Big numbers have big names. What are big numbers called?

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. It is simply worth adding one to the largest number, as it will no longer be the largest. This procedure can be continued indefinitely. Those. it turns out there is no largest number in the world? Is it infinity?

But if you ask yourself: what is the largest number that exists, and what is its own name? Now we all know...

There are two systems for naming numbers - American and English.

The American system is built quite simply. 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 magnifying suffix -million (see table). So 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: a 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 comes a trillion, and only then a quadrillion, followed by a quadrillion, and so on. Thus, a quadrillion according to the English and American systems are completely different numbers! You can find out the number of zeros in a number written in the English system and ending with the suffix -million using the formula 6 x + 3 (where x is a Latin numeral) and using the formula 6 x + 6 for numbers ending in -billion.

Only the number billion (10 9) passed from the English system into the Russian language, which, nevertheless, would be more correct to call it the way the Americans call it - a billion, since we have adopted the American system. 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 in the American or English system, the 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. Now I will explain why. First, let's see how the numbers from 1 to 10 33 are called:

And so, now the question arises, what next. What is a 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 - vigintillion (from lat. viginti- twenty), centillion (from lat. percent- one hundred) and a million (from lat. mille- one 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 called centena milia i.e. ten hundred thousand. And now, actually, the table:

Thus, according to a similar system, numbers greater than 10 3003, which would have its own, non-compound name, cannot be obtained! But nevertheless, numbers greater than a million are known - these are the same off-system numbers. Finally, let's 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. True, this word is outdated and practically not used, but it is curious that the word "myriad" is widely used, which does not mean a certain number at all, but an uncountable, uncountable set of something. It is believed that the word myriad (English 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 fact, the myriad gained fame precisely thanks to the Greeks. Myriad was the name for 10,000, and there were no names for numbers over ten thousand. However, in the note "Psammit" (i.e., the calculus of sand), Archimedes showed how one can systematically build 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 diameters) no more than 1063 grains of sand would fit (in our notation). It is curious that modern calculations of the number of atoms in the visible universe lead to the number 1067 (only a myriad times more). The names of the numbers Archimedes suggested are as follows:
1 myriad = 104.
1 di-myriad = myriad myriad = 108.
1 tri-myriad = di-myriad di-myriad = 1016.
1 tetra-myriad = three-myriad three-myriad = 1032.
etc.

Googol (from the English googol) is the number ten to the hundredth power, that is, one with 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, his nine-year-old nephew Milton Sirotta suggested calling a large number "googol". This number became well-known thanks to the Google search engine named after him. Note that "Google" is a trademark and googol is a number.

Edward Kasner.

On the Internet, you can often find mention that Google is the largest number in the world, but this is not so ...

In the well-known Buddhist treatise Jaina Sutra, dating back to 100 BC, the number Asankheya (from the Chinese. asentzi- incalculable), equal to 10 140. It is believed that this number is equal to the number of cosmic cycles necessary to gain nirvana.

Googolplex (English) googolplex) - a number also invented by Kasner with his nephew and meaning one with a googol of zeros, that is, 10 10100. Here 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. 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, 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 power of 79, i.e. eee79. Later, Riele (te Riele, H. J. J. "On the Sign of the Difference P(x)-Li(x)." Math. Comput. 48, 323-328, 1987) reduced Skuse's number to ee27/4, which is approximately equal to 8.185 10370. It is clear that since the value of the Skewes number depends on the number e, then it is not an integer, so we will not consider it, otherwise we would have to recall other non-natural numbers - the number pi, the number e, etc.

But it should be noted that there is a second Skewes number, which in mathematics is denoted as Sk2, which is even larger than the first Skewes number (Sk1). The second Skuse number was introduced by J. Skuse in the same article to denote a number for which the Riemann hypothesis is not valid. Sk2 is 101010103, which is 1010101000 .

As you understand, the more degrees there are, the more difficult it is to understand which of the numbers is greater. For example, looking at the Skewes numbers, without special calculations, it is almost impossible to understand which of these two numbers is larger. Thus, for superlarge 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, what a page! They won't even fit into 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 Stenhaus (H. Steinhaus. Mathematical Snapshots, 3rd edn. 1983), which is quite simple. Steinhouse suggested writing large numbers inside geometric shapes - a triangle, a square and a circle:

Steinhouse came up with two new super-large numbers. He called 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 necessary to write numbers much larger than a megiston, difficulties and inconveniences arose, since many circles had to be drawn one inside the other. Moser suggested drawing not circles after squares, but pentagons, then hexagons, and so on. He also proposed a formal notation for these polygons, so that numbers could be written without drawing complex patterns. Moser notation looks like this:

- n[k+1] = "n in n k-gons" = n[k]n.

Thus, according to Moser's notation, Steinhouse's mega is written as 2, and megiston as 10. In addition, Leo Moser suggested 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 the Moser's number, or simply as a moser.

But the moser is not the largest number. The largest number ever used in a mathematical proof is the limiting value known as Graham's number, first used in 1977 in the proof of one estimate in Ramsey theory. It is associated with bichromatic hypercubes and cannot be expressed without the special 64-level system of special mathematical symbols introduced by Knuth in 1976.

Unfortunately, the number written in the Knuth notation cannot be translated into the Moser notation. Therefore, this system will also have to be explained. 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 superpower, which he proposed to write with arrows pointing up:

In general, it looks like this:

I think that everything is clear, so let's get back to Graham's number. Graham proposed the so-called G-numbers:

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 listed in the Guinness Book of Records.

So there are numbers bigger than Graham's number? There is, of course, the Graham number + 1 for starters. As for the significant number… well, there are some fiendishly difficult areas of mathematics (particularly the field known as combinatorics) and computer science where numbers even larger than the Graham number occur. But we have almost reached the limit of what can be rationally and clearly explained.

sources http://ctac.livejournal.com/23807.html
http://www.uznayvse.ru/interesting-facts/samoe-bolshoe-chislo.html
http://www.vokrugsveta.ru/quiz/310/

https://masterok.livejournal.com/4481720.html

John Sommer

Put zeros after any number or multiply with tens raised to an arbitrarily large power. It won't seem like much. It will seem like a lot. But naked recordings, after all, are not too impressive. The heaping zeros in the humanities cause not so much surprise as a slight yawn. In any case, to any largest number in the world that you can imagine, you can always add one more ... And the number will come out even more.

And yet, are there words in Russian or any other language for designating very large numbers? Those that are more than a million, billion, trillion, billion? And in general, a billion is how much?

It turns out that there are two systems for naming numbers. But not Arabic, Egyptian, or any other ancient civilizations, but American and English.

In the American system numbers are called like this: the Latin numeral is taken + - million (suffix). Thus, the numbers are obtained:

Trillion - 1,000,000,000,000 (12 zeros)

Quadrillion - 1,000,000,000,000,000 (15 zeros)

Quintillion - 1 and 18 zeros

Sextillion - 1 and 21 zero

Septillion - 1 and 24 zero

octillion - 1 followed by 27 zeros

Nonillion - 1 and 30 zeros

Decillion - 1 and 33 zero

The formula is simple: 3 x + 3 (x is a Latin numeral)

In theory, there should also be numbers anilion (unus in Latin - one) and duolion (duo - two), but, in my opinion, such names are not used at all.

English naming system more widespread.

Here, too, the Latin numeral is taken and the suffix -million is added to it. However, the name of the next number, which is 1,000 times greater than the previous one, is formed using the same Latin number and the suffix - billion. I mean:

Trillion - 1 and 21 zero (in the American system - sextillion!)

Trillion - 1 and 24 zeros (in the American system - septillion)

Quadrillion - 1 and 27 zeros

Quadribillion - 1 followed by 30 zeros

Quintillion - 1 and 33 zero

Quinilliard - 1 followed by 36 zeros

Sextillion - 1 followed by 39 zeros

Sextillion - 1 and 42 zero

The formulas for counting the number of zeros are:

For numbers ending in - illion - 6 x+3

For numbers ending in - billion - 6 x+6

As you can see, confusion is possible. But let's not be afraid!

In Russia, the American system for naming numbers has been adopted. From the English system, we borrowed the name of the number "billion" - 1,000,000,000 \u003d 10 9

And where is the "cherished" billion? - Why, a billion is a billion! American style. And although we use the American system, we took the "billion" from the English one.

Using the Latin names of numbers and the American system, let's call the numbers:

- vigintillion- 1 and 63 zeros

- centillion- 1 and 303 zeros

- Million- one and 3003 zeros! Oh-hoo...

But this, it turns out, is not all. There are also off-system numbers.

And the first one is probably myriad- one hundred hundreds = 10,000

googol(it is in honor of him that the famous search engine is named) - one and one hundred zeros

In one of the Buddhist treatises, a number is named asankhiya- one and one hundred and forty zeros!

Number name googolplex(like Google) was invented by the English mathematician Edward Kasner and his nine-year-old nephew - unit c - dear mother! - googol zeros!!!

But that's not all...

The mathematician Skewes named the Skewes number after himself. It means e to the extent e to the extent e to the power of 79, i.e. e e e 79

And then a big problem arose. You can think of names for numbers. But how to write them down? The number of degrees of degrees of degrees is already such that it simply does not fit on the page! :)

And then some mathematicians began to write numbers in geometric figures. And the first, they say, such a method of recording was invented by the outstanding writer and thinker Daniil Ivanovich Kharms.

And yet, what is the BIGGEST NUMBER IN THE WORLD? - It is called STASPLEX and is equal to G 100,

where G is the Graham number, the largest number ever used in mathematical proofs.

This number - stasplex - was invented by a wonderful person, our compatriot Stas Kozlovsky, to LJ to which I address you :) - ctac

June 17th, 2015

“I see clumps of vague numbers lurking out there in the dark, behind the little spot of light that the mind candle gives. They whisper to each other; talking about who knows what. Perhaps they do not like us very much for capturing their little brothers with our minds. Or maybe they just lead an unambiguous numerical way of life, out there, beyond our understanding.''
Douglas Ray

We continue ours. Today we have numbers...

But if you ask yourself: what is the largest number that exists, and what is its own name?

Now we all know...

There are two systems for naming numbers - American and English.

Only the number billion (10 9 ) passed from the English system into the Russian language, which, nevertheless, would be more correct to call it the way the Americans call it - a billion, since we have adopted the American system. 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.

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. Now I will explain why. Let's first see how the numbers from 1 to 10 33 are called:

And so, now the question arises, what next. What is a 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 - vigintillion (from lat.viginti- twenty), centillion (from lat.percent- one hundred) and a million (from lat.mille- one 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 calledcentena miliai.e. ten hundred thousand. And now, actually, the table:

Thus, according to a similar system, numbers are greater than 10 3003 , which would have its own, non-compound name, it is impossible to get! But nevertheless, numbers greater than a million are known - these are the very non-systemic numbers. Finally, let's talk about them.

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, and there were no names for numbers over ten thousand. However, in the note "Psammit" (i.e., the calculus of sand), Archimedes showed how one can systematically build 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) 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 (only a myriad of times more). The names of the numbers Archimedes suggested are as follows:
1 myriad = 10 4 .
1 di-myriad = myriad myriad = 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 with 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, 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 mention that - but this is not so ...

Googolplex (English) googolplex) - a number also invented by Kasner with his nephew and meaning one with a googol of zeros, that is, 10 10100 . Here 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. 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 larger than the googolplex number, Skewes' number was proposed by Skewes in 1933 (Skewes. J. London Math. soc. 8, 277-283, 1933.) in proving the Riemann conjecture concerning primes. It means e to the extent e to the extent e to the power of 79, i.e. ee e 79 . Later, Riele (te Riele, H. J. J. "On the Sign of the Difference P(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 Skewes number depends on the number e, then it is not an integer, so we will not consider it, otherwise we would have to recall other non-natural numbers - the number pi, the number e, etc.

But it should be noted that there is a second Skewes number, which in mathematics is denoted as Sk2 , which is even larger than the first Skewes number (Sk1 ). Skuse's second 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 , i.e. 1010 101000 .

Steinhouse came up with two new super-large numbers. He called the number - Mega, and the number - Megiston.

In general, it looks like this:

I think that everything is clear, so let's get 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 superpower arrows is 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 listed in the Guinness Book of Records. And here

The question "What is the largest number in the world?" is, to say the least, incorrect. There are both different systems of calculus - decimal, binary and hexadecimal, as well as various categories of numbers - semi-simple and prime, the latter being divided into legal and illegal. In addition, there are the numbers of Skewes (Skewes "number), Steinhaus and other mathematicians who either jokingly or seriously invent and put to the public such exotics as "megiston" or "moser".

What is the largest decimal number in the world

From the decimal system, most "non-mathematicians" are well aware of the million, billion and trillion. Moreover, if a million among Russians is mainly associated with a dollar bribe that can be carried away in a suitcase, then where to shove a billion (not to mention a trillion) North American banknotes - most do not have enough imagination. However, in the theory of large numbers, there are such concepts as quadrillion (ten to the fifteenth power - 1015), sextillion (1021) and octillion (1027).

In English, the most widely used decimal system in the world, the maximum number is decillion - 1033.

In 1938, in connection with the development of applied mathematics and the expansion of the micro- and macrocosms, Professor of Columbia University (USA), Edward Kasner published on the pages of the journal "Scripta Mathematica" the proposal of his nine-year-old nephew to use the decimal system as the most a large number "googol" ("googol") - representing ten to the hundredth power (10100), which on paper is expressed as a unit with one hundred zeros. However, they did not stop there and a few years later they proposed to put into circulation the new largest number in the world - "googolplex" (googolplex), which is ten raised to the tenth power and again raised to the hundredth power - (1010) 100, expressed by one, to which a googol of zeros is assigned to the right. However, for the majority of even professional mathematicians, both "googol" and "googolplex" are of purely speculative interest, and it is unlikely that they can be applied to anything in everyday practice.

exotic numbers

What is the largest number in the world among prime numbers - those that can only be divided by themselves and by one. One of the first to record the largest prime number, 2,147,483,647, was the great mathematician Leonhard Euler. As of January 2016, this number is an expression calculated as 274 207 281 - 1.

10 to 3003 degrees

The debate about what is the largest figure in the world is ongoing. Different calculus systems offer different options and people do not know what to believe, and which number is considered the largest.

This question has interested scientists since the time of the Roman Empire. The biggest snag lies in the definition of what is a "number" and what is a "number". At one time, people for a long time considered the largest number to be decillion, that is, 10 to the 33rd power. But, after scientists began to actively study the American and English metric systems, it was found that the largest number in the world is 10 to the power of 3003 - a million. People in everyday life believe that the biggest number is a trillion. Moreover, this is quite formal, because after a trillion, names are simply not given, because the account starts too complicated. However, purely theoretically, the number of zeros can be added indefinitely. Therefore, to imagine even a purely visual trillion and what follows it is almost impossible.

in roman numerals

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

The important thing is that numbers are used as constituent numbers, but not only that. The figure, however, is the same number if we are talking about some things, counting them from zero to nine. Such a system of signs applies not only to the Arabic numerals familiar to us, but also to the Roman I, V, X, L, C, D, M. These are Roman numerals. On the other hand, V I I I is a Roman number. In Arabic reckoning, 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, and therefore cannot be the largest number in the world. A trillion can be called the largest number in the world, and then purely nominally, since numbers can be counted to infinity. The number of digits is strictly limited - from 0 to 9.

It should also be remembered that the numbers and numbers of different calculus systems do not match, as we saw from the examples with Arabic and Roman numbers and numerals. This is because numbers and numbers are simple concepts that a person himself invents. Therefore, the number of one system of calculation can easily be the number of another and vice versa.

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

Portal for the student. Self-training

What is the largest decimal number in the world

exotic numbers

RELATED ARTICLES