40 zeros what a number. The largest number in the world

It is known that an infinite number of numbers and only a few have names of their own, for most numbers have been given names consisting of small numbers. The largest numbers must be denoted in some way.

"Short" and "long" scale

Number names used today began to receive in the fifteenth century, then the Italians first used the word million, meaning "big thousand", bimillion (million squared) and trimillion (million cubed).

This system was described in his monograph by the Frenchman Nicholas Shuquet, he recommended using Latin numerals, adding to them the inflection "-million", so bimillion became a billion, and three million became a trillion, and so on.

But according to the proposed system of numbers between a million and a billion, he called "a thousand millions." It was not comfortable to work with such a gradation and in 1549 the Frenchman Jacques Peletier advised to call the numbers that are in the specified interval, again using Latin prefixes, while introducing another ending - “-billion”.

So 109 was called a billion, 1015 - billiard, 1021 - trillion.

Gradually, this system began to be used in Europe. But some scientists confused the names of numbers, this created a paradox when the words billion and billion became synonymous. Subsequently, the United States created its own naming convention for large numbers. According to him, the construction of names is carried out in a similar way, but only the numbers differ.

The old system continued to be used in the UK, and therefore was called British, although it was originally created by the French. But since the seventies of the last century, Great Britain also began to apply the system.

Therefore, in order to avoid confusion, the concept created by American scientists is usually called short scale, while the original French-British - long scale.

The short scale has found active use in the USA, Canada, Great Britain, Greece, Romania, and Brazil. In Russia, it is also in use, with only one difference - the number 109 is traditionally called a billion. But the French-British version was preferred in many other countries.

In order to designate numbers larger than a decillion, scientists decided to combine several Latin prefixes, so the undecillion, quattordecillion and others were named. If you use Schuecke system, then according to it, giant numbers will acquire the names "vigintillion", "centillion" and "millionillion" (103003), respectively, according to the long scale, such a number will receive the name "millionillion" (106003).

Numbers with unique names

Many numbers were named without reference to various systems and parts of words. There are a lot of these numbers, for example, this Pi", a dozen, as well as numbers over a million.

IN Ancient Russia has long used its own numerical system. Hundreds of thousands were called legion, a million were called leodroms, tens of millions were crows, hundreds of millions were called decks. It was a “small account”, but the “great account” used the same words, only a different meaning was put into them, for example, leodr could mean a legion of legions (1024), and a deck could already mean ten ravens (1096).

It happened that children came up with names for numbers, for example, mathematician Edward Kasner was given the idea young Milton Sirotta, who proposed giving a name to a number with a hundred zeros (10100) simply googol. This number received the most publicity in the nineties of the twentieth century, when the Google search engine was named after him. The boy also suggested the name "Googleplex", a number that has a googol of zeros.

But Claude Shannon in the middle of the twentieth century, evaluating the moves in a chess game, calculated that there are 10118 of them, now it is "Shannon number".

In an old Buddhist work "Jaina Sutras", written almost twenty-two centuries ago, the number "asankheya" (10140) is noted, which is exactly how many cosmic cycles, according to Buddhists, it is necessary to achieve nirvana.

Stanley Skuse described large quantities, so "the first Skewes number", equal to 10108.85.1033, and the "second Skewes number" is even more impressive and equals 1010101000.

Notations

Of course, depending on the number of degrees contained in a number, it becomes problematic to fix it on writing, and even reading, error bases. some numbers cannot fit on multiple pages, so mathematicians have come up with notations to capture large numbers.

It is worth considering that they are all different, each has its own principle of fixation. Among these, it is worth mentioning notations by Steinghaus, Knuth.

However, the largest number, the Graham number, was used Ronald Graham in 1977 when doing mathematical calculations, and this number is G64.

This is a tablet for learning numbers from 1 to 100. The manual is suitable for children over 4 years old.

Those who are familiar with Montesori education have probably already seen such a sign. She has many applications and now we will get to know them.

The child must know numbers up to 10 perfectly before starting work with the table, since counting up to 10 is the basis of learning numbers up to 100 and above.

With the help of this table, the child will learn the names of numbers up to 100; count up to 100; sequence of numbers. You can also practice counting after 2, 3, 5, etc.

The table can be copied here

It consists of two parts (two-sided). We copy on one side of the sheet a table with numbers up to 100, and on the other, empty cells where you can practice. Laminate the table so that the child can write on it with markers and wipe it off easily.

How to use the table

	1. The table can be used to study numbers from 1 to 100. Starting at 1 and counting up to 100. Initially the parent/teacher shows how this is done. It is important that the child notices the principle by which numbers are repeated.
	2. Mark one number on the laminated chart. The child must say the next 3-4 numbers.
	3. Mark some numbers. Ask the child to name their names. The second version of the exercise - the parent calls arbitrary numbers, and the child finds and marks them.
	4. Count in 5. The child counts 1,2,3,4,5 and notes the last (fifth) number.
	5. If you copy the template with numbers again and cut it, you can make cards. They can be placed in the table as you will see in the following lines In this case, the table is copied on blue cardboard, which would be easily distinguished from white background table.
	6. Cards can be placed on the table and counted - call the number by putting its card. This helps the child learn all the numbers. Thus he will exercise. Before that, it is important that the parent divide the cards into 10s (1 to 10; 11 to 20; 21 to 30, etc.). The child takes a card, puts it down and calls a number.
	7. When the child has already advanced with the score, you can go to an empty table and arrange the cards there.
	8. Account horizontally or vertically. Arrange the cards in a column or row and read all the numbers in order, following the pattern of their change - 6, 16, 26, 36, etc.
	9. Write the missing number. The parent writes arbitrary numbers to an empty table. The child must complete the empty cells.

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

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

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

"Short" and "long" scale

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

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

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

This confusion continued for a long time and led to the fact that in the USA they created their own system for naming large numbers. According to the American system, the names of numbers are built in the same way as in the Schücke system - the Latin prefix and the ending "million". However, these numbers are different. If in the Schuecke system names with the ending "million" received numbers that were powers of a million, then in the American system the ending "-million" received the powers of a thousand. That is, a thousand million (1000 3 \u003d 10 9) began to be called a "billion", 1000 4 (10 12) - "trillion", 1000 5 (10 15) - "quadrillion", etc.

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

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

The short naming scale is now used in the United States, United Kingdom, Canada, Ireland, Australia, Brazil and Puerto Rico. Russia, Denmark, Turkey, and Bulgaria also use the short scale, except that the number 109 is not called "billion" but "billion". The long scale continues to be used today in most other countries.

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

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

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

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

However, there are names for even larger numbers.

Numbers outside the system

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

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

The number 10100 also has its own name and was invented by a nine-year-old boy. And it was like that. 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 Sirott, suggested calling this number "googol". In 1940, Edward Kasner, together with James Newman, wrote the non-fiction book Mathematics and the Imagination, where he taught mathematics lovers about the googol number. Google became even more widely known in the late 1990s, thanks to the Google search engine named after it.

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

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

Nine-year-old Milton Sirotta entered the history of mathematics not only by inventing the number googol, but also by suggesting another number at the same time - “googolplex”, which is equal to 10 to the power of “googol”, that is, one with a googol of zeros.

Two more numbers larger than the googolplex were proposed by the South African mathematician Stanley Skewes (1899-1988) when proving the Riemann hypothesis. The first number, which later came to be called "Skeuse's first number", is equal to e to the extent e to the extent e to the power of 79, that is e e e 79 = 10 10 8.85.10 33 . However, the "second Skewes number" is even larger and is 10 10 10 1000 .

Obviously, the more degrees in the number of degrees, the more difficult it is to write down numbers and understand their meaning when reading. Moreover, it is possible to come up with such numbers (and they, by the way, have already been invented), when the degrees of degrees simply do not fit on the page. Yes, what a page! They won't even fit in a book the size of the entire universe! In this case, the question arises how to write down such numbers. The problem is, fortunately, resolvable, and mathematicians have developed several principles for writing such numbers. True, each mathematician who asked this problem came up with his own way of writing, which led to the existence of several unrelated ways to write large numbers - these are the notations of Knuth, Conway, Steinhaus, etc. We will now have to deal with some of them.

Other notations

In 1938, the same year that nine-year-old Milton Sirotta came up with the googol and googolplex numbers, Hugo Dionizy Steinhaus, 1887-1972, a book about entertaining mathematics, The Mathematical Kaleidoscope, was published in Poland. This book became very popular, went through many editions and was translated into many languages, including English and Russian. In it, Steinhaus, discussing large numbers, offers a simple way to write them using three geometric figures- triangle, square and circle:

"n in a triangle" means " n n»,
« n square" means " n in n triangles",
« n in a circle" means " n in n squares."

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

Having determined the number "mega", Steinhaus invites readers to independently evaluate another number - "medzon", equal to 3 in a circle. In another edition of the book, Steinhaus instead of the medzone proposes to estimate an even larger number - “megiston”, equal to 10 in a circle. Following Steinhaus, I will also recommend that readers take a break from this text for a while and try to write these numbers themselves using ordinary powers in order to feel their gigantic magnitude.

However, there are names for about higher numbers. So, the Canadian mathematician Leo Moser (Leo Moser, 1921-1970) finalized the Steinhaus notation, which was limited by the fact that if it were necessary to write down numbers much larger than a megiston, then difficulties and inconveniences would arise, since one would have to draw many circles one inside another. 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:

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

Thus, according to Moser's notation, the Steinhausian "mega" is written as 2, "medzon" as 3, and "megiston" as 10. In addition, Leo Moser suggested calling a polygon with a 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 number or simply as "moser".

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

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

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

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

And finally

Having written this article, I can not resist the temptation and come up with my own number. Let this number be called stasplex» and will be equal to the number G 100 . Memorize it, and when your children ask what is the largest number in the world, tell them that this number is called stasplex.

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Countless different numbers surround us every day. Surely many people at least once wondered 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, one has only to add one to the number every time, and it will become more and more - this happens ad infinitum. But if you disassemble the numbers that have names, you can find out what the largest number in the world is called.

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

To date, 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 around the world. The American one allows you to give names to large numbers like this: first, the ordinal number in Latin is indicated, and then the suffix “million” 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 like this: the numeral in Latin is “plus” with the suffix “million”, and the next (a thousand times greater) number is “plus” “billion”. For example, a trillion comes first, followed by a trillion, a quadrillion follows a quadrillion, and so on.

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

Off-system numbers

In addition to numbers that are written according to known systems (given above), there are also off-system ones. They have their own names, which do not include Latin prefixes.

You can start their consideration 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 countless. Even Dahl's dictionary will kindly provide a definition of such a number.

Next after the myriad is the googol, denoting 10 to the power of 100. For the first time this name was used in 1938 by an American mathematician E. Kasner, who noted that his nephew came up with this name.

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

Even larger than the googolplex is the Skuses number (e to the power of e to the power of e79), proposed by Skuse when proving the Riemann conjecture about prime numbers(1933). There is another Skewes number, but it is used when the Rimmann hypothesis is unfair. Which of them is more difficult to say, especially when it comes to to a large extent. 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 conduct proofs in the field of mathematical science (1977).

When we are talking about 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 suggested using the up arrows. So we learned what the largest number in the world is called. It is worth noting that this number G got into the pages of the famous Book of Records.

Back in the fourth grade, I was interested in the question: "What are the numbers more than a billion called? And why?". Since then, I have been looking for all the information on this issue for a long time and collecting it bit by bit. But with the advent of access to the Internet, the search has accelerated significantly. Now I present all the information I found so that others can answer the question: "What are large and very large numbers called?".

A bit of history

The southern and eastern Slavic peoples used alphabetical numbering to record numbers. Moreover, among the Russians, not all letters played the role of numbers, but only those that are in the Greek alphabet. Above the letter, denoting a number, a special "titlo" icon was placed. At the same time, the numerical values ​​of the letters increased in the same order as the letters in the Greek alphabet followed (the order of the letters Slavic alphabet was somewhat different).

In Russia, Slavic numbering survived until the end of the 17th century. Under Peter I, the so-called "Arabic numbering" prevailed, which we still use today.

There were also changes in the names of the numbers. For example, until the 15th century, the number "twenty" was designated as "two ten" (two tens), but then it was reduced for faster pronunciation. Until the 15th century, the number "forty" was denoted by the word "fourty", and in the 15-16th centuries this word was supplanted by the word "forty", which originally meant a bag in which 40 squirrel or sable skins were placed. There are two options about the origin of the word "thousand": from the old name "fat hundred" or from a modification of the Latin word centum - "one hundred".

The name "million" first appeared in Italy in 1500 and was formed by adding an augmentative suffix to the number "mille" - a thousand (i.e. it meant "big thousand"), it penetrated into the Russian language later, and before that the same meaning in Russian was denoted by the number "leodr". The word "billion" came into use only from the time of the Franco-Prussian war (1871), when the French had to pay Germany an indemnity of 5,000,000,000 francs. Like "million", the word "billion" comes from the root "thousand" with the addition of an Italian magnifying suffix. In Germany and America, for some time, the word "billion" meant the number 100,000,000; this explains why the word billionaire was used in America before any of the rich had $1,000,000,000. In the old (XVIII century) "Arithmetic" of Magnitsky, there is a table of names of numbers, brought to the "quadrillion" (10 ^ 24, according to the system through 6 digits). Perelman Ya.I. in the book "Entertaining Arithmetic" the names of large numbers of that time are given, somewhat 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".

Principles of naming and the list of large numbers

All the names of large numbers are built in a rather simple way: 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 thousand (mille) and the magnifying suffix -million. There are two main types of names for large numbers in the world:
3x+3 system (where x is a Latin ordinal number) - this system is used in Russia, France, USA, Canada, Italy, Turkey, Brazil, Greece
and the 6x system (where x is a Latin ordinal number) - this system is the most common in the world (for example: Spain, Germany, Hungary, Portugal, Poland, Czech Republic, Sweden, Denmark, Finland). In it, the missing intermediate 6x + 3 ends with the suffix -billion (from it we borrowed a billion, which is also called a billion).

The general list of numbers used in Russia is presented below:

...
• 10 100 - googol (the number was invented by the 9-year-old nephew of the American mathematician Edward Kasner)
• 10 123 - quadragintillion (quadragaginta, XL)
• 10 153 - quinquagintillion (quinquaginta, L)
• 10 183 - sexagintillion (sexaginta, LX)
• 10 213 - septuagintillion (septuaginta, LXX)
• 10 243 - octogintillion (octoginta, LXXX)
• 10 273 - nonagintillion (nonaginta, XC)
• 10 303 - centillion (Centum, C)

Further names may be obtained either directly or reverse order Latin numerals (as it is not known correctly):

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

I believe that the second spelling will be the most correct, since it is more consistent with the construction of numerals in Latin and allows you to avoid ambiguities (for example, in the number trecentillion, which, according to the first spelling, is also 10 903 and 10312).