It is known that numbers are infinite and only a few have their own names, because most of the numbers received names consisting of small numbers. The largest numbers need to be labeled in some way.
"Short" and "long" scale
Number names in use today began to receive in the fifteenth century, then the Italians first used the word million, meaning "big thousand", bimillion (million squared) and trillion (million cubed).
This system was described in his monograph by a Frenchman Nicolas Schuquet, he recommended using the numerals of the Latin language, adding the inflection "-million" to them, thus a bimillion became a billion, and a trillion became a trillion, and so on.
But according to the proposed system of numbers between a million and a billion, he called "a thousand million." It was not comfortable to work with such a gradation and in 1549 the Frenchman Jacques Peletier advised the numbers in the specified interval to be called again using Latin prefixes, while introducing another ending - "-billion".
So 109 got the name 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, in the United States, its own order of naming large numbers was created. According to him, the construction of names is carried out in the same way, but only the numbers differ.
The previous system continued to be applied in the UK, therefore 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, 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 greater than a decillion, scientists decided to combine several Latin prefixes, so the undecillion, quattordecillion and others were named. If you use the Schuecke system, then, according to her, gigantic numbers will acquire the names "Vigintillion", "Centillion" and "Million" (103003), respectively, according to the long scale, such a number will receive the name "Millionbillion" (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.
V Ancient Rus its own number system has long been used. Hundreds of thousands were denoted by the word legion, a million were called leodrome, tens of millions were crows, hundreds of millions were called a deck. It was "small count", but "great count" used the same words, but the meaning was different, for example, leodr could mean a legion of legions (1024), and a deck - already ten ravens (1096).
It happened that the names of the numbers were invented by children, so the mathematician Edward Kasner gave the idea young Milton Sirotta, who suggested giving a name to a number with a hundred zeros (10100) just Googol... This number received the greatest publicity in the nineties of the twentieth century, when the search engine Google was named in his honor. The boy also suggested the name "googlex", a number with googol zeros.
But Claude Shannon in the middle of the twentieth century, evaluating the moves in the chess game, calculated that there are 10118, now it is "Shannon's number".
In the ancient work of Buddhists Jaina Sutras, written almost twenty two centuries ago, the number "asankheya" (10140) is noted, this is how many cosmic cycles, according to Buddhists, are needed to find nirvana.
Stanley Skewes described large quantities as "The first Skewes number", equal to 10108.85.1033, and the "second Skewes number" is even more impressive and is equal to 1010101000.
Notations
Of course, depending on the number of degrees contained in the number, there is a problem in fixing it in writing, and reading, error bases. some numbers can't fit on multiple pages, so mathematicians have come up with notations for capturing large numbers.
It is worth considering that they are all different, each has its own principle of fixation. Among those it is worth mentioning notations of Steinghaus, Knut.
However, the largest number, the "Graham number", was used By Ronald Graham in 1977 when performing mathematical calculations, and this number is G64.
Even in the fourth grade, I was interested in the question: "What are the names of numbers over a billion? 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 Internet access, searches have accelerated significantly. Now I present all the information I have found so that others can also answer the question: "What are the names of large and very large numbers?"
A bit of history
The southern and eastern Slavic peoples used alphabetical numbering to write numbers. Moreover, among the Russians, not all letters played the role of numbers, but only those that are in the Greek alphabet. A special "titlo" icon was placed above the letter denoting the number. At the same time, the numerical values of the letters increased in the same order in which the letters in the Greek alphabet followed (the order of the letters in the Slavic alphabet was somewhat different).
In Russia, Slavic numbering was preserved 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 shortened for a faster pronunciation. Until the 15th century the number "forty" was denoted by the word "fourty", and in the 15th and 16th centuries this word was supplanted by the word "forty", which originally meant a sack containing 40 squirrel or sable skins. There are two variants of the origin of the word "thousand": from the old name "thick one hundred" or from the modification of the Latin word centum - "one hundred".
The name "million" first appeared in Italy in 1500 and was formed by adding an augmenting suffix to the number "millet" - a thousand (that is, it meant "a large thousand"), it penetrated into the Russian language later, and before that the same meaning in in Russian it was denoted by the number "leodr". The word "billion" came into use only since 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 augmentation suffix. In Germany and America for some time the word "billion" meant the number 100,000,000; this explains that the word billionaire was used in America before any of the wealthy had $ 1,000,000,000. In the old (XVIII century) "Arithmetic" of Magnitsky, a table of the names of numbers is given, brought to "quadrillion" (10 ^ 24, according to the system after 6 digits). Perelman Ya.I. in the book "Entertaining arithmetic" the names of large numbers of that time are given, somewhat different from those of today: septillion (10 ^ 42), octalion (10 ^ 48), nonalion (10 ^ 54), decallion (10 ^ 60), endecalion (10 ^ 66), dodecalion (10 ^ 72) and it is written that "there are no further names".
Naming Principles and List of Large Numbers
All the names of large numbers are constructed 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 augmenting 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 end 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:
| Number | Name | Latin numeral | Increasing prefix SI | Reducing prefix SI | Practical value |
| 10 1 | ten | deca | deci- | Number of fingers on 2 hands | |
| 10 2 | hundred | hecto- | centi- | About half the number of all states on Earth | |
| 10 3 | thousand | kilo | Milli- | Approximate number of days in 3 years | |
| 10 6 | million | unus (I) | mega- | micro- | 5 times the number of drops in a 10 liter bucket of water |
| 10 9 | billion (billion) | duo (II) | giga- | nano- | Approximate population of India |
| 10 12 | trillion | tres (III) | tera- | pico | 1/13 of the gross domestic product of Russia in rubles for 2003 |
| 10 15 | quadrillion | quattor (IV) | peta- | femto- | 1/30 parsec length in meters |
| 10 18 | quintillion | quinque (V) | ex- | atto- | 1/18 of the number of grains from the legendary chess inventor award |
| 10 21 | sextillion | sex (VI) | zetta- | chain | 1/6 the mass of the planet Earth in tons |
| 10 24 | septillion | septem (VII) | yotta- | yokto- | The number of molecules in 37.2 liters of air |
| 10 27 | octillion | octo (VIII) | no- | sieve- | Half the mass of Jupiter in kilograms |
| 10 30 | quintillion | novem (IX) | de- | thread- | 1/5 of all microorganisms on the planet |
| 10 33 | decillion | decem (X) | una- | roaring | Half the mass of the Sun in grams |
The pronunciation of the numbers below is often different.
| Number | Name | Latin numeral | Practical value |
| 10 36 | andecillion | undecim (XI) | |
| 10 39 | duodecillion | duodecim (XII) | |
| 10 42 | tredecillion | tredecim (XIII) | 1/100 of the number of air molecules on Earth |
| 10 45 | quattordecillion | quattuordecim (XIV) | |
| 10 48 | quindecillion | quindecim (XV) | |
| 10 51 | sexdecillion | sedecim (XVI) | |
| 10 54 | septemdecillion | septendecim (XVII) | |
| 10 57 | octodecillion | So many elementary particles in the sun | |
| 10 60 | novemdecillion | ||
| 10 63 | vigintillion | viginti (XX) | |
| 10 66 | anvigintillion | unus et viginti (XXI) | |
| 10 69 | duovigintillion | duo et viginti (XXII) | |
| 10 72 | trevigintillion | tres et viginti (XXIII) | |
| 10 75 | quattorvigintillion | ||
| 10 78 | quinvigintillion | ||
| 10 81 | sexvigintillion | So many elementary particles in the universe | |
| 10 84 | septemwigintillion | ||
| 10 87 | octovigintillion | ||
| 10 90 | novemvigintillion | ||
| 10 93 | trigintillion | triginta (XXX) | |
| 10 96 | antrigintillion |
- ...
- 10 100 - googol (the number was invented by the 9-year-old nephew of the American mathematician Edward Kasner)
- 10 123 - quadragintillion (quadraginta, XL)
- 10 153 - quinquaginta, L
- 10,183 - sexaginta (LX)
- 10 213 - septuaginta, LXX
- 10 243 - octogintillion (octoginta, LXXX)
- 10 273 - nonaginta, XC
- 10,303 - centillion (Centum, C)
- 10 306 - antcentillion or centunillion
- 10 309 - duocentillion or centduollion
- 10 312 - trecentillion or centtrillion
- 10 315 - quattorcentillion or centquadrillion
- 10 402 - tretrigintacentillion or centtretrigintillion
Numbers further:
Some literary references:
- Perelman Ya.I. "Entertaining arithmetic". - M .: Triada-Litera, 1994, pp. 134-140
- Vygodsky M. Ya. "Handbook of Elementary Mathematics". - S-Pb., 1994, pp. 64-65
- "Encyclopedia of Knowledge". - comp. IN AND. Korotkevich. - St. Petersburg: Owl, 2006, p. 257
- "Interesting about physics and mathematics." - Library Kvant. no. 50. - M .: Nauka, 1988, p. 50
In everyday life, most people operate on fairly small numbers. Tens, hundreds, thousands, very rarely millions, almost never billions. About such numbers are limited to the usual idea of a person about quantity or magnitude. Almost everyone has heard about trillions, but very few people have ever used them, in any calculations.
What are the giant numbers?
Meanwhile, numbers denoting degrees of a thousand have been known to people for a long time. In Russia and many other countries, a simple and logical notation system is used:
Thousand;
Million;
Billion;
Trillion;
Quadrillion;
Quintillion;
Sextillion;
Septillion;
Octillion;
Quintillion;
Decillion.
In this system, each next number is obtained by multiplying the previous one by a thousand. A billion is usually called a billion.
Many adults can accurately write numbers such as a million - 1,000,000 and a billion - 1,000,000,000. With a trillion it is already more difficult, but almost everyone will cope - 1,000,000,000,000. And then a territory unknown to many begins.
Getting to know the big numbers closer
However, there is nothing complicated, the main thing is to understand the system of formation of large numbers and the principle of naming. As already mentioned, each next number exceeds the previous one by a thousand times. This means that in order to correctly write the next number in ascending order, you need to add three more zeros to the previous one. That is, a million has 6 zeros, a billion has 9, a trillion has 12, a quadrillion has 15, and a quintillion has 18.
The names can also be dealt with if you wish. The word "million" comes from the Latin "mille", which means "more than a thousand." The following numbers were formed by adding the Latin words “bi” (two), “three” (three), “quadro” (four), etc.
Now let's try to visualize these numbers. Most people have a pretty good idea of the difference between a thousand and a million. Everyone understands that a million rubles is good, but a billion is more. Much more. Also, everyone has the idea that a trillion is something absolutely immense. But how much is a trillion more than a billion? How big is it?
For many more than a billion, the concept of "the mind is incomprehensible" begins. Indeed, a billion kilometers or a trillion is not a very big difference in the sense that such a distance still cannot be covered in a lifetime. A billion rubles or a trillion is also not very different, because such money still cannot be earned in a lifetime. But let's count a little by connecting imagination.
The housing stock of Russia and four football fields as examples
For every person on earth, there is a land area of 100x200 meters. These are about four football fields. But if there are not 7 billion people, but seven trillion, then everyone will get only a piece of land 4x5 meters. Four football fields against the front garden area in front of the entrance - this is the ratio of a billion to a trillion.
In absolute terms, the picture is also impressive.
If you take a trillion bricks, you can build more than 30 million one-story houses of 100 square meters. That is, about 3 billion square meters of private buildings. This is comparable to the total housing stock of the Russian Federation.
If you build ten-story houses, you will get about 2.5 million houses, that is, 100 million two-three-room apartments, about 7 billion square meters of housing. This is 2.5 times more than the total housing stock in Russia.
In short, there will not be a trillion bricks in all of Russia.
One quadrillion of student notebooks will cover the entire territory of Russia with a double layer. And one quintillion of the same notebooks will cover the entire land with a layer 40 centimeters thick. If we manage to get a sextillion of notebooks, then the entire planet, including the oceans, will be under a layer 100 meters thick.
Let's count to a decillion
Let's count some more. For example, a matchbox enlarged a thousand times would be the size of a sixteen-story building. An increase in a million times will give "boxes" that are larger in area than St. Petersburg. Enlarged a billion times, the box won't fit on our planet. On the contrary, the Earth will fit into such a "box" 25 times!
An increase in the box gives an increase in its volume. It will be almost impossible to imagine such volumes with further increase. For ease of perception, we will try to increase not the object itself, but its quantity, and arrange the matchboxes in space. This will make it easier to navigate. A quintillion of boxes lined up in a row would extend beyond the star α Centauri by 9 trillion kilometers.
Another thousandfold magnification (sextillion) will allow matchboxes lined up to screen our entire Milky Way galaxy laterally. A septillion matchbox would stretch over 50 quintillion kilometers. Light can travel such a distance in 5 million 260 thousand years. And the boxes laid out in two rows would stretch as far as the Andromeda galaxy.
There are only three numbers left: octillion, nonillion and decillion. You have to strain your imagination. An octillion of boxes forms a continuous line of 50 sextillion kilometers. It is over five billion light years. Not every telescope mounted on one edge of such an object could see its opposite edge.
Do we count further? A non-million matchboxes would fill the entire space of the part of the Universe known to mankind with an average density of 6 pieces per cubic meter. By earthly standards, it seems that there are not very many - 36 matchboxes in the back of a standard Gazelle. But a nonillion matchboxes will have a mass billions of times greater than the mass of all material objects in the known universe put together.
Decillion. The magnitude, or rather even the majesty of this giant from the world of numbers, is hard to imagine. Just one example - six decillion boxes would no longer fit in the entire part of the Universe accessible to mankind for observation.
Even more strikingly the majesty of this number is visible if you do not multiply the number of boxes, but increase the object itself. A matchbox, enlarged by a decillion, would contain the entire part of the Universe known to mankind 20 trillion times. It is impossible even to imagine something like that.
Small calculations showed how huge the numbers have been known to mankind for several centuries. In modern mathematics, numbers many times exceeding a decillion are known, but they are used only in complex mathematical calculations. Only professional mathematicians have to deal with such numbers.
The most famous (and smallest) of these numbers is the googol, denoted by one followed by one hundred zeros. Googol is greater than the total number of elementary particles in the visible part of the universe. This makes googol an abstract number that has little practical use.
Even in the fourth grade, I was interested in the question: "What are the names of numbers over a billion? 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 Internet access, searches have accelerated significantly. Now I present all the information I have found so that others can also answer the question: "What are the names of large and very large numbers?"
A bit of history
The southern and eastern Slavic peoples used alphabetical numbering to write numbers. Moreover, among the Russians, not all letters played the role of numbers, but only those that are in the Greek alphabet. A special "titlo" icon was placed above the letter denoting the number. At the same time, the numerical values of the letters increased in the same order in which the letters in the Greek alphabet followed (the order of the letters in the Slavic alphabet was somewhat different).
In Russia, Slavic numbering was preserved 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 shortened for a faster pronunciation. Until the 15th century the number "forty" was denoted by the word "fourty", and in the 15th and 16th centuries this word was supplanted by the word "forty", which originally meant a sack containing 40 squirrel or sable skins. There are two variants of the origin of the word "thousand": from the old name "thick one hundred" or from the modification of the Latin word centum - "one hundred".
The name "million" first appeared in Italy in 1500 and was formed by adding an augmenting suffix to the number "millet" - a thousand (that is, it meant "a large thousand"), it penetrated into the Russian language later, and before that the same meaning in in Russian it was denoted by the number "leodr". The word "billion" came into use only since 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 augmentation suffix. In Germany and America for some time the word "billion" meant the number 100,000,000; this explains that the word billionaire was used in America before any of the wealthy had $ 1,000,000,000. In the old (XVIII century) "Arithmetic" of Magnitsky, a table of the names of numbers is given, brought to "quadrillion" (10 ^ 24, according to the system after 6 digits). Perelman Ya.I. in the book "Entertaining arithmetic" the names of large numbers of that time are given, somewhat different from those of today: septillion (10 ^ 42), octalion (10 ^ 48), nonalion (10 ^ 54), decallion (10 ^ 60), endecalion (10 ^ 66), dodecalion (10 ^ 72) and it is written that "there are no further names".
Naming Principles and List of Large Numbers
All the names of large numbers are constructed 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 augmenting 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 end 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:
| Number | Name | Latin numeral | Increasing prefix SI | Reducing prefix SI | Practical value |
| 10 1 | ten | deca | deci- | Number of fingers on 2 hands | |
| 10 2 | hundred | hecto- | centi- | About half the number of all states on Earth | |
| 10 3 | thousand | kilo | Milli- | Approximate number of days in 3 years | |
| 10 6 | million | unus (I) | mega- | micro- | 5 times the number of drops in a 10 liter bucket of water |
| 10 9 | billion (billion) | duo (II) | giga- | nano- | Approximate population of India |
| 10 12 | trillion | tres (III) | tera- | pico | 1/13 of the gross domestic product of Russia in rubles for 2003 |
| 10 15 | quadrillion | quattor (IV) | peta- | femto- | 1/30 parsec length in meters |
| 10 18 | quintillion | quinque (V) | ex- | atto- | 1/18 of the number of grains from the legendary chess inventor award |
| 10 21 | sextillion | sex (VI) | zetta- | chain | 1/6 the mass of the planet Earth in tons |
| 10 24 | septillion | septem (VII) | yotta- | yokto- | The number of molecules in 37.2 liters of air |
| 10 27 | octillion | octo (VIII) | no- | sieve- | Half the mass of Jupiter in kilograms |
| 10 30 | quintillion | novem (IX) | de- | thread- | 1/5 of all microorganisms on the planet |
| 10 33 | decillion | decem (X) | una- | roaring | Half the mass of the Sun in grams |
The pronunciation of the numbers below is often different.
| Number | Name | Latin numeral | Practical value |
| 10 36 | andecillion | undecim (XI) | |
| 10 39 | duodecillion | duodecim (XII) | |
| 10 42 | tredecillion | tredecim (XIII) | 1/100 of the number of air molecules on Earth |
| 10 45 | quattordecillion | quattuordecim (XIV) | |
| 10 48 | quindecillion | quindecim (XV) | |
| 10 51 | sexdecillion | sedecim (XVI) | |
| 10 54 | septemdecillion | septendecim (XVII) | |
| 10 57 | octodecillion | So many elementary particles in the sun | |
| 10 60 | novemdecillion | ||
| 10 63 | vigintillion | viginti (XX) | |
| 10 66 | anvigintillion | unus et viginti (XXI) | |
| 10 69 | duovigintillion | duo et viginti (XXII) | |
| 10 72 | trevigintillion | tres et viginti (XXIII) | |
| 10 75 | quattorvigintillion | ||
| 10 78 | quinvigintillion | ||
| 10 81 | sexvigintillion | So many elementary particles in the universe | |
| 10 84 | septemwigintillion | ||
| 10 87 | octovigintillion | ||
| 10 90 | novemvigintillion | ||
| 10 93 | trigintillion | triginta (XXX) | |
| 10 96 | antrigintillion |
- ...
- 10 100 - googol (the number was invented by the 9-year-old nephew of the American mathematician Edward Kasner)
- 10 123 - quadragintillion (quadraginta, XL)
- 10 153 - quinquaginta, L
- 10,183 - sexaginta (LX)
- 10 213 - septuaginta, LXX
- 10 243 - octogintillion (octoginta, LXXX)
- 10 273 - nonaginta, XC
- 10,303 - centillion (Centum, C)
- 10 306 - antcentillion or centunillion
- 10 309 - duocentillion or centduollion
- 10 312 - trecentillion or centtrillion
- 10 315 - quattorcentillion or centquadrillion
- 10 402 - tretrigintacentillion or centtretrigintillion
Numbers further:
Some literary references:
- Perelman Ya.I. "Entertaining arithmetic". - M .: Triada-Litera, 1994, pp. 134-140
- Vygodsky M. Ya. "Handbook of Elementary Mathematics". - S-Pb., 1994, pp. 64-65
- "Encyclopedia of Knowledge". - comp. IN AND. Korotkevich. - St. Petersburg: Owl, 2006, p. 257
- "Interesting about physics and mathematics." - Library Kvant. no. 50. - M .: Nauka, 1988, p. 50
June 17th, 2015
“I see clusters of vague numbers that are hiding there, in the darkness, behind a small spot of light that the candle of the mind gives. They whisper to each other; conspiring who knows what. Perhaps they don't like us very much for capturing their little brothers with our minds. Or, perhaps, they simply lead an unambiguous numerical way of life, out there, beyond our understanding ''.
Douglas Ray
We continue ours. Today we have numbers ...
Sooner or later, everyone is tormented by the question, what is the largest number. A child's question can be answered in a million. What's next? Trillion. And even further? In fact, the answer to the question of what are the largest numbers is simple. You just need to add one to the largest number, as it will no longer be the largest. This procedure can be continued indefinitely.
And if you ask the question: what is the largest number that exists, and what is its own name?
Now we will all find out ...
There are two systems for naming numbers - American and English.
The American system is pretty simple. All the names of large numbers are built like this: at the beginning there is a Latin ordinal number, and at the end the suffix-million is added to it. The exception is the name "million" which is the name of the number one thousand (lat. mille) and the increasing suffix-million (see table). This is how the numbers are obtained - trillion, quadrillion, quintillion, sextillion, septillion, octillion, nonillion and decillion. The American system is used in the USA, Canada, France and Russia. You can find out the number of zeros in a number written in the American system using the simple formula 3 x + 3 (where x is a Latin numeral).
The English naming system is the most common in the world. It is used, for example, in Great Britain and Spain, as well as in most of the former English and Spanish colonies. The names of numbers in this system are built like this: 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 is -billion. That is, after a trillion in the English system, there is a trillion, and only then a quadrillion, followed by a quadrillion, etc. Thus, a quadrillion in the English and American systems are completely different numbers! You can find out the number of zeros in a number written in the English system and ending with the suffix-million by the formula 6 x + 3 (where x is a Latin numeral) and by the formula 6 x + 6 for numbers ending in -billion.
Only the number billion (10 9) passed from the English system to the Russian language, which would still be more correct to call it as the Americans call it - a billion, since it is the American system that has been adopted in our country. But who in our country does something according to the rules! ;-) By the way, sometimes the word trillion is also used in Russian (you can see for yourself by running a search in Google or Yandex) and it means, apparently, 1000 trillion, i.e. quadrillion.
In addition to numbers written using Latin prefixes according to the American or English system, so-called off-system numbers are also known, i.e. numbers that have their own names without any Latin prefixes. There are several such numbers, but I will talk about them in more detail a little later.
Let's go back to writing using Latin numerals. It would seem that they can write numbers to infinity, but this is not entirely true. Let me explain why. Let's see for a start how the numbers from 1 to 10 33 are called:
And so, now the question arises, what's next. What's behind the decillion? In principle, it is possible, of course, by combining prefixes to generate such monsters as: andecilion, duodecillion, tredecillion, quattordecillion, quindecillion, sexdecillion, septemdecillion, octodecillion and novemdecillion, but these will already be compound names, but we were interested in numbers. Therefore, according to this system, in addition to those indicated above, you can still get only three - vigintillion (from lat.viginti- twenty), centillion (from lat.centum- one hundred) and a million (from lat.mille- thousand). The Romans did not have more than a thousand of their own names for numbers (all numbers over a thousand were composite). For example, a million (1,000,000) Romans calleddecies centena milia, that is, "ten hundred thousand". And now, in fact, the table:
Thus, according to a similar system, the numbers are greater than 10 3003 , which would have its own, non-compound name, it is impossible to get! But nevertheless, numbers over a million million are known - these are the very off-system numbers. Let's finally tell you about them.
The smallest such number is myriad (it is even in Dahl's dictionary), which means one hundred hundred, that is, 10,000 does not mean a definite number at all, but an uncountable, uncountable set of something. It is believed that the word myriad came to European languages from ancient Egypt.
There are different opinions about the origin of this number. Some believe that it originated in Egypt, while others believe that it was born only in Ancient Greece. Be that as it may in reality, but the myriad gained fame thanks to the Greeks. Myriad was the name for 10,000, but there were no names for numbers over ten thousand. However, in the note "Psammit" (ie the calculus of sand), Archimedes showed how one can systematically construct and name arbitrarily large numbers. In particular, placing 10,000 (myriad) grains of sand in a poppy seed, he finds that in the Universe (a sphere with a diameter of a myriad of Earth's diameters) no more than 10 63
grains of sand. It is curious that modern calculations of the number of atoms in the visible Universe lead to the number 10 67
(just a myriad of times more). Archimedes suggested the following names for numbers:
1 myriad = 10 4.
1 d-myriad = myriad myriad = 10 8
.
1 three-myriad = di-myriad di-myriad = 10 16
.
1 tetra-myriad = three-myriad three-myriad = 10 32
.
etc.
Googol (from the English googol) is the number ten to the hundredth power, that is, one with one hundred zeros. Googol was first written about in 1938 in the article "New Names in Mathematics" in the January issue of Scripta Mathematica by the American mathematician Edward Kasner. According to him, his nine-year-old nephew Milton Sirotta suggested calling a large number "googol". This number became well-known thanks to the search engine named after him. Google... Note that "Google" is a trademark and googol is a number.
Edward Kasner.
On the Internet, you can often find it mentioned that - but it is not ...
In the famous Buddhist treatise Jaina Sutra, dating back to 100 BC, the number asankheya (from Ch. asenci- uncountable) equal to 10 140. It is believed that this number is equal to the number of cosmic cycles required to attain nirvana.
Googolplex (eng. googolplex) is a number also invented by Kasner with his nephew and means one with a googol of zeros, that is, 10 10100 ... This is how Kasner himself describes this "discovery":
Words of wisdom are spoken by children at least as often as by scientists. The name "googol" was invented by a child (Dr. Kasner "s nine-year-old nephew) who was asked to think up a name for a very big number, namely, 1 with a hundred zeros after it. He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. At the same time that he suggested "googol" he gave a name for a still larger number: "Googolplex." A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out.
Mathematics and the Imagination(1940) by Kasner and James R. Newman.
An even larger number than a googolplex, the Skewes "number was proposed by Skewes in 1933 (Skewes. J. London Math. Soc. 8, 277-283, 1933.) in proving the Riemann conjecture concerning prime numbers. It means e to the extent e to the extent e to the 79th power, that is, ee e 79 ... Later, Riele (te Riele, H. J. J. "On the Sign of the Difference NS(x) -Li (x). " Math. Comput. 48, 323-328, 1987) reduced Skuse's number to ee 27/4 , which is approximately equal to 8.185 · 10 370. It is clear that since the value of the Skuse number depends on the number e, then it is not an integer, therefore we will not consider it, otherwise we would have to remember other non-natural numbers - pi, e, etc.
But it should be noted that there is a second Skuse number, which in mathematics is denoted as Sk2, which is even greater than the first Skuse number (Sk1). Second Skewes number, was introduced by J. Skuse in the same article to denote a number for which the Riemann hypothesis is not valid. Sk2 is 1010 10103 , that is, 1010 101000 .
As you understand, the more there are in the number of degrees, the more difficult it is to understand which of the numbers is greater. For example, looking at the Skuse numbers, without special calculations, it is almost impossible to understand which of these two numbers is greater. Thus, it becomes inconvenient to use powers for very large numbers. Moreover, you can think of such numbers (and they have already been invented) when the degrees of degrees simply do not fit on the page. Yes, what a page! They will not fit, even in a book the size of the entire Universe! In this case, the question arises how to write them down. The problem, as you understand, is solvable, and mathematicians have developed several principles for writing such numbers. True, every mathematician who asked this problem came up with his own way of writing, which led to the existence of several unrelated ways to write numbers - these are the notations of Knuth, Conway, Steinhouse, etc.
Consider the notation of Hugo Steinhaus (H. Steinhaus. Mathematical Snapshots, 3rd edn. 1983), which is pretty simple. Stein House proposed to write large numbers inside geometric shapes - a triangle, a square and a circle:
Steinhaus came up with two new super-large numbers. He named the number Mega and the number Megiston.
The mathematician Leo Moser refined Stenhouse's notation, which was limited by the fact that if it was required to write numbers much larger than the megiston, difficulties and inconveniences arose, since many circles had to be drawn inside one another. Moser suggested drawing not circles, but pentagons after the squares, then hexagons, and so on. He also proposed a formal notation for these polygons so that numbers could be written down without drawing complex drawings. Moser's notation looks like this:
Thus, according to Moser's notation, the Steinhaus mega is written as 2, and the megiston as 10. In addition, Leo Moser suggested calling a polygon with the number of sides equal to a mega - megaagon. And he proposed the number "2 in Megagon", that is, 2. This number became known as the Moser's number (Moser's number) or simply as moser.
But the moser is not the largest number either. The largest number ever used in mathematical proof is a limiting quantity known as the Graham "s number, first used in 1977 to prove one estimate in Ramsey theory. It is associated with bichromatic hypercubes and cannot be expressed. without the special 64-level system of special mathematical symbols introduced by Knuth in 1976.
Unfortunately, the number written in Knuth notation cannot be translated into the Moser system. Therefore, we will have to explain this system as well. In principle, there is nothing complicated in it either. Donald Knuth (yes, yes, this is the same Knuth who wrote "The Art of Programming" and created the TeX editor) came up with the concept of superdegree, which he proposed to write down with arrows pointing up:
In general, it looks like this:
I think everything is clear, so let's go back to Graham's number. Graham proposed the so-called G-numbers:
- G1 = 3..3, where the number of superdegree arrows is 33.
- G2 = ..3, where the number of superdegree arrows is equal to G1.
- G3 = ..3, where the number of superdegree arrows is equal to G2.
- G63 = ..3, where the number of overdegree arrows is equal to G62.
The number G63 became known as the Graham number (it is often denoted simply as G). This number is the largest known number in the world and is even included in the Guinness Book of Records. And here
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