Countless different numbers surrounds 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 most big number in the world.
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 by 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 he who was used for the first time to conduct evidence in the field mathematical science(1977).
When we're talking about 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 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.
It is impossible to answer this question correctly, because number series doesn't have upper limit. So, to any number you just need to add one to get an even larger number. Although the numbers themselves are infinite, proper names they don't have much, since most of them are content with names made up of smaller numbers. So, for example, numbers have their own names “one” and “one hundred”, and the name of the number is already compound (“one hundred and one”). It is clear that in the finite set of numbers that humanity has awarded own name, there must be some largest number. But what is it called and what does it equal? Let's try to figure this out and at the same time find out how big numbers invented by mathematicians.
"Short" and "long" scale
Story 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 - large 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 (ca. 1450 - ca. 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, “bimillion” for Schuke turned into a billion, “trimillion” became a trillion, and a million to the fourth power became “quadrillion”.
In the Chuquet system, a number between a million and a billion did not have its own name and was simply called “a thousand millions”, similarly called “a thousand billion”, “a thousand trillion”, etc. This was not very convenient, and in 1549 the French writer and scientist Jacques Peletier du Mans (1517–1582) proposed naming such “intermediate” numbers using the same Latin prefixes, but with the ending “-billion”. So, it began to be called “billion”, - “billiard”, - “trillion”, etc.
The Chuquet-Peletier system gradually became popular and was used throughout Europe. However, in the 17th century there arose unexpected problem. It turned out that for some reason some scientists began to get confused and call the number not “billion” or “thousand millions”, but “billion”. Soon this error quickly spread, and a paradoxical situation arose - “billion” became simultaneously synonymous with “billion” () and “million millions” ().
This confusion continued for quite a long time and led to the fact that the United States created its own system for naming large numbers. According to the American system, the names of numbers are constructed in the same way as in the Schuquet system - the Latin prefix and the ending “million”. However, the magnitudes of these numbers are different. If in the Schuquet system names with the ending “illion” received numbers that were powers of a million, then in the American system the ending “-illion” received powers of a thousand. That is, a thousand million () began to be called a “billion”, () - a “trillion”, () - a “quadrillion”, etc.
The old system of naming large numbers continued to be used in conservative Great Britain and began to be called “British” throughout the world, despite the fact that it was invented by the French Chuquet 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".
To avoid confusion, let's summarize:
| Number name | Short scale value | Long scale value |
| Million | ||
| Billion | ||
| Billion | ||
| Billiards | - | |
| Trillion | ||
| trillion | - | |
| Quadrillion | ||
| Quadrillion | - | |
| Quintillion | ||
| Quintilliard | - | |
| Sextillion | ||
| Sextillion | - | |
| Septillion | ||
| Septilliard | - | |
| Octillion | ||
| Octilliard | - | |
| Quintillion | ||
| Nonilliard | - | |
| Decillion | ||
| Decilliard | - | |
| Vigintillion | ||
| Wigintilliard | - | |
| Centillion | ||
| Centilliard | - | |
| Million | ||
| Millebillion | - |
The short naming scale is currently used in the USA, UK, Canada, Ireland, Australia, Brazil and Puerto Rico. Russia, Denmark, Turkey and Bulgaria also use a short scale, except that the number is called “billion” rather than “billion.” The long scale continues to be used in most other countries.
It is curious that in our country the final transition to a short scale occurred only in the second half of the 20th century. For example, Yakov Isidorovich Perelman (1882–1942) in his “ Entertaining arithmetic» mentions parallel existence in the USSR there are two scales. 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 let's return to the search for the largest number. After decillion, the names of numbers are obtained by combining prefixes. This produces numbers such as undecillion, duodecillion, tredecillion, quattordecillion, quindecillion, sexdecillion, septemdecillion, octodecillion, novemdecillion, etc. However, these names are no longer interesting to us, since we agreed to find the largest number with its own non-composite name.
If we turn to Latin grammar, we find that the Romans had only three non-compound names for numbers greater than ten: viginti - “twenty”, centum - “hundred” and mille - “thousand”. The Romans did not have their own names for numbers greater than a thousand. For example, a million () The Romans called it "decies centena milia", that is, "ten times a hundred thousand." According to Chuquet's rule, these three remaining Latin numerals give us such names for numbers as "vigintillion", "centillion" and "millillion".
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- this is “million” (). If Russia adopted a “long scale” for naming numbers, then the largest number with its own name would be “billion” ().
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, recall the number e, the number “pi”, dozen, the number of the beast, etc. However, since we are now interested in large numbers, we will consider only those numbers with their own non-composite name that more than a million.
Until the 17th century in Rus' it was used own system names of numbers. Tens of thousands were called "darkness", hundreds of thousands were called "legions", millions were called "leoders", tens of millions were called "ravens", and hundreds of millions were called "decks". This count of up to hundreds of millions was called the “small count,” and in some manuscripts the authors considered “ great score”, in which the same names were used for large numbers, but with a different meaning. So, “darkness” no longer meant ten thousand, but a thousand thousand () , “legion” - the darkness of those () ; "leodr" - legion of legions () , "raven" - leodr leodrov (). For some reason, “deck” in the great Slavic counting was not called “raven of ravens” () , but only ten “ravens”, that is (see table).
| Number name | Meaning in "small count" | Meaning in the "great count" | Designation |
| Dark | |||
| Legion | |||
| Leodre | |||
| Raven (corvid) | |||
| Deck | |||
| Darkness of topics |  |
The number also has its own name and was invented by a nine-year-old boy. And it was like this. In 1938, American mathematician 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 a hundred zeros, which did not have its own name. One of the nephews, nine-year-old Milton Sirott, suggested calling this number “googol.” In 1940, Edward Kasner, together with James Newman, wrote the popular science book “Mathematics and the Imagination,” where he told mathematics lovers about the googol number. Googol 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 originated in 1950 thanks to the father of computer science, Claude Elwood Shannon (1916–2001). In his article "Programming a Computer to Play Chess" he tried to estimate the number possible options chess game. According to it, each game lasts on average of moves and on each move the player makes a choice on average from the options, which corresponds to (approximately equal to) the 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 . It is believed that this number is equal to the number of cosmic cycles required to achieve nirvana.
Nine-year-old Milton Sirotta went down in the history of mathematics not only because he came up with the number googol, but also because at the same time he proposed another number - the “googolplex”, which is equal 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) in his proof of the Riemann hypothesis. The first number, which later became known as the "Skuse number", is equal to the power to the power to the power of , that is, . However, the “second Skewes number” is even larger and amounts to .
Obviously, the more powers there are in the powers, the more difficult it is to write the numbers and understand their meaning when reading. Moreover, it is possible to come up with such numbers (and, by the way, 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 even fit into a book the size of the entire Universe! In this case, the question arises of how to write such numbers. The problem, fortunately, 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 methods for writing large numbers - these are the notations of Knuth, Conway, Steinhaus, etc. We now have to deal with some of them.
Other notations
In 1938, the same year that nine-year-old Milton Sirotta invented the numbers googol and googolplex, a book about entertaining mathematics « Math kaleidoscope", written by Hugo Dionizy Steinhaus, 1887–1972. 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 - a triangle, a square and a circle:
"in a triangle" means "",
"squared" means "in triangles"
"in a circle" means "in squares".
Explaining this method of notation, Steinhaus comes up with the number “mega”, which is equal in a circle and shows that it is equal in a “square” or in triangles. To calculate it, you need to raise it to the power of , raise the resulting number to the power of , then raise the resulting number to the power of the resulting number, and so on, raise it to the power of times. For example, a calculator in MS Windows cannot calculate due to overflow even in two triangles. This huge number is approximately .
Having determined the “mega” number, Steinhaus invites readers to independently estimate another number - “medzon”, equal in a circle. In another edition of the book, Steinhaus, instead of the medzone, suggests estimating an even larger number - “megiston”, equal in a circle. Following Steinhaus, I also recommend that readers break away 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 large numbers. Thus, the Canadian mathematician Leo Moser (Leo Moser, 1921–1970) modified the Steinhaus notation, which was limited by the fact that if it were necessary to write numbers much larger than megiston, then difficulties and inconveniences would arise, since it would be necessary to draw many circles one inside another. 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 drawings. Moser notation looks like this:
"triangle" = = ;
"squared" = = "triangles" = ;
"in a pentagon" = = "in squares" = ;
"in -gon" = = "in -gon" = .
Thus, according to Moser’s notation, Steinhaus’s “mega” is written as , “medzone” as , and “megiston” as . In addition, Leo Moser proposed calling a polygon with the number of sides equal to mega - “megagon”. And suggested a number « in megagon", that is. This number became known as the Moser number or simply "Moser".
But even “Moser” is not the largest number. So, the largest number ever used in mathematical proof, is the "Graham number". This number was first used by the American mathematician Ronald Graham in 1977 when proving one estimate in Ramsey theory, namely when calculating the dimension of certain -dimensional bichromatic hypercubes. Graham's number became famous only after it was described in Martin Gardner's 1989 book, From Penrose Mosaics to Reliable Ciphers.
To explain how large Graham's number is, we have to explain another way of writing large numbers, introduced by Donald Knuth in 1976. American professor Donald Knuth came up with the concept of superpower, which he proposed to write with arrows pointing upward.
Regular arithmetic operations- addition, multiplication and exponentiation can naturally be expanded into a sequence of hyperoperators as follows.
Multiplication natural numbers can be defined through a repeated addition operation (“add copies of a number”):
For example,
Raising a number to a power can be defined as a repeated multiplication operation ("multiplying copies of a number"), and in Knuth's notation this notation looks like a single arrow pointing up:
For example,
This single up arrow was used as the degree icon in the Algol programming language.
For example,
Here and below, the expression is always evaluated from right to left, and Knuth's arrow operators (as well as the operation of exponentiation) by definition have right associativity (order from right to left). According to this definition,
This already leads to quite large numbers, but the notation system does not end there. The triple arrow operator is used to write the repeated exponentiation of the double arrow operator (also known as pentation):
Then the “quad arrow” operator:
Etc. General rule operator "-I arrow", in accordance with right associativity, continues to the right in a sequential series of operators « arrow." Symbolically, this can be written as follows,
For example:
The notation form is usually used for notation with arrows.
Some numbers are so large that even writing with Knuth's arrows becomes too cumbersome; in this case, the use of the -arrow operator is preferable (and also for descriptions with a variable number of arrows), or is equivalent to hyperoperators. But some numbers are so huge that even such a notation is insufficient. For example, Graham's number.
Using Knuth's Arrow notation, the Graham number can be written as
Where the number of arrows in each layer, starting from the top, is determined by the number in the next layer, that is, where , where the superscript of the arrow indicates the total number of arrows. In other words, it is calculated in steps: in the first step we calculate with four arrows between threes, in the second - with arrows between threes, in the third - with arrows between threes, and so on; at the end we calculate with the arrows between the triplets.
This can be written as , where , where the superscript y denotes function iterations.
If other numbers with “names” can be matched corresponding number objects (for example, the number of stars in the visible part of the Universe is estimated at sextillions - , and the number of atoms that make up Earth has the order of dodecalions), then the googol is already “virtual”, not to mention the Graham number. The scale of the first term alone is so large that it is almost impossible to comprehend, although the notation above is relatively easy to understand. Although this is just the number of towers in this formula for , this number is already a lot more quantity Planck volumes (the smallest possible physical volume) contained in the observable universe (approximately ). After the first member, we are expecting another member of the rapidly growing sequence.
The question “What is the largest number in the world?” is, to say the least, incorrect. There are both various systems calculus - decimal, binary and hexadecimal, and various categories of numbers - semi-prime and simple, the latter being divided into legal and illegal. In addition, there are Skewes numbers, Steinhouse and other mathematicians who, either as a joke or seriously, invent and present to the public such exotics as “Megiston” or “Moser”.
What is the largest number in the world in decimal system
Of the decimal system, most “non-mathematicians” are familiar with million, billion and trillion. Moreover, if Russians generally associate a million with a dollar bribe that can be carried away in a suitcase, then where to stuff a billion (not to mention a trillion) North American banknotes - most people lack imagination. However, in the theory of large numbers there are such concepts as quadrillion (ten to the fifteenth power - 1015), sextillion (1021) and octillion (1027).
In English, the most widely spoken in the world decimal system The maximum number is considered to be a decillion - 1033.
In 1938, in connection with the development of applied mathematics and the expansion of the micro- and macrocosm, professor at Columbia University (USA), Edward Kasner published in the pages of the journal Scripta Mathematica his nine-year-old nephew’s proposal to use the decimal system as the most the large number "googol" - representing ten to the hundredth power (10100), which on paper is expressed as one followed by one hundred zeros. However, they did not stop there and a few years later proposed introducing a new largest number in the world - the “googolplex”, which represents ten raised to the tenth power and again raised to the hundredth power - (1010)100, expressed by a unit, to which a googol of zeros is assigned to the right. However, for the majority even professional mathematicians both “googol” and “googolplex” are of purely speculative interest, and are unlikely to everyday practice they can be applied to anything.
Exotic numbers
What is the largest number in the world among prime numbers– those that can only be divided into themselves and one. One of the first to record the largest prime number, equal to 2,147,483,647, was great mathematician Leonard Euler. As of January 2016, this number is recognized as the expression calculated as 274,207,281 – 1.
“I see clusters of vague numbers that are hidden there in the darkness, behind the small spot of light that the candle of reason gives. They whisper to each other; conspiring about who knows what. Perhaps they don't like us very much for capturing their little brothers in our minds. Or perhaps they simply lead a single-digit life, out there, beyond our understanding.
Douglas Ray
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.
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 is absolutely 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.
From English system Only the number billion (10 9) has passed 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 possible, of course, by combining prefixes to generate such monsters as: andecillion, duodecillion, tredecillion, quattordecillion, quindecillion, sexdecillion, septemdecillion, octodecillion and novemdecillion, but these will already be compound names, and we were interested in the proper names of the 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, numbers are greater than 10 3003 , which would have its own, non-compound name is impossible to obtain! 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, doesn't mean at all a certain number, but an uncountable, uncountable set of something. It is believed that the word myriad came from European languages from ancient Egypt.
Regarding the origin of this number, there are different opinions. Some believe that it originated in Egypt, while others believe that it was born only in Ancient Greece. Be that as it may in fact, the myriad gained fame precisely thanks to the Greeks. Myriad was the name for 10,000, 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 Earth diameters) there would fit (in our notation) 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
(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.
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.
Edward Kasner.
On the Internet you can often find it mentioned that - but this is not true...
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 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 the before 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 - Skewes number (Skewes" number) was proposed by Skewes in 1933 (Skewes. 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, ee 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 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, 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). Second Skewes number, was introduced by J. Skuse in the same article to denote a number for which the Riemann hypothesis does not hold. Sk2 equals 1010 10103 , that is 1010 101000 .
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 asked 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 that:
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 view 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 G63 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 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 are there numbers greater than Graham's number? There is, of course, for starters there is Graham's number. Concerning significant number...okay, there are some fiendishly complex areas of mathematics (specifically 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 rationally and clearly explained.
John SommerPlace zeros after any number or multiply with tens raised to any number you like greater degree. It won't seem enough. It will seem like a lot. But the bare records are still not very impressive. The piling up of zeros in the humanities causes 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 larger.
And yet, are there words in Russian or any other language to denote very large numbers? Those that are more than a million, a billion, a trillion, a 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 like this: take the Latin numeral + - illion (suffix). This gives the numbers:
Trillion - 1,000,000,000,000 (12 zeros)
Quadrillion - 1,000,000,000,000,000 (15 zeros)
Quintillion - 1 followed by 18 zeros
Sextillion - 1 and 21 zeros
Septillion - 1 and 24 zeros
octillion - 1 followed by 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 numbers anilion (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, the Latin numeral is taken and the suffix -million is added to it. However, the title next date, which is 1,000 times larger than the previous one, is formed using the same Latin number and the suffix - illiard. I mean:
Trillion - 1 and 21 zeros (in the American system - sextillion!)
Trillion - 1 and 24 zeros (in the American system - septillion)
Quadrillion - 1 and 27 zeros
Quadrillion - 1 followed by 30 zeros
Quintillion - 1 and 33 zeros
Quinilliard - 1 and 36 zeros
Sextillion - 1 and 39 zeros
Sextillion - 1 and 42 zeros
The formulas for counting the number of zeros are:
For numbers ending in - illion - 6 x+3
For numbers ending in - billion - 6 x+6
As you can see, confusion is possible. But let us not be afraid!
In Russia, the American system of naming numbers has been adopted. We borrowed the name of the number “billion” from the English system - 1,000,000,000 = 10 9
Where is the “cherished” billion? - But a billion is a billion! American style. And even though we use American system, and “billion” was taken from English.
Using the Latin names of numbers and the American system, we name the numbers:
- vigintillion- 1 and 63 zeros
- centillion- 1 and 303 zeros
- million- one and 3003 zeros! Oh-ho-ho...
But this, it turns out, is not all. There are also non-system numbers.
And the first of them is probably myriad- one hundred hundreds = 10,000
Google(the famous search engine is named after him) - one and one hundred zeros
In one of the Buddhist treatises the number is named asankheya- one and one hundred and forty zeros!
Number name googolplex(like googol) was invented by the English mathematician Edward Kasner and his nine-year-old nephew - unit c - dear mother! - googol zeros!!!
But that's not all...
The mathematician Skuse named the Skuse number after himself. It means e to a degree e to a degree e to the power of 79, that is e e e 79
And then a big 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 cannot be removed onto the page! :)
And then some mathematicians began to write numbers in geometric shapes. And they say he was the first to come up with this method of recording outstanding writer and thinker Daniil Ivanovich Kharms.
And yet, what is the BIGGEST NUMBER IN THE WORLD? - It’s called STASPLEX and is equal to G 100,
where G is Graham's number, the largest number ever used in mathematical proof.
This number - stasplex - was invented wonderful person, our compatriot Stas Kozlovsky, LJ to which I am directing you :) - ctac