All the biggest numbers. The biggest numbers in the world

10 to the 3003rd power

Disputes about which one is the most big number in the world, are ongoing constantly. Different calculus systems offer different options and people don’t know what to believe, and which figure to consider as the largest.

This question has interested scientists since the times of the Roman Empire. The biggest problem lies in the definition of what a “number” is and what a “digit” is. At one time people long time The largest number was considered to be a decillion, that is, 10 to the 33rd power. But, after scientists began to actively study the American and English metric systems, it was discovered that the most large number in the world it is 10 to the 3003rd power - a million. People in everyday life They believe that the largest figure is a trillion. Moreover, this is quite formal, since after a trillion, names are simply not given, because the counting begins to be too complex. However, purely theoretically, the number of zeros can be added indefinitely. Therefore, it is almost impossible to imagine even purely visually a trillion and what follows it.

In Roman numerals

On the other hand, the definition of “number” as understood by mathematicians is a little different. A number means a sign that is universally accepted and is used to indicate a quantity expressed in a numerical equivalent. The second concept “number” means the expression quantitative characteristics in a convenient form through the use of numbers. From this it follows that numbers consist of digits. It is also important that the number has symbolic properties. They are conditioned, recognizable, unchangeable. Numbers also have sign properties, but they follow from the fact that numbers consist of digits. From this we can conclude that a trillion is not a number at all, but a number. Then what is the largest number in the world if it is not a trillion, which is a number?

The important thing is that numbers are used as components of numbers, but not only that. A number, however, is the same number if we are talking about some things, counting them from zero to nine. This system of features applies not only to the familiar Arabic numerals, but also to Roman I, V, X, L, C, D, M. These are Roman numerals. On the other hand, V I I I is roman numeral. In Arabic calculus it corresponds to the number eight.

IN Arabic numerals

Thus, it turns out that counting units from zero to nine are considered numbers, and everything else is numbers. Hence the conclusion that the largest number in the world is nine. 9 is a sign, and a number is a simple quantitative abstraction. A trillion is a number, and not a number at all, and therefore cannot be the largest number in the world. A trillion can be called the largest number in the world, and that is purely nominally, since numbers can be counted ad infinitum. The number of digits is strictly limited - from 0 to 9.

It should also be remembered that the numerals and numbers of different number systems do not coincide, as we saw from the examples with Arabic and Roman numerals and numerals. This happens because numbers and numbers are simple concepts that are invented by man himself. Therefore, a number in one number system can easily be a number in another and vice versa.

Thus, the largest number is innumerable, because it can continue to be added indefinitely from digits. As for the numbers themselves, in the generally accepted system, 9 is considered the largest number.

June 17th, 2015

“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 what are the most big numbers 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. The 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 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 former English and Spanish colonies. The names of numbers in this system are built like this: like this: the suffix -million is added to the Latin numeral, the next number (1000 times larger) is built according to the principle - the same Latin numeral, but the suffix - billion. That is, after a trillion in the English system there is a trillion, and only then a quadrillion, followed by a quadrillion, etc. Thus, a quadrillion according to the English and American systems is absolutely different numbers! You can find out the number of zeros in a number written according to the English system and ending with the suffix -million, using the formula 6 x + 3 (where x is a Latin numeral) and using the formula 6 x + 6 for numbers ending in - billion.

From the English system only the number billion (10 9) passed into the Russian language, which would still be more correct to be called as the Americans call it - a billion, since we have adopted exactly American system. But who in our country does anything according to the rules! ;-) By the way, sometimes the word trillion is used in Russian (you can see this for yourself by running a search in Google or Yandex) and, apparently, it means 1000 trillion, i.e. quadrillion.

In addition to numbers written using Latin prefixes according to the American or English system, so-called non-system numbers are also known, i.e. numbers that have their own names without any Latin prefixes. There are several such numbers, but I will tell you more about them a little later.

Let's return to writing using Latin numerals. It would seem that they can write down numbers to infinity, but this is not entirely true. Now I will explain why. Let's first see what the numbers from 1 to 10 33 are called:

And now the question arises, what next. What's behind the decillion? In principle, it is possible, of course, by combining prefixes to generate such monsters as: andecillion, duodecillion, tredecillion, quattordecillion, quindecillion, sexdecillion, septemdecillion, octodecillion and novemdecillion, but these will already be compound names, and we were interested in 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 from 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 trademark, 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 complicated 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 limit value, known as Graham's number, first used in 1977 to prove an estimate in Ramsey theory. It is related to 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 using the Moser system. Therefore, we will have to explain this system too. In principle, there is nothing complicated about it either. Donald Knuth (yes, yes, this is the same Knuth who wrote “The Art of Programming” and created the TeX editor) came up with the concept of superpower, which he proposed to write with arrows pointing upward:

IN general view it looks like this:

I think everything is clear, so let’s return to Graham’s number. Graham proposed so-called G-numbers:

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. Oh, here you go

Countless different numbers surround us every day. Surely many people have at least once wondered what number is considered the largest. You can simply say to a child that this is a million, but adults understand perfectly well that other numbers follow a million. For example, all you have to do is add one to a number each time, and it will become larger and larger - this happens ad infinitum. But if you look at the numbers that have names, you can find out what the largest number in the world is called.

The appearance of number names: what methods are used?

Today there are 2 systems according to which names are given to numbers - American and English. The first is quite simple, and the second is the most common throughout the world. The American one allows you to give names to large numbers as follows: first, the ordinal number in Latin is indicated, and then the suffix “million” is added (the exception here is million, meaning a thousand). This system is used by Americans, French, Canadians, and it is also used in our country.

English is widely used in England and Spain. According to it, numbers are named as follows: the numeral in Latin is “plus” with the suffix “illion”, and the next (a thousand times larger) number is “plus” “billion”. For example, the trillion comes first, the trillion comes after it, the quadrillion comes after the quadrillion, etc.

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

Extra-system numbers

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

You can start considering them with a number called a myriad. It is defined as one hundred hundreds (10000). But according to its intended purpose, this word is not used, but is used as an indication of an innumerable multitude. Even Dahl's dictionary will kindly provide a definition of such a number.

Next after the myriad is googol, denoting 10 to the power of 100. This name was first used in 1938 by American mathematician E. Kasner, who noted that this name was invented by his nephew.

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

Even larger compared to the googolplex is the Skuse number (e to the power of e to the power of e79), proposed by Skuse when proving the Rimmann hypothesis about prime numbers(1933). There is another Skuse number, but it is used when the Rimmann hypothesis is not true. Which one is greater is quite difficult to say, especially when it comes to high degrees. However, this number, despite its “hugeness,” cannot be considered the very best of all those that have their own names.

And the leader among the largest numbers in the world is the Graham number (G64). It was used for the first time to carry out proofs in the field of mathematical science (1977).

When we're talking about about such a number, you need to know that you cannot do without a special 64-level system created by Knuth - the reason for this is the connection of the number G with bichromatic hypercubes. Knuth invented the superdegree, and in order to make it convenient to record it, he proposed the use of up arrows. So we found out what the largest number in the world is called. It is worth noting that this number G was included in the pages of the famous Book of Records.

Once upon a time in childhood, we learned to count to ten, then to a hundred, then to a thousand. So what's the biggest number you know? A thousand, a million, a billion, a trillion... And then? Petallion, someone will say, and he will be wrong, because he confuses the SI prefix with a completely different concept.

In fact, the question is not as simple as it seems at first glance. Firstly, we are talking about naming the names of powers of a thousand. And here, the first nuance that many know from American films is that they call our billion a billion.

Further, there are two types of scales - long and short. In our country, a short scale is used. In this scale, at each step the mantissa increases by three orders of magnitude, i.e. multiply by a thousand - thousand 10 3, million 10 6, billion/billion 10 9, trillion (10 12). In the long scale, after a billion 10 9 there is a billion 10 12, and subsequently the mantissa increases by six orders of magnitude, and the next number, which is called a trillion, already means 10 18.

But let's return to our native scale. Want to know what comes after a trillion? Please:

10 3 thousand
10 6 million
10 9 billion
10 12 trillion
10 15 quadrillion
10 18 quintillion
10 21 sextillion
10 24 septillion
10 27 octillion
10 30 nonillion
10 33 decillion
10 36 undecillion
10 39 dodecillion
10 42 tredecillion
10 45 quattoordecillion
10 48 quindecillion
10 51 cedecillion
10 54 septdecillion
10 57 duodevigintillion
10 60 undevigintillion
10 63 vigintillion
10 66 anvigintillion
10 69 duovigintillion
10 72 trevigintillion
10 75 quattorvigintillion
10 78 quinvigintillion
10 81 sexvigintillion
10 84 septemvigintillion
10 87 octovigintillion
10 90 novemvigintillion
10 93 trigintillion
10 96 antigintillion

At this number, our short scale cannot stand it, and subsequently the mantis increases progressively.

10 100 googol
10,123 quadragintillion
10,153 quinquagintillion
10,183 sexagintillion
10,213 septuagintillion
10,243 octogintillion
10,273 nonagintillion
10,303 centillion
10,306 centunillion
10,309 centullion
10,312 centtrillion
10,315 centquadrillion
10,402 centretrigintillion
10,603 decentillion
10,903 trcentillion
10 1203 quadringentillion
10 1503 quingentillion
10 1803 sescentillion
10 2103 septingentillion
10 2403 oxtingentillion
10 2703 nongentillion
10 3003 million
10 6003 duo-million
10 9003 three million
10 3000003 mimiliaillion
10 6000003 duomimiliaillion
10 10 100 googolplex
10 3×n+3 zillion

Google(from the English googol) - a number in the decimal number system represented by a unit followed by 100 zeros:
10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
In 1938, American mathematician Edward Kasner (1878-1955) was walking in the park with his two nephews and discussing large numbers with them. During the conversation, we talked about a number with a hundred zeros, which did not have its own name. One of the nephews, nine-year-old Milton Sirotta, suggested calling this number “googol.” In 1940, Edward Kasner, together with James Newman, wrote the popular science book “Mathematics and Imagination” (“New Names in Mathematics”), where he told mathematics lovers about the googol number.
The term "googol" does not have a serious theoretical and practical significance. Kasner proposed it to illustrate the difference between an unimaginably large number and infinity, and the term is sometimes used in mathematics teaching for this purpose.

Googolplex(from the English googolplex) - a number represented by a unit with a googol of zeros. Like googol, the term "googolplex" was coined by American mathematician Edward Kasner and his nephew Milton Sirotta.
The number of googols is greater than the number of all particles in the part of the universe known to us, which ranges from 1079 to 1081. Thus, the number googolplex, consisting of (googol + 1) digits, cannot be written down in the classical “decimal” form, even if all matter in the known parts of the universe turned into paper and ink or computer disk space.

Zillion(eng. zillion) - common name for very large numbers.

This term does not have a strict mathematical definition. In 1996, Conway (eng. J. H. Conway) and Guy (eng. R. K. Guy) in their book English. The Book of Numbers defined the nth power zillion as 10 3×n+3 for the short scale number naming system.

The appearance of number names: what methods are used?

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

Extra-system numbers

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

Next after the myriad is googol, denoting 10 to the power of 100. This name was first used in 1938 by American mathematician E. Kasner, who noted that this name was invented by his nephew.

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

Even larger than the googolplex is the Skuse number (e to the power of e to the power of e79), proposed by Skuse in his proof of the Rimmann conjecture about prime numbers (1933). There is another Skuse number, but it is used when the Rimmann hypothesis is not true. Which one is greater is quite difficult to say, especially when it comes to large degrees. However, this number, despite its “hugeness,” cannot be considered the very best of all those that have their own names.

And the leader among the largest numbers in the world is the Graham number (G64). It was used for the first time to carry out proofs in the field of mathematical science (1977).

When it comes to such a number, you need to know that you cannot do without a special 64-level system created by Knuth - the reason for this is the connection of the number G with bichromatic hypercubes. Knuth invented the superdegree, and in order to make it convenient to record it, he proposed the use of up arrows. So we found out what the largest number in the world is called. It is worth noting that this number G was included in the pages of the famous Book of Records.