10 to the 3003rd power
Disputes about what is the largest figure in the world are ongoing. Different calculus systems offer different variants 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 American and English metric systems, it was discovered that the largest number in the world is 10 to the 3003rd power - a million. Men in Everyday life believe that the most big number 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. It follows from this that numbers are made up 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 a 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 numbers and figures different systems the calculations do not coincide, as we saw from the examples with Arabic and Roman numbers and numerals. This happens because numbers and numbers are simple concepts, which are invented by the person 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 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 titles large numbers are constructed like this: at the beginning there is a Latin ordinal number, and at the end the suffix -illion 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 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 English system comes trillion, and only then quadrillion, followed by 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, of course, possible, 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). More than a thousand proper names The Romans did not have any 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.
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 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 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 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 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 mathematical proof, is a limiting quantity known as Graham's number, first used in 1977 to prove an estimate in Ramsey theory. It is associated with 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 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 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. And here
John SommerPlace zeros after any number or multiply with tens raised to any number you like greater degree. It won't seem enough. It will seem like a lot. But the bare records are still not very impressive. The piling up of zeros in the humanities causes 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 another one... And the number will come out even larger.
And yet, are there words in Russian or any other language to denote very large numbers? Those who more than a million, billion, trillion, billion? And in general, how much is a billion?
It turns out that there are two systems for naming numbers. But not Arab, Egyptian, or any other ancient civilizations, but American and English.
In the American system numbers are called like this: take the Latin numeral + - illion (suffix). This gives the numbers:
Trillion - 1,000,000,000,000 (12 zeros)
Quadrillion - 1,000,000,000,000,000 (15 zeros)
Quintillion - 1 followed by 18 zeros
Sextillion - 1 and 21 zeros
Septillion - 1 and 24 zeros
octillion - 1 followed by 27 zeros
Nonillion - 1 and 30 zeros
Decillion - 1 and 33 zeros
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 number 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 - illiard. I mean:
Trillion - 1 and 21 zeros (in the American system - sextillion!)
Trillion - 1 and 24 zeros (in the American system - septillion)
Quadrillion - 1 and 27 zeros
Quadrillion - 1 followed by 30 zeros
Quintillion - 1 and 33 zeros
Quinilliard - 1 and 36 zeros
Sextillion - 1 and 39 zeros
Sextillion - 1 and 42 zeros
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 us not be afraid!
In Russia, the American system of naming numbers has been adopted. We borrowed the name of the number “billion” from the English system - 1,000,000,000 = 10 9
Where is the “cherished” billion? - But a billion is a billion! American style. And although we use the American system, we took “billion” from the English one.
Using the Latin names of numbers and the American system, we name the numbers:
- vigintillion- 1 and 63 zeros
- centillion- 1 and 303 zeros
- million- one and 3003 zeros! Oh-ho-ho...
But this, it turns out, is not all. There are also non-system numbers.
And the first of them is probably myriad- one hundred hundreds = 10,000
Google(the famous search engine is named after him) - one and one hundred zeros
In one of the Buddhist treatises the number is named asankheya- one and one hundred and forty zeros!
Number name googolplex(like googol) 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 Skuse named the Skuse number after himself. It means e to a degree e to a degree e to the power of 79, that is e e e 79
And then a big difficulty arose. You can come up with names for numbers. But how to write them down? The number of degrees of degrees of degrees is already such that it simply cannot be removed onto the page! :)
And then some mathematicians began to write numbers in geometric figures. And they say he was the first to come up with this method of recording outstanding writer and thinker Daniil Ivanovich Kharms.
And yet, what is the BIGGEST NUMBER IN THE WORLD? - It’s called STASPLEX and is equal to G 100,
where G is Graham's number, the largest number ever used in mathematical proof.
This number - stasplex - was invented wonderful person, our compatriot Stas Kozlovsky, LJ to which I am directing you :) - ctac
A child asked today: “What is the name of the largest number in the world?” Interesting question. I went online and found a detailed article in LiveJournal on the first line of Yandex. 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 are completely different numbers! The biggest is not 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 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 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
Passed from the English system to the 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
namely the 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, but an innumerable, uncountable
a lot of something. It is believed that the word myriad
(eng. 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 therefore equally certain that
it had to have a name. At the same time that he suggested "googol" he gave a
name for a still larger number: "Googolplex." A googolplex is much larger than a
googol, but is still finite, as the inventor of the name was quick to point out.
Mathematics and the Imagination(1940) by Kasner and James R.
Newman.
An even larger number than a googolplex 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
systems of special 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 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.
Many people are interested in questions about what large numbers are called and what number is the largest in the world. With these interesting questions and we will look into this in this article.
Story
Southern and eastern Slavic peoples Alphabetical numbering was used to record numbers, and only those letters that are in the Greek alphabet. A special “title” icon was placed above the letter that designated the number. Numeric values The letters increased in the same order as the letters in the Greek alphabet (in the Slavic alphabet the order of the letters was slightly different). In Russia, Slavic numbering was preserved until the end of the 17th century, and under Peter I they switched to “Arabic numbering,” which we still use today.
The names of the numbers also changed. Thus, until the 15th century, the number “twenty” was designated as “two tens” (two tens), and then it was shortened for faster pronunciation. The number 40 was called “fourty” until the 15th century, then it was replaced by the word “forty,” which originally meant a bag containing 40 squirrel or sable skins. The name “million” appeared in Italy in 1500. It was formed by adding an augmentative suffix to the number “mille” (thousand). Later this name came to the Russian language.
In the ancient (18th century) “Arithmetic” of Magnitsky, a table of the names of numbers is given, brought to the “quadrillion” (10^24, according to the system through 6 digits). Perelman Ya.I. in the book " Entertaining arithmetic» the names of large numbers of that time are given, slightly different from today's: septillion (10^42), octalion (10^48), nonalion (10^54), decalion (10^60), endecalion (10^66), dodecalion ( 10^72) and it is written that “there are no further names.”
Ways to construct names for large numbers
There are 2 main ways to name large numbers:
- American system, which is used in the USA, Russia, France, Canada, Italy, Turkey, Greece, Brazil. The names of large numbers are constructed quite simply: the Latin ordinal number comes first, and the suffix “-million” is added to it at the end. An exception is the number “million”, which is the name of the number thousand (mille) and the augmentative suffix “-million”. The number of zeros in a number, which is written according to the American system, can be found out by the formula: 3x+3, where x is the Latin ordinal number
- English system most common in the world, it is used in Germany, Spain, Hungary, Poland, Czech Republic, Denmark, Sweden, Finland, Portugal. The names of numbers according to this system are constructed in the following way: the suffix “-million” is added to the Latin numeral, next number(1000 times greater) – the same Latin numeral, but the suffix “-billion” is added. The number of zeros in a number, which is written according to the English system and ends with the suffix “-million,” can be found out by the formula: 6x+3, where x is the Latin ordinal number. The number of zeros in numbers ending with the suffix “-billion” can be found using the formula: 6x+6, where x is the Latin ordinal number.
Only the word billion passed from the English system into the Russian language, which is still more correctly called as the Americans call it - billion (since the Russian language uses the American system for naming numbers).
In addition to numbers that are written according to the American or English system using Latin prefixes, non-system numbers are known that have their own names without Latin prefixes.
Proper names for large numbers
| Number | Latin numeral | Name | Practical significance | |
| 10 1 | 10 | ten | Number of fingers on 2 hands | |
| 10 2 | 100 | one hundred | About half the number of all states on Earth | |
| 10 3 | 1000 | thousand | Approximate number of days in 3 years | |
| 10 6 | 1000 000 | unus (I) | million | 5 times more than the number of drops per 10 liter. bucket of water |
| 10 9 | 1000 000 000 | duo (II) | billion (billion) | Estimated Population of India |
| 10 12 | 1000 000 000 000 | tres (III) | trillion | |
| 10 15 | 1000 000 000 000 000 | quattor (IV) | quadrillion | 1/30 of the length of a parsec in meters |
| 10 18 | quinque (V) | quintillion | 1/18th of the number of grains from the legendary award to the inventor of chess | |
| 10 21 | sex (VI) | sextillion | 1/6 of the mass of planet Earth in tons | |
| 10 24 | septem (VII) | septillion | Number of molecules in 37.2 liters of air | |
| 10 27 | octo (VIII) | octillion | Half of Jupiter's mass in kilograms | |
| 10 30 | novem (IX) | quintillion | 1/5 of all microorganisms on the planet | |
| 10 33 | decem (X) | decillion | Half the mass of the Sun in grams | |
- Vigintillion (from Latin viginti - twenty) - 10 63
- Centillion (from Latin centum - one hundred) - 10,303
- Million (from Latin mille - thousand) - 10 3003
For numbers greater than a thousand, the Romans did not have their own names (all names for numbers were then composite).
Compound names of large numbers
In addition to proper names, for numbers greater than 10 33 you can obtain compound names by combining prefixes.
Compound names of large numbers
| Number | Latin numeral | Name | Practical significance |
| 10 36 | undecim (XI) | andecillion | |
| 10 39 | duodecim (XII) | duodecillion | |
| 10 42 | tredecim (XIII) | thredecillion | 1/100 of the number of air molecules on Earth |
| 10 45 | quattuordecim (XIV) | quattordecillion | |
| 10 48 | quindecim (XV) | quindecillion | |
| 10 51 | sedecim (XVI) | sexdecillion | |
| 10 54 | septendecim (XVII) | septemdecillion | |
| 10 57 | octodecillion | So many elementary particles in the sun | |
| 10 60 | novemdecillion | ||
| 10 63 | viginti (XX) | vigintillion | |
| 10 66 | unus et viginti (XXI) | anvigintillion | |
| 10 69 | duo et viginti (XXII) | duovigintillion | |
| 10 72 | tres et viginti (XXIII) | trevigintillion | |
| 10 75 | quattorvigintillion | ||
| 10 78 | quinvigintillion | ||
| 10 81 | sexvigintillion | So many elementary particles in the universe | |
| 10 84 | septemvigintillion | ||
| 10 87 | octovigintillion | ||
| 10 90 | novemvigintillion | ||
| 10 93 | triginta (XXX) | trigintillion | |
| 10 96 | antigintillion |
- 10 123 - quadragintillion
- 10 153 — quinquagintillion
- 10 183 — sexagintillion
- 10,213 - septuagintillion
- 10,243 — octogintillion
- 10,273 — nonagintillion
- 10 303 - centillion
Further names can be obtained directly or in reverse order Latin numerals (which is correct is not known):
- 10 306 - ancentillion or centunillion
- 10 309 - duocentillion or centullion
- 10 312 - trcentillion or centtrillion
- 10 315 - quattorcentillion or centquadrillion
- 10 402 - tretrigyntacentillion or centretrigintillion
The second spelling is more consistent with the construction of numerals in the Latin language and allows us to avoid ambiguities (for example, in the number trecentillion, which according to the first spelling is both 10,903 and 10,312).
- 10 603 - decentillion
- 10,903 - trcentillion
- 10 1203 - quadringentillion
- 10 1503 — quingentillion
- 10 1803 - sescentillion
- 10 2103 - septingentillion
- 10 2403 — octingentillion
- 10 2703 — nongentillion
- 10 3003 - million
- 10 6003 - duo-million
- 10 9003 - three million
- 10 15003 — quinquemilliallion
- 10 308760 -ion
- 10 3000003 — mimiliaillion
- 10 6000003 — duomimiliaillion
Myriad– 10,000. The name is outdated and practically not used. However, the word “myriads” is widely used, which means not certain number, but an uncountable, uncountable set of something.
Googol ( English . googol) — 10 100. The American mathematician Edward Kasner first wrote about this number in 1938 in the journal Scripta Mathematica in the article “New Names in Mathematics.” According to him, his 9-year-old nephew Milton Sirotta suggested calling the number this way. This number became well known thanks to the Google search engine named after him.
Asankheya(from Chinese asentsi - uncountable) - 10 1 4 0 . This number is found in the famous Buddhist treatise Jaina Sutra (100 BC). It is believed that this number is equal to the number of cosmic cycles required to achieve nirvana.
Googolplex ( English . Googolplex) — 10^10^100. This number was also invented by Edward Kasner and his nephew; it means one followed by a googol of zeros.
Skewes number (Skewes' number, Sk 1) means e to the power of e to the power of e to the power of 79, that is, e^e^e^79. This number was proposed by Skewes in 1933 (Skewes. J. London Math. Soc. 8, 277-283, 1933.) when proving the Riemann hypothesis concerning prime numbers. Later, Riele (te Riele, H. J. J. “On the Sign of the Difference П(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. However, this number is not an integer, so it is not included in the table of large numbers.
Second Skewes number (Sk2) equals 10^10^10^10^3, that is, 10^10^10^1000. This number was introduced by J. Skuse in the same article to indicate the number up to which the Riemann hypothesis is valid.
For super-large numbers it is inconvenient to use powers, so there are several ways to write numbers - Knuth, Conway, Steinhouse notations, etc.
Hugo Steinhouse proposed writing large numbers inside geometric shapes (triangle, square and circle).
Mathematician Leo Moser refined Steinhouse's notation, proposing to draw pentagons, then hexagons, etc. after squares rather than circles. Moser also proposed a formal notation for these polygons so that the numbers could be written without drawing complex pictures.
Steinhouse came up with two new super-large numbers: Mega and Megiston. In Moser notation they are written as follows: Mega – 2, Megiston– 10. Leo Moser also proposed to call a polygon with the number of sides equal to mega – megagon, and also proposed the number “2 in Megagon” - 2. The last number is known as Moser's number or just like Moser.
There are numbers larger than Moser. The largest number that has been used in a mathematical proof is number Graham(Graham's number). It was first used in 1977 to prove an estimate in Ramsey theory. This number is associated with bichromatic hypercubes and cannot be expressed without a special 64-level system of special mathematical symbols introduced by Knuth in 1976. Donald 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
Graham proposed G-numbers:
The number G 63 is called the Graham number, often denoted simply G. This number is the largest known number in the world and is listed in the Guinness Book of Records.