Many people are interested in questions about what large numbers are called and what number is the largest in the world. With these interesting questions and we will look into this 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
| Number | Latin numeral | Name | Practical significance | |
| 10 1 | 10 | ten | Number of fingers on 2 hands | |
| 10 2 | 100 | one hundred | About half the number of all states on Earth | |
| 10 3 | 1000 | thousand | Approximate number of days in 3 years | |
| 10 6 | 1000 000 | unus (I) | million | 5 times more than the number of drops per 10 liter. bucket of water |
| 10 9 | 1000 000 000 | duo (II) | billion (billion) | Estimated Population of India |
| 10 12 | 1000 000 000 000 | tres (III) | trillion | |
| 10 15 | 1000 000 000 000 000 | quattor (IV) | quadrillion | 1/30 of the length of a parsec in meters |
| 10 18 | quinque (V) | quintillion | 1/18th of the number of grains from the legendary award to the inventor of chess | |
| 10 21 | sex (VI) | sextillion | 1/6 of the mass of planet Earth in tons | |
| 10 24 | septem (VII) | septillion | Number of molecules in 37.2 liters of air | |
| 10 27 | octo (VIII) | octillion | Half of Jupiter's mass in kilograms | |
| 10 30 | novem (IX) | quintillion | 1/5 of all microorganisms on the planet | |
| 10 33 | decem (X) | decillion | Half the mass of the Sun in grams | |
- Vigintillion (from 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
| Number | Latin numeral | Name | Practical significance |
| 10 36 | undecim (XI) | andecillion | |
| 10 39 | duodecim (XII) | duodecillion | |
| 10 42 | tredecim (XIII) | thredecillion | 1/100 of the number of air molecules on Earth |
| 10 45 | quattuordecim (XIV) | quattordecillion | |
| 10 48 | quindecim (XV) | quindecillion | |
| 10 51 | sedecim (XVI) | sexdecillion | |
| 10 54 | septendecim (XVII) | septemdecillion | |
| 10 57 | octodecillion | So many elementary particles on the Sun | |
| 10 60 | novemdecillion | ||
| 10 63 | viginti (XX) | vigintillion | |
| 10 66 | unus et viginti (XXI) | anvigintillion | |
| 10 69 | duo et viginti (XXII) | duovigintillion | |
| 10 72 | tres et viginti (XXIII) | trevigintillion | |
| 10 75 | quattorvigintillion | ||
| 10 78 | quinvigintillion | ||
| 10 81 | sexvigintillion | So many elementary particles in the universe | |
| 10 84 | septemvigintillion | ||
| 10 87 | octovigintillion | ||
| 10 90 | novemvigintillion | ||
| 10 93 | triginta (XXX) | trigintillion | |
| 10 96 | antigintillion |
- 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 — quinquemillillion
- 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.
As a child, I was tormented by the question of what the most big number, and I tormented almost everyone with this stupid question. Having learned the number one million, I asked if there was a number greater than a million. Billion? A 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.
| Number | Latin name | Russian prefix |
| 1 | unus | an- |
| 2 | duo | duo- |
| 3 | tres | three- |
| 4 | quattuor | quadri- |
| 5 | quinque | quinti- |
| 6 | sex | sexty |
| 7 | septem | septi- |
| 8 | octo | octi- |
| 9 | novem | noni- |
| 10 | decem | deci- |
There are two systems for naming numbers - American and English.
The American system is built quite simply. All names of large numbers are 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:
| Name | Number |
| Unit | 10 0 |
| Ten | 10 1 |
| One hundred | 10 2 |
| Thousand | 10 3 |
| Million | 10 6 |
| Billion | 10 9 |
| Trillion | 10 12 |
| Quadrillion | 10 15 |
| Quintillion | 10 18 |
| Sextillion | 10 21 |
| Septillion | 10 24 |
| Octillion | 10 27 |
| Quintillion | 10 30 |
| Decillion | 10 33 |
And 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.
| Name | Number |
| Myriad | 10 4 |
| 10 100 | |
| Asankheya | 10 140 |
| Googolplex | 10 10 100 |
| Second Skewes number | 10 10 10 1000 |
| Mega | 2 (in Moser notation) |
| Megiston | 10 (in Moser notation) |
| Moser | 2 (in Moser notation) |
| Graham number | G 63 (in Graham notation) |
| Stasplex | G 100 (in Graham notation) |
The smallest such number is myriad(it is even in Dahl’s dictionary), which means a hundred 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 trademark, 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.
- 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.
- 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). - 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 - 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".
- 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 -
It is known that an infinite number of numbers and only a few have their own names, because most numbers received names consisting of small numbers. The largest numbers need to be designated somehow.
"Short" and "long" scale
Number names used today began to receive in the fifteenth century, then the Italians first used the word million, meaning “large thousand,” bimillion (million squared) and trimillion (million cubed).
This system was described in his monograph by the Frenchman Nicolas Chuquet, he recommended using Latin numerals, adding the inflection “-million” to them, so bimillion became billion, and three million became trillion, and so on.
But according to the proposed system, he called the numbers between a million and a billion “a thousand millions.” It was not comfortable to work with such a gradation and in 1549 by the Frenchman Jacques Peletier advised to name the numbers located in the indicated interval, again using Latin prefixes, while introducing a different ending - “-billion”.
So 109 was called billion, 1015 - billiard, 1021 - trillion.
Gradually this system began to be used in Europe. But some scientists confused the names of the numbers, this created a paradox when the words billion and billion became synonymous. Subsequently, the United States created its own procedure for naming large numbers. According to him, the construction of names is carried out in a similar way, but only the numbers differ.
The previous system continued to be used in Great Britain, which is why it was called British, although it was originally created by the French. But already in 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 used, 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 denote numbers larger than a decillion, scientists decided to combine several Latin prefixes, so undecillion, quattordecillion and others were named. If you use Schuke system, then, according to it, giant numbers will receive the names “vigintillion”, “centillion” and “million” (103003), respectively, according to the long scale, such a number will receive the name “billion” (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, and numbers over a million.
IN Ancient Rus' its own numerical system has been used for a long time. Hundreds of thousands were designated by the word legion, a million were called leodromes, tens of millions were ravens, hundreds of millions were called a deck. This was the “small count,” but the “great count” used the same words, only they had a different meaning, for example, leodr could mean a legion of legions (1024), and a deck could mean ten ravens (1096).
It happened that children came up with names for numbers, so the mathematician Edward Kasner gave the idea young Milton Sirotta, who proposed to name the number with a hundred zeros (10100) simply "googol". This number received the greatest publicity in the nineties of the twentieth century, when the Google search engine was named in its honor. The boy also suggested the name “googloplex,” a number with a googol of zeros.
But Claude Shannon in the middle of the twentieth century, evaluating moves in a chess game, calculated that there were 10,118 of them, now this "Shannon number".
In the ancient work of Buddhists "Jaina Sutras", written almost twenty-two centuries ago, notes the number “asankheya” (10140), which is exactly how many cosmic cycles, according to Buddhists, are necessary to achieve nirvana.
Stanley Skuse described large quantities as "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 record it in writing, and even in reading, error databases. Some numbers cannot be contained on several 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 Steinhaus and Knuth notations.
However, the largest number, the “Graham number,” was used Ronald Graham in 1977 when performing mathematical calculations, and this is the number G64.
“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
We continue ours. Today we have numbers...
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 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, 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, 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 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.
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 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 asankheya (from Chinese. 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 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, 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 - 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 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:
- G1 = 3..3, where the number of superpower arrows is 33.
- G2 = ..3, where the number of superpower arrows is equal to G1.
- G3 = ..3, where the number of superpower arrows is equal to G2.
- G63 = ..3, where the number of superpower arrows is G62.
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. And here
In the names of Arabic numbers, each digit belongs to its own category, and every three digits form a class. Thus, the last digit in a number indicates the number of units in it and is called, accordingly, the ones place. The next, second from the end, digit indicates the tens (tens place), and the third from the end digit indicates the number of hundreds in the number - the hundreds place. Further, the digits are repeated in the same way in turn in each class, already denoting units, tens and hundreds in the classes of thousands, millions, and so on. If the number is small and does not have a tens or hundreds digit, it is customary to take them as zero. Classes group digits in numbers of three, often placing a period or space between classes in computing devices or records to visually separate them. This is done to make large numbers easier to read. Each class has its own name: the first three digits are the class of units, followed by the class of thousands, then millions, billions (or billions), and so on.
Since we use the decimal system, the basic unit of quantity is ten, or 10 1. Accordingly, as the number of digits in a number increases, the number of tens also increases: 10 2, 10 3, 10 4, etc. Knowing the number of tens, you can easily determine the class and rank of the number, for example, 10 16 is tens of quadrillions, and 3 × 10 16 is three tens of quadrillions. The decomposition of numbers into decimal components occurs in the following way - each digit is displayed in a separate term, multiplied by the required coefficient 10 n, where n is the position of the digit from left to right.
For example: 253 981=2×10 6 +5×10 5 +3×10 4 +9×10 3 +8×10 2 +1×10 1
The power of 10 is also used in writing decimal fractions: 10 (-1) is 0.1 or one tenth. In a similar way to the previous paragraph, you can also expand a decimal number, n in this case will indicate the position of the digit from the decimal point from right to left, for example: 0.347629= 3×10 (-1) +4×10 (-2) +7×10 (-3) +6×10 (-4) +2×10 (-5) +9×10 (-6 )
Names of decimal numbers. Decimal numbers are read by the last digit after the decimal point, for example 0.325 - three hundred twenty-five thousandths, where the thousandth is the place of the last digit 5.
Table of names of large numbers, digits and classes
| 1st class unit | 1st digit of the unit 2nd digit tens 3rd place hundreds |
1 = 10 0 10 = 10 1 100 = 10 2 |
| 2nd class thousand | 1st digit of unit of thousands 2nd digit tens of thousands 3rd category hundreds of thousands |
1 000 = 10 3 10 000 = 10 4 100 000 = 10 5 |
| 3rd class millions | 1st digit of unit of millions 2nd category tens of millions 3rd category hundreds of millions |
1 000 000 = 10 6 10 000 000 = 10 7 100 000 000 = 10 8 |
| 4th class billions | 1st digit of unit of billions 2nd category tens of billions 3rd category hundreds of billions |
1 000 000 000 = 10 9 10 000 000 000 = 10 10 100 000 000 000 = 10 11 |
| 5th grade trillions | 1st digit unit of trillions 2nd category tens of trillions 3rd category hundreds of trillions |
1 000 000 000 000 = 10 12 10 000 000 000 000 = 10 13 100 000 000 000 000 = 10 14 |
| 6th grade quadrillions | 1st digit unit of quadrillion 2nd rank tens of quadrillions 3rd digit tens of quadrillions |
1 000 000 000 000 000 = 10 15 10 000 000 000 000 000 = 10 16 100 000 000 000 000 000 = 10 17 |
| 7th grade quintillions | 1st digit of quintillion unit 2nd category tens of quintillions 3rd digit hundred quintillion |
1 000 000 000 000 000 000 = 10 18 10 000 000 000 000 000 000 = 10 19 100 000 000 000 000 000 000 = 10 20 |
| 8th grade sextillions | 1st digit of the sextillion unit 2nd rank tens of sextillions 3rd rank hundred sextillion |
1 000 000 000 000 000 000 000 = 10 21 10 000 000 000 000 000 000 000 = 10 22 1 00 000 000 000 000 000 000 000 = 10 23 |
| 9th grade septillions | 1st digit of septillion unit 2nd category tens of septillions 3rd digit hundred septillion |
1 000 000 000 000 000 000 000 000 = 10 24 10 000 000 000 000 000 000 000 000 = 10 25 100 000 000 000 000 000 000 000 000 = 10 26 |
| 10th grade octillion | 1st digit of the octillion unit 2nd digit tens of octillions 3rd digit hundred octillion |
1 000 000 000 000 000 000 000 000 000 = 10 27 10 000 000 000 000 000 000 000 000 000 = 10 28 100 000 000 000 000 000 000 000 000 000 = 10 29 |
