Many are interested in questions about how large numbers are called and what number is the largest in the world. With these interesting questions and we will understand this article.
History
Southern and Eastern Slavic nations for recording numbers used alphabetical numbering, and only those letters that are in the Greek alphabet. Above the letter that marked the figure, put a special "Title" icon. The numerical values \u200b\u200bof letters increased in the same way, in what order letters followed in the Greek alphabet (in the Slavic alphabet, the order of letters was a little different). In Russia, Slavic numbering has been preserved until the end of the 17th century, and under Peter I switched to "Arab numbering" we use and now.
The names of the numbers also changed. So, up to the 15th century, the number Twenty was designated as "two ten" (two dozen), and then decreased for a faster pronunciation. The number 40 to the 15th century was called "Fourth", then it was displaced by the word "forty", denoting the original bag, which en deems 40 squirrels or sobular skins. The name "Million" appeared in Italy in 1500. It was formed by adding a magnifying suffix to the Mille (thousand). Later, this name came to Russian.
In the old (XVIII century), the "arithmetic" of Magnitsky, the table of the names of the numbers brought to the "quadrillion" (10 ^ 24, by system through 6 digits). Perelman Ya.I. In the book "Entertaining arithmetic", the names of large numbers of the time are given, somewhat different from today: septylon (10 ^ 42), Occlicon (10 ^ 48), nonalone (10 ^ 54), decalon (10 ^ 60), Endecalon (10 ^ 66), Dodecalon (10 ^ 72) and it is written that "then the names are not available."
Ways to build big numbers
There are 2 main ways of large numbers:
- American systemwhich is used in the USA, Russia, France, Canada, Italy, Turkey, Greece, Brazil. The names of large numbers are built quite simply: first there is a Latin order numerical, and the suffix "-lion" is added to it. Exceptions are the number "Million", which is the name of the number of a thousand (Mille) and the magnifying suffix "-LI10". The number of zeros among which is recorded on the American system can be found in the formula: 3x + 3, where x - Latin sequence numerical
- English system The most common in the world is used in Germany, Spain, Hungary, Poland, the Czech Republic, Denmark, Sweden, Finland, Portugal. The names of the numbers on this system are structured as follows: the "-Lion" suffix is \u200b\u200badded to the Latin numerical, the following number (1000 times more) is the same latin numerical, but suffix "-lilliard" is added. The number of zeros among which is recorded in the English system and ends with the suffix "-lion", can be found in the formula: 6x + 3, where x - Latin sequence is numerical. The number of zeros in the numbers ending with the suffix "-lilliard" can be found in the formula: 6x + 6, where x - Latin sequence is numerical.
From the English system to the Russian language, only the word billion, which is still more correct to call as the Americans call it - Billion (since the American Nizhny Name System is used in Russian).
In addition to the numbers that are recorded in the American or English system with the help of Latin prefixes, some-system numbers that have their own names without Latin prefixes are known.
Own names of large numbers
| Number | Latin numerical | Name | Practical value | |
| 10 1 | 10 | ten | The number of fingers on 2 hands | |
| 10 2 | 100 | one hundred | Approximately half of the number of all states on Earth | |
| 10 3 | 1000 | one thousand | Approximate number of days in 3 years | |
| 10 6 | 1000 000 | unus (I) | million | 5 times more than the number of drops in a 10-liter. Water buckets |
| 10 9 | 1000 000 000 | dUO (II) | billion (Billion) | Approximate population of India |
| 10 12 | 1000 000 000 000 | tRES (III) | trillion | |
| 10 15 | 1000 000 000 000 000 | quattor (IV) | quadrillion | 1/30 Parsek length in meters |
| 10 18 | qUINQUE (V) | quintillion | 1/18 grains from the legendary award inventor chess | |
| 10 21 | sex (VI) | sextillion | 1/6 masses of the planet Earth in tons | |
| 10 24 | sEPTEM (VII) | septillion | Number of molecules in 37.2 l air | |
| 10 27 | oCTO (VIII) | octillion | Half of the mass of Jupiter in kilograms | |
| 10 30 | novem (IX) | quintillion | 1/5 of the number of all microorganisms on the planet | |
| 10 33 | decem (X) | decillion | Half of the mass of the Sun in grams | |
- Vigintillion (from lat. Viginti - twenty) - 10 63
- Centillion (from lat. Centum - hundred) - 10 303
- Milleilla (from Lat. Mille - one thousand) - 10 3003
For numbers, more than a thousand in the Romans of their own names were no (all the names of numbers were further composite).
Composite names of large numbers
In addition to its own names, for numbers more than 10 33, you can get composite names by combining consoles.
Composite names of large numbers
| Number | Latin numerical | Name | Practical value |
| 10 36 | undecim (xi) | andesillion | |
| 10 39 | duodecim (XII) | doodecillion | |
| 10 42 | tredecim (XIII) | treadcillion | 1/100 on the number of air molecules on earth |
| 10 45 | qUATTUORDECIM (XIV) | kvattordecillion | |
| 10 48 | qUINDECIM (XV) | quendecyllion | |
| 10 51 | sedecim (XVI) | sexotilion | |
| 10 54 | septendecim (XVII) | sepemdiscillion | |
| 10 57 | oktodecillion | So many elementary particles in the sun | |
| 10 60 | novmetsillion | ||
| 10 63 | viginti (XX) | vigintillion | |
| 10 66 | uNUS ET VIGINTI (XXI) | anvigintillion | |
| 10 69 | duo et Viginti (XXII) | duviygintillion | |
| 10 72 | tres et Viginti (XXIII) | tremgintillion | |
| 10 75 | kvattorvigintillion | ||
| 10 78 | queenvigintillion | ||
| 10 81 | sexVigintillion | So many elementary particles in the universe | |
| 10 84 | septemvigintillion | ||
| 10 87 | octovigintillion | ||
| 10 90 | nov'vvigintillion | ||
| 10 93 | triginta (XXX) | trigintillion | |
| 10 96 | annigintillion. |
- 10 123 - Quadchantillion
- 10 153 - Quecilwagintillion
- 10 183 - Sexagintillion
- 10 213 - Septuagintillion
- 10 243 - Oktogintillion
- 10 273 - Nonagintillion
- 10 303 - Centillion
Further names can be obtained by direct or reverse Latin numerical order (as proper, it is not known):
- 10 306 - Angentillion or Centunillion
- 10 309 - Duocenteillion or centindollion
- 10 312 - Tirettyllion or Centrillion
- 10 315 - Quartercertillion or Cenkvadrillion
- 10 402 - Ferrigintantyaltyillion or Centraletrigintillion
The second version of writing more corresponds to the construction of numeral in Latin and avoids ambiguities (for example, among the number of Tientymalillion, which is 1,093 and 10 312, and 10 312).
- 10 603 - Dutentillion
- 10 903 - Tientyllion
- 10 1203 - Quadringentillion
- 10 1503 - Quingventillion
- 10 1803 - Sedsertillion
- 10 2103 - Septingsentillion
- 10 2403 - Oaktingtillion
- 10 2703 - Nonhentillion
- 10 3003 - Milleillion
- 10 6003 - Domillalion
- 10 9003 - Tremlillion
- 10 15003 - QUINKVEMILION
- 10 308760 - DucenduomylanionenTeemecillion
- 10 3000003 - Miliamilialion
- 10 6000003 - DomoilyamiliaIillion
Miriada - 10 000. The name is obsolete and practically not used. However, the word "Miriada" is widely used, which means not a certain number, but countless, uncountable many of something.
Gugol (english . googol) — 10 100. For the first time, American mathematician Edward Kasner (Edward Kasner) wrote about this number in 1938 in the Journal of Scripta Mathematica in the article "New Names in Mathematics". According to him, to call so the number suggested his 9-year-old nephew Milton Sirotta (Milton Sirotta). This number has become well known for the Google search engine called in honor of him.
Asankhaya(from whale. Asianzi - innumerable) - 10 1 4 0. This number is found in the famous Buddhist treatise Jaina-Sutra (100 g. BC). It is believed that this number is equal to the number of space cycles required to gain nirvana.
Gugolplex (english . Googolplex.) — 10 ^ 10 ^ 100. This number also came up with Edward Casner with his nephew, means it is a unit with a google zerule.
Number of Skusza (Skewes' Number,SK 1) means e to the degree E into the degree E to the degree 79, that is, E ^ E ^ E ^ 79. This number was suggested by Skews in 1933 (Skewes. J. London Math. Soc. 8, 277-283, 1933.) In the proof of Riman's hypothesis relating to prime numbers. Later, Riele (Te Riele, HJJ "On the Sign of the Difference P (X) -LI (X)." Math. Comput. 48, 323-328, 1987) reduced the number of skuse to E ^ E ^ 27/4, That approximately equal to 8.185 · 10 ^ 370. However, this number is not a whole, so it is not included in the table of large numbers.
Second number of Skuse (SK2) Equally 10 ^ 10 ^ 10 ^ 10 ^ 3, that is, 10 ^ 10 ^ 10 ^ 1000. This number was introduced by J. Skews in the same article for the designation of the number, to which the Hypothesis of Riman is valid.
For super-high numbers, it is inconvenient to use degrees, therefore there are several ways to write numbers - the notation of the whip, Konveya, Steinhaus, etc.
Hugo Steinhause offered to record large numbers inside the geometric figures (triangle, square and circle).
Mathematics Leo Moser finalized the notation of Steinhaus, offering after squares not circles, but pentagons, then hexagons, etc. Moser also offered a formal entry for these polygons, so that the numbers can be recorded without drawing complex drawings.
Steinhauses came up with two new super-high numbers: Mega and Megiston. In the notation of Moor, they are recorded like this: Mega – 2, Megiston - 10. Leo Moser also offered to call a polygon with the number of parties equal to Mega - magagonand also offered the number "2 in the megagon" - 2. The last number is known as moser's number (Moser's Number) or just as Moser.
There are numbers, more Moser. The largest number that was used in mathematical proof is number Graham (Graham's Number). It was first used in 1977 in proof of one assessment in the Ramsey theory. This number is associated with bichromatic hypercubs and cannot be expressed without a special 64-level system of special mathematical symbols introduced by the whip in 1976. Donald Knut (who wrote the "Programming Art" and created the TeX editor) invented the concept of a superpope, which offered to record the arrows directed upwards:
In general
Graham offered G-numbers:
The number G 63 is called the Graham number, often indicated by G. This number is the largest known number in the world and is listed in the "Guinness Book of Records".
In everyday life, most people operate quite small numbers. Tens, hundreds, thousands, very rarely - millions, almost never - billions. Approximately such numbers are limited to the usual representation of a person about quantity or magnitude. About the trillions had to hear almost everyone, but to use them, in any counts, few people have come.
What are they, giants?
Meanwhile, the numbers denoting the degrees of thousands are known to people for a long time. In Russia and many other countries, a simple and logical system of designations are used:
One thousand;
Million;
Billion;
Trillion;
Quadrillion;
Quintillion;
Sextillion;
Septillion;
Octillion;
Quintillion;
Decillion.
In this system, each next number is obtained by multiplying the previous one. Billion is usually called a billion.
Many adults can accurately write such numbers as a million - 1,000,000 and a billion - 1,000,000,000. It's already more difficult with a trillion, but almost everything will be cope with - 1,000,000,000,000. And then it starts unknown to many territory.
Get acquainted closer with big numbers
Complex, however, there is nothing, the main thing is to understand the system of formation of large numbers and the principle of the name. As already mentioned, each next number exceeds the previous one thousand times. This means that in order to properly write the following in order of increasing the number, you need to attribute three more scratch to the previous one. That is, a million 6 zeros, a billion of them 9, trillion - 12, in quadrillion - 15, and Quintillion is already 18.
The names can also be sorted out if there is a desire. The word "Million" happened from the Latin "Mille", which means "more than a thousand". The following numbers were formed by attracting the Latin words "bi" (two), "three" (three), "quadro" (four), etc.
Now let's try to imagine these numbers clearly. Most pretty well imagine the difference between thousand and million. Everyone understands that a million rubles is good, but a billion is more. Much more. Also, everyone has an idea that the trillion is something absolutely immense. But how much is the trillion more than a billion? How big is he?
For many, more than a billion begins the concept of "incomprehensible". Indeed, a billion kilometers or a trillion - the difference is not very big in the sense that such a distance still does not go throughout life. A billion rubles or a trillion is also not particularly different, because there is still no such money for all life. But let's count a little by connecting fantasy.
Resident Fund of Russia and four football fields as examples
For each person on Earth there is an area of \u200b\u200bsushi size of 100x200 meters. This is about four soccer fields. But if people are not 7 billion, but seven trillion, then everyone will get only a piece of sushi 4x5 meters. Four football fields against the area of \u200b\u200bthe parisader before the entrance is such a billion ratio to Trillion.
In absolute values, the picture is also impressive.
If you take a trillion bricks, you can build more than 30 million single-storey houses with an area of \u200b\u200b100 square meters. That is, about 3 billion square meters of private building. It is comparable to the common residential Fund of the Russian Federation.
If you build ten-story houses, you will get about 2.5 million homes, that is, 100 million two-two-bedroom apartments, about 7 billion square meters of housing. This is 2.5 times the most residential fund of Russia.
In a word, in all Russia, the trillion of bricks is not scored.
One quadrillion of student notebooks will cover the entire territory of Russia by a double layer. And one quintillion of the same notebooks will cover the whole drying layer with a thickness of 40 centimeters. If it is possible to get the sextillion of notebooks, the entire planet, including oceans, will be under a layer of 100 meters thick.
Consider Decillion
Let's consider it yet. For example, a matchbox, increased a thousand times, will be the size of a sixteen-storey house. The increase in a million times will give "boxes", which is more than St. Petersburg in the area. Increased billion times, the boxes will not fit on our planet. On the contrary, the Earth will fit in such "boxes" 25 times!
Increase box gives an increase in its volume. Imagine such volumes with further magnification will be almost impossible. For simplicity of perception, we will try to increase not the subject itself, but its number, and place the matchboxes in space. So it will be easier to navigate. Quintillion boxes laid out into one row would stretch further than the stars α centaution of 9 trillion kilometers.
Another millennial increase (sextillion) will allow matchboxes built into the line, overcoat the entire Milky path in the transverse direction. Septillion match boxes would be stretched for 50 quintillion kilometers. Such a distance of light can fly for 5 million 260 thousand years. And the boxes laid out in two rows would stretch to Andromeda Galaxy.
There are only three numbers: Octillion, Nonillion and Decillion. We will have to strain imagination. Octillion boxes forms a continuous line in 50 sextillion kilometers. This is more than five billion light years. Not every telescope installed on one edge of such an object could see his opposite edge.
Count further? Nonillion of matchboxes would fill in the entire space of famous humanity part of the universe with an average density of 6 pieces per cubic meter. For earthly standards, it seems to be not very many - 36 matched boxes in the body of standard "Gazelles". But nonillion of match boxes will have a lot of billions times more than the mass of all material objects of the well-known universe combined.
Decillion. Quantity, but rather, even the majesty of this gigid from the world of numbers, it is difficult to imagine yourself. Only one example - six decyllini boxes would no longer fit in all accessible humanity to observe part of the universe.
Even more strikingly, the majesty of this number is visible, if not multiply the number of boxes, and increase the subject itself. Matchboxes, enlarged in Decillion times, would hold all the most famous humanity part of the universe 20 trillion times. It is impossible to even imagine such yourself.
Small calculations showed how huge numbers, famous for humanity for several centuries for several centuries. In modern mathematics, the number is known many times superior decyllion, but they are used only in complex mathematical calculations. Faced with similar numbers accounts for only professional mathematicians.
The most famous (and the smallest) of such numbers is Google, denoted by a unit with a hundred zeros. Gugol is greater than the total number of elementary particles in the visible part of the universe. This makes Gugol an abstract number that does not have a large practical application.
Have you ever thought how many zeros are in one million? This is a fairly simple question. What about a billion or trillion? Unit with nine zeros (10,000,000,000) - what is the name of the number?
Brief list of numbers and their quantitative designation
- Ten (1 zero).
- One hundred (2 zero).
- Thousand (3 zero).
- Ten thousands (4 scratch).
- One hundred thousand (5 zeros).
- Million (6 zeros).
- Billion (9 zeros).
- Trillion (12 zeros).
- Quadrillion (15 zeros).
- Quintillon (18 zeros).
- Sextillion (21 zero).
- Septylon (24 zero).
- Occlicon (27 zeros).
- Nonalon (30 zeros).
- Decalon (33 zero).
Grouping zeros.
10,000,000 - what is the name of which there are 9 zeros? This is a billion. For convenience, large numbers are accepted to group three sets separated from each other with a space or such punctuation marks as a comma or point.
This is done in order to make it easier to read and understand quantitative importance. For example, what is the name of the number of 100,000,000? In this form, it is necessary to say a little, calculate. And if you write 1,000,000,000, then immediately visually the task is facilitated, so it is necessary to consider not zeros, but the top of the zeros.
Numbers with a very large number of zeros
Million and billion are from the most popular (1,000,000,000). What is the number having a 100 zeros? This is a number googol, called so Milton Sirette. This is wildly a huge amount. Do you think that this number is big? Then how about googolplex, the units behind which googol zerule? This figure is so great that it makes sense to come up with difficult for her. In fact, there is no need for such giants, except to count the number of atoms in the infinite universe.
1 billion is a lot?
There are two measurement scales - short and long. Worldwide in the field of science and finance 1 billion is 1,000 million. This is a short scale. There is a number with 9 zeros.
There is also a long scale that is used in some European countries, including in France, and used to be used in the UK (until 1971), where the billion was 1 million million, that is, a unit and 12 zeros. This gradation is also called a long-term scale. A short scale is now the predominant in solving financial and scientific issues.
Some European languages \u200b\u200bsuch as Swedish, Danish, Portuguese, Spanish, Italian, Dutch, Norwegian, Polish, German, use a billion (or Billion) in this system. In Russian, a number of 9 zeros is also described for a short scale of thousands of millions, and a trillion is a million million. This avoids unnecessary confusion.
Conversational options
In Russian spoken speech after the events of 1917 - the Great October Revolution - and the period of hyperinflation in the early 1920s. 1 billion rubles called Limard. And in the dashing 1990s for a billion, a new slang "Watermelon" appeared, a million called "Lemon".
The word "billion" is now used internationally. This is a natural number that is depicted in the decimal system, like 10 9 (unit and 9 zeros). There is also another name - Billion, which is not used in Russia and the CIS countries.
Billion \u003d Billion?
Such a word as Billion is used to designate a billion only in those states in which the "short scale" is adopted as a basis. These are countries such as the Russian Federation, the United Kingdom of Great Britain and Northern Ireland, USA, Canada, Greece and Turkey. In other countries, the concept of Billion means the number 10 12, that is, one and 12 zeros. In countries with a "short scale", including in Russia, this figure corresponds to 1 trillion.
Such confusion appeared in France at a time when the formation of such science as an algebra took place. Initially, a billion had 12 zeros. However, everything changed after the emergence of the main arithmetic allowance (by Tranchan) in 1558), where a billion is an already number with 9 zeros (thousand million).
For several subsequent centuries, these two concepts were used on par with each other. In the middle of the 20th century, namely in 1948, France moved to a long scale of a system of numerical names. In this regard, a short scale, once borrowed from the French, is still different from the one they enjoy today.
Historically, the United Kingdom has used a long-term billion, but since 1974 official statistics of Great Britain used a short-term scale. Since the 1950s, the short-term scale was increasingly used in the field of technical writing and journalism, despite the fact that the long-term scale remained.
As a child, I was tormented by the question of which there is a largest number, and I got out of this stupid question of almost all in a row. Having learned the number Million, I asked if there was a number of more than a million. Billion? And more than a billion? Trillion? And more trillion? Finally, someone cleverly found, who explained to me that the question is stupid, as it is enough just to add to the largest number of one, and it turns out that it has never been the biggest, as there is a number even more.
And here, after many years, I decided to ask another question, namely: what is the largest number that has its own name? Fortunately, now there is an Internet and you can pose patient search engines that will not call my questions idiot ;-). Actually, I did it, and that's what I found out.
| Number | Latin name | Russian console |
| 1 | Unus. | An- |
| 2 | duo. | duo- |
| 3 | Tres. | three- |
| 4 | quattuor | quadry |
| 5 | QUINQUE | quint |
| 6 | Sex | sexti |
| 7 | septem. | septic |
| 8 | Octo. | octic |
| 9 | novem. | non- |
| 10 | Decem. | deci- |
There are two numbers name systems - 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 sequence numerical, and at the end, suffix is \u200b\u200badded to it. The exception is the name "Million" which is the name of the number of a thousand (lat. mille) and magnifying suffix -illion (see table). So the numbers are 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 the number written through the American system, it is possible by a simple formula 3 · X + 3 (where X is Latin numerical).
The English name system is most common in the world. She enjoyed, for example, in the UK and Spain, as well as in most former English and Spanish colonies. The names of the numbers in this system are built as follows: so: Sufifix -Ilion is added to the Latin number, the following number (1000 times more) is built on the principle - the same Latin numerical, but suffix - -lilliard. That is, after a trillion in the English system, trilliard goes, and only then the quadrillion followed by quadrilliore, etc. Thus, quadrillion in English and American systems are quite different numbers! You can find out the amount of zeros in the number recorded in the English system and the ending suffix-cylon, it is possible according to the formula 6 · X + 3 (where X is Latin numeral) and according to the formula 6 · x + 6 for the numbers ending on -ylard.
From the English system, only the number of billion (10 9) passed from the English system, which would still be more correctly called as the Americans call him - Billion, since we received the American system. But who in our country does something according to the rules! ;-) By the way, sometimes in Russian use the word trilliard (you can make sure about it, running a search in Google or Yandex) and it means, apparently, 1000 trillion, i.e. quadrillion.
In addition to the numbers recorded with the help of Latin prefixes on the American or England system, the so-called non-systemic numbers are 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 the record with Latin numerals. It would seem that they can be recorded to the numbers before concern, but it is not quite so. Now I will explain why. Let's see for a start called numbers from 1 to 10 33:
| Name | Number |
| Unit | 10 0 |
| Ten | 10 1 |
| One hundred | 10 2 |
| One 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, and what's next. What is there for Decillion? In principle, it is possible, of course, with the help of the combination of consoles to generate such monsters as: Andecilion, Duodeticillion, Treadsillion, Quarterdecillion, Quendecyllion, Semtecillion, Septecyllin, Oktodeticillion and New Smecillion, but it will already be composite names, and we were interested in our own names. numbers. Therefore, its own names on this system, in addition to the above, can still be obtained only three - Vigintillion (from Lat. viginti. - Twenty), Centillion (from Lat. centum. - One hundred) and Milleillion (from Lat. mille - one thousand). More than a thousand of their own names for numbers in the Romans was no longer (all numbers more than a thousand they had compounds). For example, a million (1,000,000) Romans called decies Centena Milia., that is, "ten hundred thousand". And now, in fact, Table:
Thus, according to a similar system, the number is greater than 10,3003, which would be their own, incompening name is impossible! Nevertheless, the number more than Milleillion is known - these are the most generic numbers. Let's tell you finally, about them.
| Name | Number |
| Miriada | 10 4 |
| Gugol. | 10 100 |
| Asankhaya | 10 140 |
| Googolplex | 10 10 100 |
| The second number of Skusza | 10 10 10 1000 |
| Mega | 2 (in the notation of Moser) |
| Megiston | 10 (in the notation of Moser) |
| Moser | 2 (in the notation of Moser) |
| Graham number | G 63 (in the Graham Notation) |
| Ostasks | G 100 (in Graham Notation) |
The smallest such number is miriada (it is even in the Dala dictionary), which means hundreds of hundreds, that is - 10,000. The word is, however, it is outdated and practically not used, but it is curious that the word "Miriada" is widely used, which means not a certain number at all, but Countless, unpleasant set of something. It is believed that the Word of Miriad (Eng. Myriad) came to European languages \u200b\u200bfrom ancient Egypt.
Gugol. (from the English. Googol) is a number of ten to a hundredth, that is, a unit with a hundred zeros. About "Google" for the first time wrote in 1938 in the article "New Names in Mathematics" in the January issue of Scripta Mathematica magazine American mathematician Edward Kasner (Edward Kasner). According to him, to call "Gugol" a large number suggested his nine-year-old nephew Milton Sirotta (Milton Sirotta). Well-known this number was due to the search engine named after him Google . Please note that "Google" is a trademark, and googol - a number.
In the famous Buddhist treatise, Jaina-Sutra, belonging to 100 g. BC, meets the number asankhaya (from whale. asianz - innumerable), equal to 10 140. It is believed that this number is equal to the number of space cycles required to gain nirvana.
Googolplex (eng. googolplex.) - the number also invented by Castner with his nephew and meaning a unit with a google of zeros, that is 10 10 100. Here's how Kasner himself describes this "Opening":
Words of Wisdom Are Spoken by Children At Least Asiss 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 CERTIAIN THIS THIS NUMBER WAS NOT INFINITE, AND THEREFORE EQUALLY CERTAIN THAT IT TIME THAT 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.
Even more than a googolplex number - the number of Skuse (Skewes "Number) was proposed by Skews in 1933 (Skewes. J. London Math. SOC. 8 , 277-283, 1933.) In case of proof of Riman's hypothesis concerning prime numbers. It means e.in degree e.in degree e.by degree 79, that is, E E E 79. Later, Riel (Te Riele, H. J. J. "On the Sign of the Difference P(x) -li (x). " Math. Comput. 48 , 323-328, 1987) reduced the number of Scyss to E E 27/4, which is approximately 8.185 · 10 370. It is clear that once the value of the number of Scyss depends on the number e., it is not a whole, so we will not consider it, otherwise I would have to recall other unprofitable numbers - the number of pi, the number E, the number of Avogadro, and the like.
But it should be noted that there is a second number of Skusza, which in mathematics is indicated as SK 2, which is even greater than the first number of Skuse (SK 1). The second number of SkuszaIt was introduced by J. Skews in the same article for the designation of the number, to which the Hypothesian of Riman is valid. SK 2 is 10 10 10 10 3, that is, 10 10 10 1000.
As you understand the more degrees, the harder it is to understand which of the numbers is more. For example, looking at the number of Skusz, without special calculations, it is almost impossible to understand which of these two numbers is more. Thus, for super-high numbers, it becomes inconvenient to use degrees. Moreover, you can come up with such numbers (and they are already invented), when the degrees are simply not climbed into the page. Yes, that on the page! They will not fit, even in a book, the size of the whole universe! In this case, the question arises how to record them. The problem, as you understand, are solvable, and mathematics have developed several principles for recording such numbers. True, every mathematician who asked this problem came up with his way of recording, which led to the existence of several not related to each other, methods for recording numbers - these are notations of Knuta, Conway, Steinhause, etc.
Consider the notation of the Hugo Roach (H. Steinhaus. Mathematical Snapshots., 3rd EDN. 1983), which is pretty simple. Stein House offered to record large numbers inside geometric figures - triangle, square and circle:
Steinhauses came up with two new super-high numbers. He called the number - Mega, and number - Megiston.
Mathematics Leo Moser finalized the notation of the wallhause, which was limited by the fact that if it was required to record numbers a lot more Megiston, difficulties and inconvenience occurred, since it had to draw a lot of circles one inside the other. Moser suggested not circles after squares, and pentagons, then hexagons and so on. He also offered a formal entry for these polygons so that the numbers can be recorded without drawing complex drawings. The notation of Moser looks like this:
Thus, according to the notation of Mosel, Steinhouse mega is recorded as 2, and Megstone as 10. In addition, Leo Moser proposed to call a polygon with the number of sides to mega-megaagon. And suggested the number "2 in the megagon", that is 2. This number became known as Moser (Moser "s Number) or just like moser.
But Moser is not the largest number. The largest number ever used in mathematical proof is the limit value known as graham number (Graham "S Number), first used in 1977 in the proof of one assessment in the Ramsey theory. It is associated with bichromatic hypercubs and cannot be expressed without a special 64-level system of special mathematical symbols introduced by the whip in 1976.
Unfortunately, the number recorded in the notation of the whip cannot be translated into a record on the Mosel system. Therefore, this system will have to explain. In principle, it also has nothing complicated. Donald Knut (yes, yes, this is the same whip that wrote the "Art of Programming" and created the TeX editor) invented the concept of a superpope, which offered to record the arrows directed upwards
In general, it looks like this:
I think everything is clear, so let us return to the number of Graham. Graham proposed the so-called G-numbers:
The number G 63 began to be called number Graham (It is often simple as G). This number is the largest number in the world in the world and entered even in the "Guinness Book of Records". A, here is that the number of Graham is greater than the number of Mosel.
P.S. To bring the great benefit to all mankind and become famous in the centuries, I decided to come up with and name the biggest number. This number will be called ostasks And it is equal to the number G 100. Remember it and when your children will ask what the world's largest number, tell them that this number is called ostasks.
Update (4.09.2003): Thank you all for the comments. It turned out that when writing text, I made several errors. I will try to fix now.
- I made several mistakes at once, just mentioning the number of Avogadro. First, several people indicated me that in fact 6,022 · 10 23 - the most that neither is a natural number. And secondly, there is an opinion and it seems to me correct that the number of Avogadro is not at all the number in its own, the mathematical sense of the word, as it depends on the system of units. Now it is expressed in the "mole -1", but if it is expressed, for example, in a moles or something else, it will be expressed by a completely different number, but the number of Avogadro will not cease to be at all.
- 10 000 - Darkness
100 000 - Legion
1 000 000 - Leodr
10 000 000 - Raven or Van
100 000 000 - deck
What is interesting, the ancient Slavs also loved big numbers able to count to a billion. Moreover, such a score was called the "Small Account". In some manuscripts, the authors were also considered "the Great Account", reaching the number of 10 50. About the numbers more than 10 50 said: "And more than one to bear the human mind of understanding." The names used in the "Small Account" were transferred to the "Great Account", but with another meaning. So, darkness meant not 10,000, but a million, legion - darkness (million million); Leodr - Legion of Legions (10 to 24 degrees), then it was said - ten Leods, one hundred leodrov, ..., and, finally, one hundred thousand topics Leodrov (10 in 47); Leodr Leodrov (10 in 48) was called Raven and, finally, a deck (10 in 49). - The topic of the national names of the numbers can be expanded if you remember the Japanese name system of numbers, which is very different from the English and American system (Ieroglyphs I will not draw, if someone is interested, then they):
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 - As for the numbers of Hugo Steinhause (in Russia, his name was translated for some reason as Hugo Steinhause). botev He assures that the idea of \u200b\u200brecording super-high numbers in the form of numbers in circles, belongs not to Steinhouse, and Daniel Harmsu, who hesibly published this idea in the article "Raising the number". I also want to thank Evgeny Sklylyevsky, the author of the most interesting site on entertaining mathematics in the Russian-speaking Internet - watermelon, for the information that Steinhauses came up with not only the number of mega and Megiston, but also offered another number medzonequal to (in his notation) "3 in a circle".
- Now about the number miriada or Mirii. What about the origin of this number there are different opinions. Some believe that it originated in Egypt, others believe that it was born only in antique Greece. Be that as it may, in fact, I received Miriad's fame thanks to the Greeks. Miriada was the name for 10,000, and for numbers more than ten thousand names was not. However, in the note "Psammit" (i.e., the calculus of sand) Archimedes showed how to systematically build and call arbitrarily large numbers. In particular, placing the grains in the poppy grain 10,000 (Miriada), it finds that in the universe (the ball with a diameter of the diameter of the earth) would fit (in our symbols) not more than 10,63 grades. It is curious that modern calculations of the amounts of atoms in the visible universe lead to a number of 10,67 (in total in a myriad of times more). The names of the numbers Archimeda suggested such:
1 Miriad \u003d 10 4.
1 di-Miriada \u003d Miriada Miriad \u003d 10 8.
1 tri-myriad \u003d di-myriad di-myriad \u003d 10 16.
1 tetra-myriad \u003d three-myriad three-myriad \u003d 10 32.
etc.
If there are comments -
Countless different numbers surrounds us every day. Surely many people at least once were interested, which number is considered the largest. The child can simply say that this is a million, but adults perfectly understand what other numbers follow and other numbers. For example, it is only possible to add a single one every time, and it will become more and more - it happens until infinity. But if you disassemble the numbers that have names, you can find out what is called the largest number in the world.
The appearance of the names of numbers: what methods are used?
Today there are 2 systems, according to which the numbers are given names - American and English. The first is quite simple, and the second is the most common worldwide. American allows you to give names to large numbers like this: first indicates the sequence numerical on Latin, and then there is an adding a suffix "Illion" (an exception here is a million, meaning a thousand). Americans, French, Canadians are used such a system, and it is also used in our country.
English is widely used in England and Spain. According to it, the numbers are referred to as so: the numeral on Latin "plunges" with the suffix "Illion", and to the subsequent (more thousand times) the number "plus" "Illyrad". For example, first goes a trillion, behind him "walks" by Trilliard, the quadrillion is kvadrillia, etc.
So, the same number in various systems can mean different, for example, the American Billion in the English system is referred to as a billion.
Intimated numbers
In addition to the numbers, which are recorded according to the well-known systems (given above), there are also generated. They possess their names in which Latin prefixes are not included.
You can start their consideration with a number called Miriadi. It is determined as hundreds of hundred (10,000). But in its assignment, this word does not apply, but is used as an instruction on countless. Even the Dala dictionary will kindly provide a definition of such a number.
The next after Miriad is a googol, denoting 10 to the degree of 100. For the first time, this name was used in 1938 - Mathematics from America E. Kasner, who noted that this name came up with his nephew.
In honor of Google, Google received its name (search engine). Then the 1st Central Committee with Google Zuli (1010100) is a googolplex - such a name has also come up with Kasner.
An even greater compared to the guggolplex is the number of Skusza (e to the degree of E79) proposed by Skews in the proof of Roman's hypothesis about the simple numbers (1933). There is another number of Skusza, but it applies when the hypothesis of the Romanman is unfair. Which one more is quite difficult to say, especially if it comes to big degrees. However, this number, despite its "greatness," can not be considered the most of all those possessed by their names.
And the leader among the largest numbers in the world is the number of Graham (G64). It was he who was used for the first time to conduct evidence in the field of mathematical science (1977).
When it comes to this number, then you need to know that without a special 64-level system created by the whip, do not do - the reason for the connection of the number G with bichromatic hypercubes. The whip was invented superpire, and in order to make it convenient to make her records, he suggested using the arrows up. So we learned how the largest number in the world is called. It is worth noting that this number G hit the pages of the famous book of records.
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