A child asked today: “What is the name of the most big number in the world?" Interesting question. I went online and on the first line of Yandex I found a detailed article in LiveJournal. Everything is described there in detail. It turns out that there are two systems for naming numbers: English and American. And, for example, a quadrillion according to the English and American systems is completely different numbers! composite number is
Million = 10 to the 3003rd power.
As a result, the son came to a completely reasonable conclusion that it is possible to count endlessly.
Original taken from ctac in The largest number in the world
As a child, I was tormented by the question of what kind of
the largest number, and I was tormented by this stupid
a question for almost everyone. Having learned the number
million, I asked if there was a higher number
million. Billion? How about more than a billion? Trillion?
How about more than a trillion? Finally, someone smart was found
who explained to me that the question is stupid, because
it is enough just to add to itself
a large number is one, and it turns out that it
has never been the biggest since there are
the number is even greater.
And so, many years later, I decided to ask myself something else
question, namely: what is the most
a large number that has its own
Name? Fortunately, now there is an Internet and it’s puzzling
they can patient search engines that do not
they will call my questions idiotic ;-).
Actually, that's what I did, and this is the result
found out.
| Number | Latin name | Russian prefix |
| 1 | unus | an- |
| 2 | duo | duo- |
| 3 | tres | three- |
| 4 | quattuor | quadri- |
| 5 | quinque | quinti- |
| 6 | sex | sexty |
| 7 | septem | septi- |
| 8 | octo | octi- |
| 9 | novem | noni- |
| 10 | decem | deci- |
There are two systems for naming numbers −
American and English.
The American system is built quite
Just. All titles 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 thousand (lat. mille)
and the magnifying suffix -illion (see table).
This is how the numbers come out - trillion, quadrillion,
quintillion, sextillion, septillion, octillion,
nonillion and decillion. American system
used in the USA, Canada, France and Russia.
Find out the number of zeros in a number written by
American system, using a simple formula
3 x+3 (where x is a Latin numeral).
The English system of naming the most
widespread in the world. It is used, for example, in
Great Britain and Spain, as well as most
former English and spanish colonies. Titles
numbers in this system are constructed like this: like this: to
a suffix is added to the Latin numeral
-million, the next number (1000 times larger)
is built on the same principle
Latin numeral, but the suffix is -billion.
That is, after a trillion in the English system
there is a trillion, and only then a quadrillion, after
followed by quadrillion, etc. So
Thus, quadrillion in English and
American systems are completely different
numbers! Find out the number of zeros in a number
written according to the English system and
ending with the suffix -illion, you can
formula 6 x+3 (where x is a Latin numeral) and
using the formula 6 x + 6 for numbers ending in
-billion
From English system passed into Russian language
only the number billion (10 9), which is still
it would be more correct to call it what it is called
Americans - a billion, as we have adopted
exactly American system. But who is in our
the country is doing something according to the rules! ;-) By the way,
sometimes in Russian they use the word
trillion (you can see this for yourself,
by running a search in Google or Yandex) and it means, judging by
in total, 1000 trillion, i.e. quadrillion.
In addition to numbers written using Latin
prefixes according to the American or English system,
the so-called non-system numbers are also known,
those. numbers that have their own
names without any Latin prefixes. Such
There are several numbers, but I will tell you more about them
I'll tell you a little later.
Let's return to recording using Latin
numerals. It would seem that they can
write down numbers to infinity, but this is not
quite like that. Now I will explain why. Let's see for
beginning of what the numbers from 1 to 10 33 are called:
| Name | Number |
| Unit | 10 0 |
| Ten | 10 1 |
| One hundred | 10 2 |
| Thousand | 10 3 |
| Million | 10 6 |
| Billion | 10 9 |
| Trillion | 10 12 |
| Quadrillion | 10 15 |
| Quintillion | 10 18 |
| Sextillion | 10 21 |
| Septillion | 10 24 |
| Octillion | 10 27 |
| Quintillion | 10 30 |
| Decillion | 10 33 |
And now the question arises, what next. What
there behind a decillion? In principle, you can, of course,
by combining prefixes to generate such
monsters like: andecillion, duodecillion,
tredecillion, quattordecillion, quindecillion,
sexdecillion, septemdecillion, octodecillion and
newdecillion, but these will already be composite
names, but we were interested specifically
proper names for numbers. Therefore, own
names according to this system, in addition to those indicated above, more
you can only get three
- vigintillion (from lat. viginti —
twenty), centillion (from lat. centum- one hundred) and
million million (from lat. mille- thousand). More
thousands of proper names for numbers among the Romans
did not have (all numbers over a thousand they had
compound). For example, a million (1,000,000) Romans
called decies centena milia, that is, "ten hundred
thousand." And now, actually, the table:
Thus, according to a similar number system
greater than 10 3003 which would have
get your own, non-compound name
impossible! But still the numbers are higher
million are known - these are the same
non-system numbers. Let's finally talk about them.
| Name | Number |
| Myriad | 10 4 |
| 10 100 | |
| Asankheya | 10 140 |
| Googolplex | 10 10 100 |
| Second Skewes number | 10 10 10 1000 |
| Mega | 2 (in Moser notation) |
| Megiston | 10 (in Moser notation) |
| Moser | 2 (in Moser notation) |
| Graham number | G 63 (in Graham notation) |
| Stasplex | G 100 (in Graham notation) |
The smallest such number is myriad
(it’s even in Dahl’s dictionary), which means
a hundred hundreds, that is, 10,000. This word, however,
outdated and practically not used, but
It's interesting that the word is widely used
"myriads", which does not mean at all
a certain number, and countless, uncountable
a lot of something. It is believed that the word myriad
(English: myriad) came to European languages from ancient
Egypt.
Google(from English googol) is the number ten in
hundredth power, that is, one followed by one hundred zeros. ABOUT
"googole" was first written in 1938 in an article
"New Names in Mathematics" in the January issue of the magazine
Scripta Mathematica American mathematician Edward Kasner
(Edward Kasner). According to him, call it "googol"
a large number was suggested by his nine-year-old
nephew Milton Sirotta.
This number became generally known thanks to
the search engine named after him Google. note that
"Google" is a brand name and googol is a number.
In the famous Buddhist treatise Jaina Sutra,
dating back to 100 BC, there is a number asankheya
(from China asenzi- uncountable), equal to 10 140.
It is believed that this number is equal to the number
cosmic cycles necessary to obtain
nirvana.
Googolplex(English) googolplex) - number also
invented by Kasner with his nephew and
meaning one followed by a googol of zeros, that is, 10 10 100.
This is how Kasner himself describes this “discovery”:
Words of wisdom are spoken by children at least as often as by scientists. The name
"googol" was invented by a child (Dr. Kasner's nine-year-old nephew) who was
asked to think up a name for a very big number, namely, 1 with a hundred zeros after it.
He was very certain that this number was not infinite, and the before equally certain that
it had to have a name. At the same time that he suggested "googol" he gave a
name for a still larger number: "Googolplex." A googolplex is much larger than a
googol, but is still finite, as the inventor of the name was quick to point out.
Mathematics and the Imagination(1940) by Kasner and James R.
Newman.
An even larger number than a googolplex is a number
Skewes "number" was proposed by Skewes in 1933
year (Skewes. J. London Math. Soc. 8
, 277-283, 1933.) with
proof of hypothesis
Riemann concerning prime numbers. It
means e to a degree e to a degree e V
degrees 79, that is, e e 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 the Skuse number to e e 27/4,
which is approximately equal to 8.185 10 370. Understandable
the point is that since the value of the Skewes number depends on
numbers e, then it is not whole, therefore
we will not consider it, otherwise we would have to
remember other non-natural numbers - number
pi, number e, Avogadro's number, etc.
But it should be noted that there is a second number
Skuse, which in mathematics is denoted as Sk 2,
which is even greater than the first Skuse number (Sk 1).
Second Skewes number, was introduced by J.
Skuse in the same article to denote the number, up to
which the Riemann hypothesis is true. Sk 2
equals 10 10 10 10 3, that is, 10 10 10 1000
.
As you understand, the greater the number of degrees,
the more difficult it is to understand which number is greater.
For example, looking at the Skewes numbers, without
special calculations are almost impossible
understand which of these two numbers is greater. So
Thus, for super-large numbers use
degrees becomes uncomfortable. Moreover, you can
come up with such numbers (and they have already been invented) when
degrees of degrees just don't fit on the page.
Yes, that's on the page! They won't fit even in a book,
the size of the entire Universe! In this case it gets up
The question is how to write them down. The problem is how you
you understand, it is solvable, and mathematicians have developed
several principles for writing such numbers.
True, every mathematician who asked this question
problem I came up with my own way of recording that
led to the existence of several unrelated
with each other, ways to write numbers are
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 extra-large
numbers. He named the number - Mega, and the number is Megiston.
Mathematician Leo Moser refined the notation
Stenhouse, which was limited to what if
it was necessary to write down much larger numbers
megiston, difficulties and inconveniences arose, so
how I had to draw many circles alone
inside another. Moser suggested after squares
draw pentagons rather than circles, then
hexagons and so on. He also suggested
formal notation for these polygons,
so you can write numbers without drawing
complex drawings. 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 suggested
call a polygon with the same number of sides
mega - megagon. And suggested the number "2 in
Megagone", that is, 2. This number became
known as Moser's number or simply
How moser.
But Moser is not the largest number. The biggest
number ever used in
mathematical proof, is
limit value known as Graham number
(Graham's number), first used in 1977
proof of one estimate in Ramsey theory. It
related to bichromatic hypercubes and not
can be expressed without special 64-level
special systems mathematical symbols,
introduced by Knuth in 1976.
Unfortunately, the number written in Knuth notation
cannot be converted into a Moser entry.
Therefore, we will have to explain this system too. IN
In principle, there is nothing complicated about it either. Donald
Knut (yes, yes, this is the same Knut who wrote
"The Art of Programming" and created
TeX editor) came up with the concept of superpower,
which he proposed to write down with arrows,
upward:
IN general view it looks like this:
I think everything is clear, so let's go back to the number
Graham. Graham proposed so-called G-numbers:
The number G 63 began to be called number
Graham(it is often designated simply as G).
This number is the largest known in
number in the world and is even included in the Book of Records
Guinness". Ah, that Graham number is greater than the number
Moser.
P.S. To bring great benefit
to all mankind and to be glorified throughout the ages, I
I decided to come up with and name the biggest
number. This number will be called stasplex And
it is equal to the number G 100. Remember it and when
your children will ask what is the biggest
number in the world, tell them what this number is called stasplex.
Answering such a difficult question as to what it is, the largest number in the world, it should first be noted that today there are 2 accepted ways of naming numbers - English and American. According to the English system, the suffixes -billion or -million are added to each large number in order, resulting in the numbers million, billion, trillion, trillion, and so on. If we proceed from the American system, then according to it, the suffix -million must be added to each large number, resulting in the formation of the numbers trillion, quadrillion and large ones. It should also be noted here that the English number system is more common in modern world, and the numbers in it are quite sufficient for the normal functioning of all systems of our world.
Of course, the answer to the question about the largest number from a logical point of view cannot be unambiguous, because if you just add one to each subsequent digit, you get a new larger number, therefore, this process has no limit. However, oddly enough, there is still the largest number in the world and it is listed in the Guinness Book of Records.
Graham's number is the largest number in the world
It is this number that is recognized in the world as the largest in the Book of Records, but it is very difficult to explain what it is and how large it is. IN in a general sense, these are triplets multiplied together, resulting in a number that is 64 orders of magnitude higher than the point of understanding of each person. As a result, we can only give the final 50 digits of Graham's number – 0322234872396701848518 64390591045756272 62464195387.
Googol number 
The history of this number is not as complex as the one mentioned above. Thus, the American mathematician Edward Kasner, talking with his nephews about large numbers, could not answer the question of how to name numbers that have 100 zeros or more. A resourceful nephew suggested his own name for such numbers - googol. It should be noted that large practical significance this number does not, however, it is sometimes used in mathematics to express infinity.
Googleplex 
This number was also invented by mathematician Edward Kasner and his nephew Milton Sirotta. In a general sense, it represents a number to the tenth power of a googol. Answering the question of many inquisitive people, how many zeros are in the Googleplex, it is worth noting that in the classical version there is no way to represent this number, even if you cover all the paper on the planet with classical zeros.
Skewes number 
Another contender for the title of largest number is the Skewes number, proven by John Littwood in 1914. According to the evidence given, this number is approximately 8.185 10370.
Moser number 
This method of naming very large numbers was invented by Hugo Steinhaus, who proposed denoting them by polygons. As a result of three mathematical operations performed, the number 2 is born in a megagon (a polygon with mega sides).
As you can already see, a huge number of mathematicians have made efforts to find it - the largest number in the world. The extent to which these attempts were successful, of course, is not for us to judge, however, it must be noted that the real applicability of such numbers is doubtful, because they are not even amenable to human understanding. In addition, there will always be a number that will be greater if you perform a very easy mathematical operation +1.
Have you ever thought how many zeros there are in one million? This is a pretty simple question. What about a billion or a trillion? One followed by nine zeros (1000000000) - what is the name of the number?
A short list of numbers and their quantitative designation
- Ten (1 zero).
- One hundred (2 zeros).
- One thousand (3 zeros).
- Ten thousand (4 zeros).
- One hundred thousand (5 zeros).
- Million (6 zeros).
- Billion (9 zeros).
- Trillion (12 zeros).
- Quadrillion (15 zeros).
- Quintilion (18 zeros).
- Sextillion (21 zeros).
- Septillion (24 zeros).
- Octalion (27 zeros).
- Nonalion (30 zeros).
- Decalion (33 zeros).
Grouping of zeros
1000000000 - what is the name of a number that has 9 zeros? This is a billion. For convenience, large numbers are usually grouped into sets of three, separated from each other by a space or punctuation marks such as a comma or period.
This is done to make it easier to read and understand. quantitative value. For example, what is the name of the number 1000000000? In this form, it’s worth straining a little and doing the math. And if you write 1,000,000,000, then the task immediately becomes visually easier, since you need to count not zeros, but triples of zeros.
Numbers with a lot of zeros
The most popular are million and billion (1000000000). What is the name of a number that has 100 zeros? This is a Googol number, so called by Milton Sirotta. This is a wildly huge amount. Do you think this number is large? Then what about a googolplex, a one followed by a googol of zeros? This figure is so large that it is difficult to come up with a meaning for it. In fact, there is no need for such giants, except to count the number of atoms in the infinite Universe.
Is 1 billion a lot?
There are two measurement scales - short and long. Around the world in science and finance, 1 billion is 1,000 million. This is on a short scale. According to it, this is a number with 9 zeros.
There is also a long scale which is used in some European countries, including in France, and was previously used in the UK (until 1971), where a billion was 1 million millions, that is, one followed by 12 zeros. This gradation is also called the long-term scale. The short scale is now predominant in financial and scientific matters.
Some European languages, such as Swedish, Danish, Portuguese, Spanish, Italian, Dutch, Norwegian, Polish, German, use billion (or billion) in this system. In Russian, a number with 9 zeros is also described for the short scale of a thousand million, and a trillion is a million million. This avoids unnecessary confusion.
Conversational options
In Russian colloquial speech after the events of 1917 - the Great October revolution- and the period of hyperinflation in the early 1920s. 1 billion rubles was called “limard”. And in the dashing 1990s, something new appeared for a billion slang expression"watermelon", a million was called "lemon".
The word "billion" is now used in international level. This natural number, which is depicted in decimal system, like 10 9 (one and 9 zeros). There is also another name - billion, which is not used in Russia and the CIS countries.
Billion = billion?
A word such 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 like Russian Federation, United Kingdom of Great Britain and Northern Ireland, USA, Canada, Greece and Türkiye. In other countries, the concept of a billion means the number 10 12, that is, one followed by 12 zeros. In countries with a “short scale”, including Russia, this figure corresponds to 1 trillion.
Such confusion appeared in France at a time when the formation of such a science as algebra was taking place. Initially, a billion had 12 zeros. However, everything changed after the appearance of the main manual on arithmetic (author Tranchan) in 1558), where a billion is already a number with 9 zeros (a thousand millions).
For several subsequent centuries, these two concepts were used on an equal basis with each other. In the mid-20th century, namely in 1948, France switched to a long scale numerical naming system. In this regard, the short scale, once borrowed from the French, is still different from the one they use today.
Historically, the United Kingdom has used the long-term billion, but since 1974 official statistics The UK used a short-term scale. Since the 1950s, the short-term scale has been increasingly used in the fields of technical writing and journalism, although the long-term scale still persists.
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 of what are the largest numbers is simple. Just add one to the largest number, and it will no longer be the largest. This procedure can be continued indefinitely.
But if you ask the question: what is the largest number that exists, and what is its proper name?
Now we will find out everything...
There are two systems for naming numbers - American and English.
The American system is built quite simply. All names of large numbers are constructed like this: at the beginning there is a Latin ordinal number, and at the end the suffix -million is added to it. An exception is the name "million" which is the name of the number thousand (lat. mille) and the magnifying suffix -illion (see table). This is how we get the numbers trillion, quadrillion, quintillion, sextillion, septillion, octillion, nonillion and decillion. The American system is used in the USA, Canada, France and Russia. You can find out the number of zeros in a number written according to the American system using the simple formula 3 x + 3 (where x is a Latin numeral).
The English naming system is the most common in the world. It is used, for example, in Great Britain and Spain, as well as in most former English and Spanish colonies. The names of numbers in this system are built like this: like this: the suffix -million is added to the Latin numeral, the next number (1000 times larger) is built according to the principle - the same Latin numeral, but the suffix - billion. That is, after a trillion in the English system there is a trillion, and only then a quadrillion, followed by a quadrillion, etc. Thus, a quadrillion according to the English and American systems 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.
Only the number billion (10 9) passed from the English system into the Russian language, which would still be more correct to be called as the Americans call it - billion, since we have adopted the American system. But who in our country does anything according to the rules! ;-) By the way, sometimes the word trillion is used in Russian (you can see this for yourself by running a search in Google or Yandex) and, apparently, it means 1000 trillion, i.e. quadrillion.
In addition to numbers written using Latin prefixes according to the American or English system, so-called non-system numbers are also known, i.e. numbers that have their own names without any Latin prefixes. There are several such numbers, but I will tell you more about them a little later.
Let's return to writing using Latin numerals. It would seem that they can write down numbers to infinity, but this is not entirely true. Now I will explain why. Let's first see what the numbers from 1 to 10 33 are called:
And now the question arises, what next. What's behind the decillion? In principle, it is 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 the proper names of the numbers. Therefore, according to this system, in addition to those indicated above, you can still get only three proper names - vigintillion (from Lat.viginti- twenty), centillion (from lat.centum- one hundred) and million (from lat.mille- thousand). The Romans did not have more than a thousand proper names for numbers (all numbers over a thousand were composite). For example, the Romans called a million (1,000,000)decies centena milia, that is, "ten hundred thousand." And now, actually, the table:
Thus, according to such a system, numbers are greater than 10 3003 , which would have its own, non-compound name is impossible to obtain! But nevertheless, numbers greater than a million are known - these are the same non-systemic numbers. Let's finally talk about them.
The smallest such number is a myriad (it is even in Dahl’s dictionary), which means a hundred hundreds, that is, 10,000. This word, however, is outdated and practically not used, but it is curious that the word “myriads” is widely used, does not mean a definite number at all, but an uncountable, uncountable multitude of something. It is believed that the word myriad came into European languages from ancient Egypt.
Regarding the origin of this number, there are different opinions. Some believe that it originated in Egypt, while others believe that it was born only in Ancient Greece. Be that as it may in fact, the myriad gained fame precisely thanks to the Greeks. Myriad was the name for 10,000, but there were no names for numbers greater than ten thousand. However, in his note “Psammit” (i.e., calculus of sand), Archimedes showed how to systematically construct and name arbitrarily large numbers. In particular, placing 10,000 (myriad) grains of sand in a poppy seed, he finds that in the Universe (a ball with a diameter of a myriad of Earth diameters) there would fit (in our notation) no more than 10 63
grains of sand It is curious that modern calculations of the number of atoms in the visible Universe lead to the number 10 67
(in total a myriad of times more). Archimedes suggested the following names for the numbers:
1 myriad = 10 4 .
1 di-myriad = myriad of myriads = 10 8
.
1 tri-myriad = di-myriad di-myriad = 10 16
.
1 tetra-myriad = three-myriad three-myriad = 10 32
.
etc.
Googol (from the English googol) is the number ten to the hundredth power, that is, one followed by one hundred zeros. The “googol” was first written about in 1938 in the article “New Names in Mathematics” in the January issue of the journal Scripta Mathematica by the American mathematician Edward Kasner. According to him, it was his nine-year-old nephew Milton Sirotta who suggested calling the large number a “googol”. This number became generally known thanks to the search engine named after it. Google. Please note that "Google" is a brand name and googol is a number.
Edward Kasner.
On the Internet you can often find it mentioned that - but this is not true...
In the famous Buddhist treatise Jaina Sutra, dating back to 100 BC, the number asankheya (from Chinese. asenzi- uncountable), equal to 10 140. It is believed that this number is equal to the number of cosmic cycles required to achieve nirvana.
Googolplex (English) googolplex) - a number also invented by Kasner and his nephew and meaning one with a googol of zeros, that is, 10 10100 . This is how Kasner himself describes this “discovery”:
Words of wisdom are spoken by children at least as often as by scientists. The name "googol" was invented by a child (Dr. Kasner's nine-year-old nephew) who was asked to think up a name for a very big number, namely, 1 with a hundred zeros after it. He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. At the same time that he suggested "googol" he gave a name for a still larger number: "A googolplex is much larger than." a googol, but is still finite, as the inventor of the name was quick to point out.
Mathematics and the Imagination(1940) by Kasner and James R. Newman.
An even larger number than the googolplex, the Skewes number, was proposed by Skewes in 1933. J. London Math. Soc. 8, 277-283, 1933.) in proving the Riemann hypothesis concerning prime numbers. It means e to a degree e to a degree e to the power of 79, that is, ee e 79 . Later, te Riele, H. J. J. "On the Sign of the Difference P(x)-Li(x)." Math. Comput. 48, 323-328, 1987) reduced the Skuse number to ee 27/4 , which is approximately equal to 8.185·10 370. It is clear that since the value of the Skuse number depends on the number e, then it is not an integer, so we will not consider it, otherwise we would have to remember other non-natural numbers - the number pi, the number e, etc.
But it should be noted that there is a second Skuse number, which in mathematics is denoted as Sk2, which is even greater than the first Skuse number (Sk1). Second Skewes number, was introduced by J. Skuse in the same article to denote a number for which the Riemann hypothesis does not hold. Sk2 equals 1010 10103 , that is 1010 101000 .
As you understand, the more degrees there are, the more difficult it is to understand which number is greater. For example, looking at Skewes numbers, without special calculations, it is almost impossible to understand which of these two numbers is larger. Thus, for super-large numbers it becomes inconvenient to use powers. Moreover, you can come up with such numbers (and they have already been invented) when the degrees of degrees simply do not fit on the page. Yes, that's on the page! They won’t fit even into a book the size of the entire Universe! In this case, the question arises of how to write them down. The problem, as you understand, is solvable, and mathematicians have developed several principles for writing such numbers. True, every mathematician who asked about this problem came up with his own way of writing, which led to the existence of several, unrelated to each other, methods for writing numbers - these are the notations of Knuth, Conway, Steinhouse, etc.
Consider the notation of Hugo Stenhouse (H. Steinhaus. Mathematical Snapshots, 3rd edn. 1983), which is quite simple. Stein House suggested writing large numbers inside geometric shapes - triangle, square and circle:
Steinhouse came up with two new superlarge numbers. He named the number - Mega, and the number - Megiston.
Mathematician Leo Moser refined Stenhouse's notation, which was limited by the fact that if it was necessary to write down numbers much larger than a megiston, difficulties and inconveniences arose, since many circles had to be drawn one inside the other. Moser suggested that after the squares, draw not circles, but pentagons, then hexagons, and so on. He also proposed a formal notation for these polygons so that numbers could be written without drawing complex pictures. Moser notation looks like this:
Thus, according to Moser's notation, Steinhouse's mega is written as 2, and megiston as 10. In addition, Leo Moser proposed calling a polygon with the number of sides equal to mega - megagon. And he proposed the number “2 in Megagon,” that is, 2. This number became known as Moser’s number or simply as Moser.
But Moser is not the largest number. The largest number ever used in a mathematical proof is the limiting quantity known as Graham's number, first used in 1977 in the proof of an estimate in Ramsey theory. It is associated with bichromatic hypercubes and cannot be expressed without the special 64-level system of special mathematical symbols introduced by Knuth in 1976.
Unfortunately, a number written in Knuth's notation cannot be converted into notation in the Moser system. Therefore, we will have to explain this system too. In principle, there is nothing complicated about it either. Donald Knuth (yes, yes, this is the same Knuth who wrote “The Art of Programming” and created the TeX editor) came up with the concept of superpower, which he proposed to write with arrows pointing upward:
In general it looks like this:
I think everything is clear, so let’s return to Graham’s number. Graham proposed so-called G-numbers:
- G1 = 3..3, where the number of superpower arrows is 33.
- G2 = ..3, where the number of superpower arrows is equal to G1.
- G3 = ..3, where the number of superpower arrows is equal to G2.
- G63 = ..3, where the number of superpower arrows is G62.
The G63 number came to be called the Graham number (it is often designated simply as G). This number is the largest known number in the world and is even listed in the Guinness Book of Records. And here
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 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 represented in the decimal number system 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 any serious theoretical or practical meaning. 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 the 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 is not strictly mathematical definition. In 1996, Conway (eng. J. H. Conway) and Guy (eng. R. K. Guy) in their book English. The Book of Numbers defined a zillion to the nth power as 10 3×n+3 for the short scale number naming system.