubles was called “limard”. And in the dashing 1990s, a new slang expression “watermelon” appeared for a billion; a million were called “lemon.”

The word "billion" is now used internationally. This is a natural number, which is represented in the decimal system as 10 9 (one followed by 9 zeros). There is also another name - billion, which is not used in Russia and the CIS countries.

Billion = billion?

A word such as billion is used to designate a billion only in those states in which the “short scale” is adopted as a basis. These are countries such as the Russian Federation, the United Kingdom of Great Britain and Northern Ireland, the USA, Canada, Greece and Turkey. In other countries, the concept of a billion means the number 10 12, that is, one followed by 12 zeros. In countries with a “short scale”, including Russia, this figure corresponds to 1 trillion.

Such confusion appeared in France at a time when the formation of such a science as algebra was taking place. Initially, a billion had 12 zeros. However, everything changed after the appearance of the main manual on arithmetic (author Tranchan) in 1558), where a billion is already a number with 9 zeros (a thousand millions).

For several subsequent centuries, these two concepts were used on an equal basis with each other. In the mid-20th century, namely in 1948, France switched to a long scale numerical naming system. In this regard, the short scale, once borrowed from the French, is still different from the one they use today.

Historically, the United Kingdom used the long-term billion, but since 1974 official UK statistics have used the short-term scale. Since the 1950s, the short-term scale has been increasingly used in the fields of technical writing and journalism, although the long-term scale still persists.

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

Story

The southern and eastern Slavic peoples used alphabetical numbering to record numbers, and only those letters that are in the Greek alphabet. A special “title” icon was placed above the letter that designated the number. The numerical values ​​of the letters increased in the same order as the letters 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. Thus, until the 15th century, the number “twenty” was designated as “two tens” (two tens), and then it was shortened for faster pronunciation. The number 40 was called “fourty” until the 15th century, then it was replaced by the word “forty,” which originally meant a bag containing 40 squirrel or sable skins. The name “million” appeared in Italy in 1500. It was formed by adding an augmentative suffix to the number “mille” (thousand). Later this name came to the Russian language.

In the ancient (18th century) “Arithmetic” of Magnitsky, a table of the names of numbers is given, brought to the “quadrillion” (10^24, according to the system through 6 digits). Perelman Ya.I. the book “Entertaining Arithmetic” gives the names of large numbers of that time, slightly different from today: septillion (10^42), octalion (10^48), nonalion (10^54), decalion (10^60), endecalion (10^ 66), dodecalion (10^72) and it is written that “there are no further names.”

Ways to construct names for large numbers

There are 2 main ways to name large numbers:

• American system, which is used in the USA, Russia, France, Canada, Italy, Turkey, Greece, Brazil. The names of large numbers are constructed quite simply: the Latin ordinal number comes first, and the suffix “-million” is added to it at the end. An exception is the number “million,” which is the name of the number thousand (mille) and the augmentative suffix “-million.” The number of zeros in a number, which is written according to the American system, can be found out by the formula: 3x+3, where x is the Latin ordinal number
• English system most common 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 constructed as follows: the suffix “-million” is added to the Latin numeral, the next number (1000 times larger) is the same Latin numeral, but the suffix “-billion” is added. The number of zeros in a number, which is written according to the English system and ends with the suffix “-million,” can be found out by the formula: 6x+3, where x is the Latin ordinal number. The number of zeros in numbers ending with the suffix “-billion” can be found using the formula: 6x+6, where x is the Latin ordinal number.

Only the word billion passed from the English system into the Russian language, which is still more correctly called as the Americans call it - billion (since the Russian language uses the American system for naming numbers).

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

Proper names for large numbers

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

For numbers greater than a thousand, the Romans did not have their own names (all names for numbers were then composite).

Compound names of large numbers

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

Compound names of large numbers

• 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 by direct or reverse order of Latin numerals (which is correct is not known):

• 10 306 - ancentillion or centunillion
• 10 309 - duocentillion or centullion
• 10 312 - trcentillion or centtrillion
• 10 315 - quattorcentillion or centquadrillion
• 10 402 - tretrigyntacentillion or centretrigintillion

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

• 10 603 - decentillion
• 10,903 - trcentillion
• 10 1203 - quadringentillion
• 10 1503 — quingentillion
• 10 1803 - sescentillion
• 10 2103 - septingentillion
• 10 2403 — octingentillion
• 10 2703 — nongentillion
• 10 3003 - million
• 10 6003 - duo-million
• 10 9003 - three million
• 10 15003 — quinquemilliallion
• 10 308760 -ion
• 10 3000003 — mimiliaillion
• 10 6000003 — duomimiliaillion

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

Googol ( English . googol) — 10 100. The American mathematician Edward Kasner first wrote about this number 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 calling the number this way. This number became publicly known thanks to the Google search engine named after it.

Asankheya(from Chinese asentsi - 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 of cosmic cycles required to achieve nirvana.

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

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

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

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

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

Mathematician Leo Moser refined Steinhouse's notation, proposing to draw pentagons, then hexagons, etc. after squares rather than circles. Moser also proposed a formal notation for these polygons so that the numbers could be written without drawing complex pictures.

Steinhouse came up with two new super-large numbers: Mega and Megiston. In Moser 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 larger than Moser. The largest number that has been used in a mathematical proof is number Graham(Graham's number). It was first used in 1977 to prove an estimate in Ramsey 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 superpower, which he proposed to write with arrows pointing up:

In general

Graham proposed G-numbers:

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

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

The appearance of number names: what methods are used?

Today there are 2 systems according to which names are given to numbers - American and English. The first is quite simple, and the second is the most common throughout the world. The American one allows you to give names to large numbers as follows: first, the ordinal number in Latin is indicated, and then the suffix “million” is added (the exception here is 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, 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” “billion”. For example, the trillion comes first, the trillion comes after it, the quadrillion comes after the quadrillion, etc.

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

Extra-system numbers

In addition to the numbers that are written according to the known systems (given 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 according to its intended purpose, this word is not used, but is used as an indication of an innumerable multitude. Even Dahl's dictionary will kindly provide a definition of such a number.

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

Google (search engine) got its name in honor of googol. Then 1 with a googol of zeros (1010100) represents a googolplex - Kasner also came up with this name.

Even larger than the googolplex is the Skuse number (e to the power of e to the power of e79), proposed by Skuse in his proof of the Rimmann conjecture about prime numbers (1933). There is another Skuse number, but it is used when the Rimmann hypothesis is not true. Which one is greater is quite difficult to say, especially when it comes to large degrees. However, this number, despite its “hugeness,” cannot be considered the very best 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 used for the first time to carry out proofs in the field of mathematical science (1977).

When it comes to such a number, you need to know that you cannot do without a special 64-level system created by Knuth - the reason for this is the connection of the number G with bichromatic hypercubes. Knuth invented the superdegree, and in order to make it convenient to record it, he proposed the use of up arrows. So we found out what the largest number in the world is called. It is worth noting that this number G was included in the pages of the famous Book of Records.