It is impossible to answer this question correctly, since the numeric number does not have an upper limit. So, to any number just enough to add a unit to get the number even greater. Although the numbers themselves are infinite, their own names are not so much, since most of them are content with the names composed of smaller numbers. For example, the numbers and have their own names "one" and "hundred", and the name of the number is already composite ("one hundred one"). It is clear that in the final set of numbers, which humanity awarded his own name, should be some greatest number. But what is it called and what is it equal? Let's try to figure it out and at the same time, how big numbers came up with mathematics.
"Short" and "Long" scale
The history of the modern system of the name of large numbers is beginning from the middle of the XV century, when in Italy began to use the words "million" (literally - a large one thousand) for thousands in square, "Bimillion" for a million in a square and trimillion for a million in Cuba. About this system, we know thanks to the French Mathematics of Nicolas Chuke (Nicolas Chuquet, Ok. 1450 - approx. 1500): In its treatise, "TRIPARTY EN LA SCIENCE DES NOMBRESS, 1484) he developed this idea, offering to use Latin Quantitatively numerical (see table) by adding them to the end of "-Lion". Thus, Bimillion has turned into Billion, Trimillion in trillion, and a million in the fourth degree became a "quadrillion".
In the Schuke system, the number that was between a million and Billion, did not have his own name and was called simply "thousand million", the "Thousand Billion" was called, - "Thousand Trillion", etc. It was not very convenient, and in 1549, the French writer and scientist Jacques Pelette (Jacques Peletier Du Mans, 1517-1582) proposed to form such "intermediate" numbers with the same Latin prefixes, but the end of the "Stalliard". So, it became known "Billion," - "Billiard", "Trilliards", etc.
The Schuke-Pelette Schuke gradually became popular and they began to use all over Europe. However, an unexpected problem arose in the XVII century. It turned out that some scientists for some reason began to be confused and called a number not "billion" or "thousand of millions", but "Billion". Soon, this error quickly spread, and a paradoxical situation arose - "Billion" became simultaneously synonymous with the "billion" () and "millions of millions" ().
This confusion continued long enough and led to the fact that in the United States created their system names of large numbers. According to the American Names System, the numbers are built in the same way as in the Schuke system - the Latin prefix and the end of Illion. However, the values \u200b\u200bof these numbers differ. If the names of the name "Illion" received the numbers that were degrees of a million in the ILION system, then in the American system, the end of the "-Illion" received a degree of thousands. That is, a thousand millions () began to be called "Billion", () - "Trillion", () - "Quadrillion", etc.
The old language of the name of large numbers continued to be used in a conservative Britain and began to be called "British" throughout the world, despite the fact that she was invented by the French shyke and Pelet. However, in the 1970s, the United Kingdom officially switched to the "American system", which led to the fact that calling one American system, and another British became somehow strange. As a result, now the American system is usually called a "short scale", and the British system or the Schuke-Pelette system is a "long scale".
In order not to get confused, we will summarize the result:
| Name of the number | Value by "short scale" | Value for a "long scale" |
| Million | ||
| Billion | ||
| Billion | ||
| Billiard | - | |
| Trillion | ||
| Trilliard | - | |
| Quadrillion | ||
| Quadrilliard | - | |
| Quintillion | ||
| Quintilliard | - | |
| Sextillion | ||
| Sextillard | - | |
| Septillion | ||
| Septilliard | - | |
| Octillion | ||
| Octallard | - | |
| Quintillion | ||
| Nonilliard | - | |
| Decillion | ||
| Decilliard. | - | |
| Vigintillion | ||
| Vigintilliard | - | |
| Centillion | ||
| Centillard | - | |
| Milleilla | ||
| Milleillado | - |
A short name scale is used now in the USA, Great Britain, Canada, Ireland, Australia, Brazil and Puerto Rico. In Russia, Denmark, Turkey and Bulgaria, a short scale is also used, except that the number is not called "Billion", but a "billion". The long scale is currently continuing to be used in most other countries.
It is curious that in our country the final transition to a short scale occurred only in the second half of the 20th century. So, for example, Jacob Isidovich Perelman (1882-1942) in its "entertaining arithmetic" mentions parallel existence in the USSR of two scales. The short scale, according to Perelman, was used in everyday use and financial calculations, and long - in scientific books on astronomy and physics. However, now use the long scale in Russia is incorrect, although the numbers there are and large.
But back to the search for the largest number. After decillion, the names of numbers are obtained by combining consoles. Thus, such numbers are as undercillion, duodeticillion, treadsillion, quotoroidicillion, quindecillion, semotecyllium, septemberion, octopesillion, newcillion, etc. are obtained. However, these names are no longer interesting for us, since we agreed to find the largest number with our own incompatible name.
If we turn to Latin grammar, it was discovered that there were only three numbers for numbers for numbers more than ten at the Romans: Viginti - "Twenty", Centum - "Hundred" and Mille - "Thousand". For numbers more than the "thousand", the own names of the Romans did not exist. For example, Million () The Romans called "Decies Centena Milia", that is, "ten times on hundred thousand". According to the rules, these three remaining Latin numerals give us such names for the numbers as "Vigintillion", "Centillion" and Milleillan.
So, we found out that in the "short scale" the maximum number that has its own name and is not composite of smaller numbers - this is "Milleilla" (). If the "long scale" of the names of numbers would be adopted in Russia, then Milleirliard () would be the largest number with their own name.
However, there are names for even large numbers.
Numbers outside the system
Some numbers have their own name, without any connection with the name system with Latin prefixes. And there are a lot of such numbers. It is possible for example, to recall the number E, the number "pi", a dozen, the number of beasts, etc. However, since we are now interested in large numbers, then consider only those numbers with your own incompetent name that are more than a million.
Until the XVII century, its own numbers name system was used in Russia. Tens of thousands were called "darkness", hundreds of thousands - "Legions", Millions - "Lodrats", tens of millions - "crowns", and hundreds of millions - "decks". This score to hundreds of millions was called a "small account", and in some manuscripts, the authors were also considered "the Grand Account", which used the same names for large numbers, but with another meaning. So, "darkness" meant not ten thousand, and a thousand thousand () , "Legion" - darkness () ; "Leodr" - Legion Legion () , "Raven" - Leodr Leodrov (). "The deck" in the great Slavic account for some reason was not called "Crow Voronov" () , but only ten "crows", that is, (see Table).
| Name of the number | Meaning in "Small Account" | Meaning in "Great Account" | Designation |
| Dark | |||
| Legion | |||
| Leodr | |||
| Raven (Van) | |||
| Deck | |||
| Darkness Tom |  |
The number also has its own name and invented his nine-year-old boy. And it was so. In 1938, American mathematician Edward Kasner (Edward Kasner, 1878-1955) walked around the park with his two nephews and discussed large numbers with them. During the conversation, we were talking about the number from a hundred zeros, which had no own name. One of the nephews, a nine-year-old Milton Sirett, offered to call this number "Google" (GOOGOL). In 1940, Edward Casner in conjunction with James Newman wrote a scientific and popular book "Mathematics and imagination", where he told Mathematics lovers about the number Gugol. Hugol received even wider fame in the late 1990s, thanks to the Google search engine named after him.
The name for an even more than Google, originated in 1950 due to the father of informatics Claud Shannon (Claude Elwood Shannon, 1916-2001). In his article "Programming a computer for playing chess", he tried to assess the number of possible chess game options. According to him, each game lasts on average moves and at each progress player makes a choice on average from options, which corresponds to (approximately equal) game options. This work has become widely known, and this number began to be called "Shannon's number".
In the famous Buddhist treatise, Jaina Sutra, belonging to 100 BC, meets the number "Asankhay" equal. It is believed that this number is equal to the number of space cycles required to gain nirvana.
Nine-year Milton Sirette entered the history of mathematics not only by what came up with the number of Guogol, but also in the fact that at the same time he was offered another number - "Gugolplex", which is equal to the degree of "Google", that is, a unit with google zerule.
Two more numbers, large than the googolplex, were proposed by South African Mathematics Stanley Skusom (Stanley Skewes, 1899-1988) in the proof of Riemann's hypothesis. The first number, which later began to call the "first number of Skusza", is equal to the degree to the degree to the degree, that is. However, the "second number of Skusza" is even more.
Obviously, the more degrees in degrees, the more difficult it is to write numbers and understand their meaning when reading. Moreover, it is possible to come up with such numbers (and, by the way, have already been invented), when the degrees are simply not placed on the page. Yes, that on the page! They will not fit even in the book size with the whole universe! In this case, the question arises as such numbers to record. The problem, fortunately, is solvable, and mathematics have developed several principles for recording such numbers. True, every mathematician who wondered by this problem came up with his way of recording, which led to the existence of several non-other ways to write large numbers - these are notations of whip, Konveya, Steinhause, etc. With some of them we have to deal with some of them.
Other notations
In 1938, in the same year, when Nine-year-old Milton Sirette came up with the number of Gugol and the Gugolplex, a book about entertaining mathematics "Mathematical Kaleidoscope" was published in Poland, written by Hugo Steinhaus (Hugo Dionizy Steinhaus, 1887-1972). This book has become very popular, withstood many publications and has been translated into many languages, including English and Russian. In it, Steinghauses, discussing large numbers, offers an easy way to write their, using three geometric shapes - triangle, square and circle:
"In a triangle" means "",
"In the square" means "in triangles",
"In the circle" means "in squares".
Explaining this method of recording, Steinghause comes up with the number of "mega", equal in the circle and shows that it is equal in the "square" or triangles. To calculate it, it is necessary to be taken to the extent resulting in the extent to the degree, then the resulting number of the resulting number and so fart all the time to erect. For example, the calculator in MS Windows cannot count due to overflow even in two triangles. Approximately this huge number is.
Having determined the number "Mega", Steinhause offers readers independently evaluate another number - "Medzon", equal in the circle. In another publication of the book, Steinhauses, instead of a medical unit, it proposes to evaluate even more - "Megiston", equal in the circle. Following the Steinhause, I will also recommend readers for a while to tear yourself away from this text and try to write these numbers yourself with the help of ordinary degrees to feel their gigantic value.
However, there are names for large numbers. So, Canadian mathematician Leo Moser (Leo Moser, 1921-1970) finalized the notation of the Stengaus, which was limited by the fact that if it were necessary to record numbers a lot of big Megiston, then there would be difficulties and inconvenience, as it would have to draw a lot of circles one inside Other. Moser suggested not circles after squares, and pentagons, then hexagons and so on. He also offered a formal entry for these polygons so that the numbers can be recorded without drawing complex drawings. The notation of Moser looks like this:
"Triangle" \u003d \u003d;
"In the square" \u003d \u003d "in triangles" \u003d;
"In a pentagon" \u003d \u003d "in squares" \u003d;
"In the fighting" \u003d \u003d "in fetters" \u003d.
Thus, according to the notation of Mosel, Steingerovsky "Mega" is recorded as, "Medzon" as, and "Megiston" as. In addition, Leo Moser suggested calling a polygon with the number of sides to Mega - Magagon. And offered the number « In Magagon, "that is. This number has become known as the Muser or simply as "Moser".
But even "Moser" is not the largest number. So, the largest number ever used in mathematical evidence is the "Graham". For the first time, this number was used by the American mathematician Ronald Gram (Ronald Graham) in 1977 in the proof of one assessment in the Ramsey theory, namely, when calculating the dimension of certain -Momes Bichromatic hypercubes. Family the sameness of Graham received only after the story about him in the book of Martin Gardner "from Mosaik Penrose to reliable ciphers in 1989.
To explain how great Graham number will have to explain another way to record large numbers introduced by Donald Knut in 1976. American Professor Donald Knut invented the concept of a superpope, which offered to record arrows directed upwards.
Conventional arithmetic operations - addition, multiplication and construction to the degree - naturally can be expanded into the sequence of hyperoperators as follows.
The multiplication of natural numbers can be determined through the re-produced operation of the addition ("folded copies of the number"):
For example,
The erection of the number can be defined as a repeated multiplication operation ("multiply copies of the number"), and in the knot designation, this entry looks like a single arrow pointing up:
For example,
Such a single upward arrow was used as a degree in Algol programming language.
For example,
Hereinafter, the calculation of the expression always goes to the right left, also the shooting operators of the whip (as well as the construction of the exercise to the degree) by definition have the right associativeness (in terms of the right to left). According to this definition,
This leads to quite large numbers, but the designation system does not end. The "Triple Arrogo" operator is used to record the re-erection of the operator "Double Arrogo" (also known as "Pentation"):
Then the "Four Arrogo" operator:
And so on. General rule Operator "-I Arrow ", in accordance with the right associativity, continues to the right to the serial series of operators « Arrogo ". Symbolically, this can be written as follows
For example:
The notation form is usually used to record with arrows.
Some numbers are so big that even the recording by the arrows of the whip becomes too cumbersome; In this case, the use of the Operator is preferable (and also to describe with a variable number of arrows), or equivalent to hyperoperators. But some numbers are so huge that even such a record is insufficient. For example, the number of Graham.
When using the shooting notation of the whip number of graves can be written as
Where the number of arrows in each layer starting from the top is determined by the number in the next layer, that is, where, where the upper index of the arrows shows the total number of arrows. In other words, it is calculated in step: in the first step, we calculate with four arrows between the top three, on the second - with the arrows between the top three, on the third - with the arrows between the top three, and so on; At the end, we calculate with the arrows between the top three.
This can be written how, where, where the upper index of U means iterations of functions.
If other numbers with the "names" can be selected the corresponding number of objects (for example, the number of stars in the visible part of the Universe is estimated in sextilones -, and the number of atoms from which the globe has the order of dodecalon), then Gugol is already "virtual", not to mention About the number of Graham. The scale of only the first member is so great that it is almost impossible to realize, although the record is above relatively simple for understanding. Although it is only a number of towers in this formula for, this number is a lot of more than the number of volumes of the plank (the lowest possible physical volume), which are contained in the observed universe (approximately). After the first member, we are waiting for another member of the rapidly growing sequence.
There are numbers that are so incredibly incredibly great, that even in order to record them, the entire Universe will be required. But that's what is really driven by ... Some of these incomprehensible large numbers are extremely important for understanding the world.
When I say "the greatest number in the universe", in fact, I mean the biggest meaningful The number, the maximum possible number, which is useful in some way. There are many applicants for this title, but I immediately warn you: In fact, there is a risk that an attempt to understand all this will explode your brain. And besides, with a breath of mathematics, you will get little pleasure.
Gugol and Gugolplex
Edward Kasner
We could start with two, very likely the biggest numbers that you have ever heard, and these are really the two largest numbers that have generally accepted definitions in English. (There is a fairly accurate nomenclature applied to designate numbers such as big as you would like, but these two numbers will currently you will not find in dictionaries.) Google, since it has become world famous (albeit with errors, notes. In fact, it is Googol) in the form of Google, born in 1920 as a way to interest children in large numbers.
To this end, Edward Casner (in the photo), took two her nephews, Milton and Edwina Sirett, for a walk through New Jersey Palisades. He offered them to put forward any ideas, and then the nine-year-old Milton offered "Gugol". Where he took this word is unknown, but Casner decided that 
or the number in which the unit cost a hundred zeros will be called Google.
But the young Milton did not stop at this, he suggested an even greater number, the googolplex. This is the number, according to Milton, in which there are 1 in the first place, and then as much zeros as you could write before you get tired. Although this idea is charming, Casner decided that a more formal definition is necessary. As he explained in his book of 1940, the "mathematics and imagination" publication, the definition of Milton leaves the open risky possibility that a random jester can become a mathematician, superior to Albert Einstein simply because he has more endurance.
Thus, Casner decided that the googolplex would be equal, or 1, and then the google zerule. Otherwise, in the notation similar to those with whom we will deal with other numbers, we will say that the googolplex is. To show how hard it fascinates, Karl Sagan once remarked that it is physically impossible to write down all the gugolplex zeros, because it simply does not have enough space in the universe. If you fill the entire amount of dust observed by the universe with small particles of approximately 1.5 microns, the number of different methods for the location of these particles will be approximately equal to one googolplex.
Linguistically speaking, Gugol and the Gugolplex are probably the two greatest significant numbers (at least in English), but, as we now install, the ways of determining the "significance '' are infinitely a lot.
Real world
If we talk about the biggest number, there is a reasonable argument that it really means that you need to find the largest number with the real value in the world. We can start with the current human population, which is currently about 6920 million. World GDP in 2010, estimated about $ 61960 billion, but both of these numbers are insignificant compared with about 100 trillion cells that make up the human body. Of course, none of these numbers can be compared with the complete number of particles in the universe, which is usually considered to be approximately, and this number is so great that our language has no word appropriate to him.
We can play a little with measures of measures, making numbers more and more. So, the mass of the sun in tons will be less than in pounds. A wonderful way to do this is to use the plank units system, which are the lowest possible measures for which the laws of physics remain in force. For example, the age of the universe in the time of the bar is about. If we return to the first unit of the plank time after a big explosion, we will see that the density of the universe was then. We get more and more, but we have not yet reached even Google.
The greatest number with any real application of the world - or, in this case, real use in the worlds is probably, one of the latest estimates of the number of universes in the multi-lane. This number is so great that the human brain will be literally unable to perceive all these different universes, since the brain is capable only about configurations. In fact, this number is probably the greatest number with any practical meaning if you do not take into account the idea of \u200b\u200bthe multiverse as a whole. However, there are still much greater numbers that are hiding there. But in order to find them, we must go to the area of \u200b\u200bclean mathematics, and there is no better beginning than simple numbers.
Simple numbers of Mersenna
Part of the difficulties is to come up with a good definition of what a "meaningful" number is. One way is to argue in terms of simple and constituent numbers. A simple number, like you, probably, remember from school mathematics - this is any natural number (notice. Not equal to one), which is divided only on and itself. So, and are simple numbers, and the components. This means that any composite number can ultimately be represented by its simple divisors. In a sense, the number is more important than, let's say, because there is no way to express it through the work of smaller numbers.
Obviously, we can go a little further. For example, in fact, simply, which means that in the hypothetical world, where our knowledge of numbers are limited by the number, the mathematician can still express the number. But the next number is simple, and it means that it is the only way to express it - to know directly about its existence. This means that the most famous simple numbers play an important role, and, say, googol - which, ultimately, just a set of numbers and multiply between themselves - not. And since simple numbers are mostly random, there are no ways to predict that an incredibly large number will actually be simple. To this day, the opening of new prime numbers is a difficult matter.
The mathematicians of ancient Greece had the concept of simple numbers, at least in 500 to our era, and 2000 years later, people still knew what numbers are simple only about 750. Thinkers of the Euclides seen the opportunity to simplify, but right up to the Renaissance Epoch Mathematics could not really use it in practice. These numbers are known as the number of Mermenna, they are named after the French scientist XVII century Marina Meresenna. The idea is quite simple: the number of Mersenna is any number of species. For example, this is a simple number, the same is true for.
It is much faster and easier to determine the simple numbers of Meressenn than any other type of prime numbers, and computers work intensively in their search over the past six decades. Until 1952, the largest known one was the number - a number with numbers. In the same year, the computer calculated that the number is simple, and this number consists of numbers, which makes it much more than Google.
Computers have since been on the hunt, and at present the number of Mersenna is the biggest one-in-one, famous humanity. Detected in 2008, it is a number with almost millions of digits. This is the largest known number that cannot be expressed through any smaller numbers, and if you want to help find an even more Merceda, you (and your computer) can always join the search for http: //www.mersenne. ORG /.
Number of Skusza
Stanley Skusz
Let's turn to simple numbers again. As I said, they behave in root incorrectly, it means that there is no way to predict what the next simple number will be. Mathematics were forced to appeal to some rather fantastic measurements to come up with some way to predict future simple numbers even in a foggy way. The most successful of these attempts is likely to be a function that considers simple numbers, which was invented at the end of the 18th century the legendary mathematician Karl Friedrich Gauss.
I will get rid of you from a more complex mathematics - anyway, we have a lot in front - but the essence of the function is as follows: for any whole, you can estimate how many simple numbers smaller. For example, if, the function predicts that there must be simple numbers if there are simply numbers smaller, and if there are smaller numbers that are simple.
The location of the simple numbers is indeed irregular, and this is just an approach of the actual number of prime numbers. In fact, we know that there are simple numbers, smaller, simple numbers of smaller, and simple numbers of smaller. This is an excellent assessment, which is, but it is always only an assessment ... and, more specifically, an estimate from above.
In all known cases, the function, which is the number of prime numbers, slightly exaggerates the actual number of simple numbers of smaller. Mathematics once thought that it would always be to infinity, that this would certainly applies to some unimaginably huge numbers, but in 1914, John Idenzor Littlewood proved that for some unknown, unimaginably huge number this function will start issuing Less number of prime numbers, and then it will switch between an estimate from above and estimate from the bottom of an infinite number of times.
The hunt was on the point of starting jumps, and here it appeared Stanley Skusz (see photo). In 1933, he proved that the upper border when the function approaching the number of prime numbers first gives a smaller value - this is the number. It is difficult to really understand even in the most abstract sense that it actually represents this number, and from this point of view it was the greatest number ever used in serious mathematical proof. Since then, mathematicians were able to reduce the upper limit to a relatively small number, but the initial number remains known as the number of Skusz.
So how much is the number that makes a dwarf even a mighty googolplex? In The Penguin Dictionary of Curious and Interesting Numbers, David Wells tells about one way, with which Mathematics Hardy managed to comprehend the size of the Skusza number:
"Hardy thought it was" the largest number ever served any specific goal in mathematics ", and suggested that if you play chess with all the particles of the universe as figures, one move would be in the permutation of two particles in places, And the game stopped when the same position would repeat the third time, the number of all possible parties would be approximately the number of Skusz.
And the latter before moving on: we talked about the smaller of two numbers of Skuse. There is another number of Skusza, which mathematician found in 1955. The first number was obtained on the grounds that the so-called Riemann hypothesis is a particularly difficult math hypothesis, which remains unproved, is very useful when it comes to simple numbers. Nevertheless, if Riemann's hypothesis is false, Skusz found that the starting point of jumps increases to.
The problem of magnitude
Before we turn to the number, next to which even the number of Skuse looks tiny, we need to talk a little about the scale, because otherwise we do not have the opportunity to appreciate where we are going to go. First, let's take a number - this is a tiny number, so small that people can really have an intuitive understanding of what it means. There are very few numbers that correspond to this description, since the numbers more than six cease to be separate numbers and become "somewhat ''," a lot '', etc.
Now let's take, i.e. . Although in reality we can not intuitively, as it was for the number, to understand what is, to imagine what is very easy. While everything goes well. But what happens if we go to? This is equal, or. We are very far from the ability to imagine this magnitude, like any other, very large - we lose the ability to comprehend certain parts somewhere around a million. (True, insanely a large amount of time would take to really count to a million of anything, but the fact is that we are still capable of perceiving this number.)
However, although we cannot imagine, we are at least able to understand in general terms what is 7600 billion, possibly comparing it with something such as the US GDP. We switched from intuition to the presentation and to a simple understanding, but at least we still have some gap in understanding what a number is. This is about to change, as we move to another step up the stairs.
To do this, we need to proceed to the designation introduced by Donald Knut, known as the direction notation. In these notation can be written in the form. When we then turn to the number that we get will be equal. This is equal to where a total of triples. We are now significantly and truly surpassed all the other numbers that have already spoken. In the end, even in the biggest of them there were only three or four members in a number of indicators. For example, even a super-number of Skusza is "only" - even with amendment that the basis and the indicators are much larger than, it is still absolutely nothing compared to the size of the numerical tower with billion members.
Obviously, there is no way to comprehend so huge numbers ... and nevertheless, the process by which they are created can still be understood. We could not understand the real number, which is asked by the Tower of degrees in which billion triples, but we can mainly imagine such a tower with many members, and a really decent supercomputer will be able to store such towers in memory, even if he cannot calculate their actual meanings. .
It becomes more abstract, but it will be only worse. You might think that the tower of degrees, the length of which is equal to (moreover, in the previous version of this post I did this error), but it's easy. In other words, imagine that you have the opportunity to calculate the exact value of the power tower from the triple, which consists of elements, and then you took this value and created a new tower with so much in it, ... which gives.
Repeat this process with each subsequent number ( note. Starting right) until you do it, and then you finally get. This is a number that is simply incredibly large, but at least the steps of his reception seem to be understandable if everyone does very slowly. We can no longer understand the numbers or submit to the procedure, thanks to which it turns out, but at least we can understand the main algorithm, only at a fairly long term.
Now prepare the mind to really blow it up.
Graham number (sin)
Ronald Gram.
This is how you get the number of Graham, which takes place in the Guinness Book of Records as the largest number that ever used in mathematical proof. It is absolutely impossible to imagine how large it is, and just as hard to explain exactly what it is. In principle, the Graham number appears when they deal with hypercubs that are theoretical geometric shapes with more than three dimensions. Mathematician Ronald Graham (see photo) wanted to find out with what the smallest number of measurements certain properties of the hypercube will remain stable. (Sorry for such a vague explanation, but I am sure that we all need to get at least two scientific degrees in mathematics to make it more accurate.)
In any case, the Graham number is an estimate from above of this minimum measurement number. So how big is this upper border? Let's go back to the number, so great that the algorithm of his receipt we can understand rather vaguely. Now, instead of just jumping up another level before, we will assume a number in which there are arrows between the first and last three. Now we are far beyond even the slightest understanding of what is this number or even from what needs to be done to calculate it.
Now we repeat this process times ( note. At each next step, we write the number of arrows equal to the number obtained in the previous step).
These are the ladies and gentlemen, the number of Graham, which approximately about the order is above the point of human understanding. This number that is so greater than any number that you can imagine is much more than any infinity that you could ever hope to imagine - it is simply not amenable to even the most abstract description.
But here is a strange thing. Since the Graham number is mostly - it is just three, multiplied with each other, we know some of its properties without the actual calculation of it. We can not imagine the number of Graham with any familiar designations for us, even if we used the whole universe to record it, but I can call you right now the last twelve digits of Graham number :. And that's not all: we know at least the last figures of Graham.
Of course, it is worth remembering that this number is only the upper bound in the original Graham problem. It is possible that the actual number of measurements required to perform the desired property are much less. In fact, since the 1980s, it was considered, according to most of the specialists in this area, which actually the number of measurements is only six - the number is so small that we can understand it at an intuitive level. Since then, the lower border has been increased before, but there is still a very big chance that the decision of the Graham's task does not lie next to the number as big as the number of Graham.
To infinity
So there are numbers more than graham? There are, of course, to begin with the number of Graham. As for the meaningful number ... Well, there are some devilish complex areas of mathematics (in particular, areas known as combinatorics) and informatics in which there are even large numbers than the number of Graham. But we almost achieved the limit of what, as I can hope, will ever be able to reasonably explain. For those who are enough reckless enough to go even further, the literature is offered for additional reading at your own risk.
Well, now an amazing quote that is attributed to Douglas Rey ( note. Honestly, it sounds pretty funny):
"I see the clusters of vague numbers that are hiding there in the dark, behind a small spot of light, which gives a mind candle. They whisper with each other; Conduousing who knows about what. Perhaps they are not very fond of the capture of their smaller brothers by our minds. Or, perhaps, they simply lead a unambiguous numeric lifestyle, there beyond our understanding.
Have you ever thought how many zeros are in one million? This is a fairly simple question. What about a billion or trillion? Unit with nine zeros (10,000,000,000) - what is the name of the number?
Brief list of numbers and their quantitative designation
- Ten (1 zero).
- One hundred (2 zero).
- Thousand (3 zero).
- Ten thousands (4 scratch).
- One hundred thousand (5 zeros).
- Million (6 zeros).
- Billion (9 zeros).
- Trillion (12 zeros).
- Quadrillion (15 zeros).
- Quintillon (18 zeros).
- Sextillion (21 zero).
- Septylon (24 zero).
- Occlicon (27 zeros).
- Nonalon (30 zeros).
- Decalon (33 zero).
Grouping zeros.
10,000,000 - what is the name of which there are 9 zeros? This is a billion. For convenience, large numbers are accepted to group three sets separated from each other with a space or such punctuation marks as a comma or point.
This is done in order to make it easier to read and understand quantitative importance. For example, what is the name of the number of 100,000,000? In this form, it is necessary to say a little, calculate. And if you write 1,000,000,000, then immediately visually the task is facilitated, so it is necessary to consider not zeros, but the top of the zeros.
Numbers with a very large number of zeros
Million and billion are from the most popular (1,000,000,000). What is the number having a 100 zeros? This is a number googol, called so Milton Sirette. This is wildly a huge amount. Do you think that this number is big? Then how about googolplex, the units behind which googol zerule? This figure is so great that it makes sense to come up with difficult for her. In fact, there is no need for such giants, except to count the number of atoms in the infinite universe.
1 billion is a lot?
There are two measurement scales - short and long. Worldwide in the field of science and finance 1 billion is 1,000 million. This is a short scale. There is a number with 9 zeros.
There is also a long scale that is used in some European countries, including in France, and used to be used in the UK (until 1971), where the billion was 1 million million, that is, a unit and 12 zeros. This gradation is also called a long-term scale. A short scale is now the predominant in solving financial and scientific issues.
Some European languages \u200b\u200bsuch as Swedish, Danish, Portuguese, Spanish, Italian, Dutch, Norwegian, Polish, German, use a billion (or Billion) in this system. In Russian, a number of 9 zeros is also described for a short scale of thousands of millions, and a trillion is a million million. This avoids unnecessary confusion.
Conversational options
In Russian spoken speech after the events of 1917 - the Great October Revolution - and the period of hyperinflation in the early 1920s. 1 billion rubles called Limard. And in the dashing 1990s for a billion, a new slang "Watermelon" appeared, a million called "Lemon".
The word "billion" is now used internationally. This is a natural number that is depicted in the decimal system, like 10 9 (unit and 9 zeros). There is also another name - Billion, which is not used in Russia and the CIS countries.
Billion \u003d Billion?
Such a word as Billion is used to designate a billion only in those states in which the "short scale" is adopted as a basis. These are countries such as the Russian Federation, the United Kingdom of Great Britain and Northern Ireland, USA, Canada, Greece and Turkey. In other countries, the concept of Billion means the number 10 12, that is, one and 12 zeros. In countries with a "short scale", including in Russia, this figure corresponds to 1 trillion.
Such confusion appeared in France at a time when the formation of such science as an algebra took place. Initially, a billion had 12 zeros. However, everything changed after the emergence of the main arithmetic allowance (by Tranchan) in 1558), where a billion is an already number with 9 zeros (thousand million).
For several subsequent centuries, these two concepts were used on par with each other. In the middle of the 20th century, namely in 1948, France moved to a long scale of a system of numerical names. In this regard, a short scale, once borrowed from the French, is still different from the one they enjoy today.
Historically, the United Kingdom has used a long-term billion, but since 1974 official statistics of Great Britain used a short-term scale. Since the 1950s, the short-term scale was increasingly used in the field of technical writing and journalism, despite the fact that the long-term scale remained.
"I see the clusters of vague numbers that are hiding there in the dark, behind a small spot of light, which gives a mind candle. They whisper with each other; Conduousing who knows about what. Perhaps they are not very fond of the capture of their smaller brothers by our minds. Or, perhaps, they simply lead a unambiguous numeric lifestyle, there beyond our understanding.
Douglas Ray
Each early or later torments the question, and what the largest number. On the question of the child can be answered by a million. What's next? Trillion. And even further? In fact, the answer to the question is what the largest numbers are simple. To the large number, it is simply worth adding a unit, as it will not be the largest. This procedure can be continued to infinity.
And if you wonder: what is the largest number, and what is his own name?
Now we will find out ...
There are two numbers name systems - American and English.
The American system is pretty simple. All the names of large numbers are built like this: at the beginning there is a Latin sequence numerical, and at the end, suffix is \u200b\u200badded to it. The exception is the name "Million" which is the name of the number of a thousand (lat. mille) and magnifying suffix -illion (see table). So the numbers are trillion, quadrillion, quintillion, sextillion, septillion, octillion, nonillion and decillion. The American system is used in the USA, Canada, France and Russia. You can find out the number of zeros in the number written through the American system, it is possible by a simple formula 3 · X + 3 (where X is Latin numerical).
The English name system is most common in the world. She enjoyed, for example, in the UK and Spain, as well as in most former English and Spanish colonies. The names of the numbers in this system are built as follows: so: Sufifix -Ilion is added to the Latin number, the following number (1000 times more) is built on the principle - the same Latin numerical, but suffix - -lilliard. That is, after a trillion in the English system, trilliard goes, and only then the quadrillion followed by quadrilliore, etc. Thus, quadrillion in English and American systems are quite different numbers! You can find out the amount of zeros in the number recorded in the English system and the ending suffix-cylon, it is possible according to the formula 6 · X + 3 (where X is Latin numeral) and according to the formula 6 · x + 6 for the numbers ending on -ylard.
From the English system, only the number of billion (10 9) passed from the English system, which would still be more correctly called as the Americans call him - Billion, since we received the American system. But who in our country does something according to the rules! ;-) By the way, sometimes in Russian use the word trilliard (you can make sure about it, running the search in Google or Yandex) and it means, apparently, 1000 trillion, i.e. quadrillion.
In addition to the numbers recorded with the help of Latin prefixes on the American or England system, the so-called non-systemic numbers are known, i.e. Numbers that have their own names without any Latin prefixes. There are several such numbers, but I will tell you more about them a little later.
Let's return to the record with Latin numerals. It would seem that they can be recorded to the numbers before concern, but it is not quite so. Now I will explain why. Let's see for a start called numbers from 1 to 10 33:
And now, the question arises, and what's next. What is there for Decillion? In principle, it is possible, of course, with the help of the combination of consoles to generate such monsters as: Andecilion, Duodeticillion, Treadsillion, Quarterdecillion, Quendecyllion, Semtecillion, Septecyllin, Oktodeticillion and New Smecillion, but it will already be composite names, and we were interested in our own names. numbers. Therefore, its own names on this system, in addition to the above, can still be obtained only three - Vigintillion (from Lat.viginti. - Twenty), Centillion (from Lat.centum. - One hundred) and Milleillion (from Lat.mille - one thousand). More than a thousand of their own names for numbers in the Romans was no longer (all numbers more than a thousand they had compounds). For example, a million (1,000,000) Romans calleddecies Centena Milia., that is, "ten hundred thousand". And now, in fact, Table:
Thus, according to a similar system, the number is greater than 10 3003 Which would be own, the inexpensive name is not possible! Nevertheless, the number more than Milleillion is known - these are the most generic numbers. Let's tell you finally, about them.
The smallest such number is Miriada (it is even in the Dala dictionary), which means hundreds of hundreds, that is - 10,000. The word is, however, it is outdated and practically not used, but it is curious that the word "Miriada" is widely used, which is widely used There is not a certain number at all, but countless, the incredible set of something. It is believed that the Word of Miriad (Eng. Myriad) came to European languages \u200b\u200bfrom ancient Egypt.
What about the origin of this number there are different opinions. Some believe that it originated in Egypt, others believe that it was born only in antique Greece. Be that as it may, in fact, I received Miriad's fame thanks to the Greeks. Miriada was the name for 10,000, and for numbers more than ten thousand names was not. However, in the note "Psammit" (i.e., the calculus of sand) Archimedes showed how to systematically build and call arbitrarily large numbers. In particular, placing grains in the poppy seeds of 10,000 (Miriad), he finds that in the universe (the ball with a diameter of the diameter of the earth) would fit (in our designations) not more than 1063
peschin. It is curious that modern counting of the number of atoms in the visible universe leads to67
(In total, Miriad times more). The names of the numbers Archimeda suggested such:
1 Miriad \u003d 10 4.
1 di-Miriada \u003d Miriad Miriad \u003d 108
.
1 tri-myriad \u003d di-myriad di-myriad \u003d 1016
.
1 tetra-myriad \u003d three-myriad three-myriad \u003d 1032
.
etc.
Gugol.(from the English. Googol) is a number of ten to a hundredth, that is, a unit with a hundred zeros. About "Google" for the first time wrote in 1938 in the article "New Names in Mathematics" in the January issue of Scripta Mathematica magazine American mathematician Edward Kasner (Edward Kasner). According to him, to call "Gugol" a large number suggested his nine-year-old nephew Milton Sirotta (Milton Sirotta). Well-known this number was due to the search engine named after him Google . Please note that "Google" is a trademark, and googol - a number.
Edward Kasner (Edward Kasner).
On the Internet, you can often meet the mention that - but it is not so ...
In the famous Buddhist treatise, Jaina-Sutra, belonging to 100 g. BC, meets the number asankhaya (from whale. asianz - innumerable), equal to 10 140. It is believed that this number is equal to the number of space cycles required to gain nirvana.
Googolplex(eng. googolplex.) - the number also invented by Castner with his nephew and meaning a unit with google zeros, that is 10 10100 . Here's how Kasner himself describes this "Opening":
Words of Wisdom Are Spoken by Children At Least Asiss AS by Scientists. The Name "Googol" Was Invented by A Child (Dr. Kasner "S Nine-Year-Old NEPHEW) Who Was Asked to Think Up a Name For a Very Big Number, Namely, 1 With a Hundred Zeros After IT. He Was Very CERTIAIN THIS THIS NUMBER WAS NOT INFINITE, AND THEREFORE EQUALLY CERTAIN THAT IT TIME THAT A NAME. AT THE SAME TIME THAT HE SUGGESTED "GOOGOL" HE GAVE A NAME FOR A STILL LARGER NUMBER: "GOOGOLPLEX." A GOOGOLPLEX IS MUCH LARGER THAN A Googol, But Is Still Finite, As The Inventor of the Name Was Quick to Point Out.
Mathematics and the Imagination (1940) by Kasner and James R. NEWMAN.
Even greater than the googolplex number - number of Skusza (Skewes "Number) was proposed by Skusom in 1933 (Skewes. J. London Math. SOC. 8, 277-283, 1933.) In the proof of Riman's hypothesis concerning prime numbers. It means e.in degree e.in degree e.to degree 79, that is, EE e. 79 . Later, Riel (Te Riele, H. J. J. "On the Sign of the Difference P(x) -li (x). " Math. Comput. 48, 323-328, 1987) reduced the number of Skuse to EE 27/4 that is approximately 8,185 · 10 370. It is clear that once the value of the number of Scyss depends on the number e., it is not a whole, so we will not consider it, otherwise I would have to remember other insignificant numbers - the number Pi, the number E, and the like.
But it should be noted that there is a second number of Skuse, which in mathematics is indicated as SK2, which is even more than the first number of Skusz (SK1). The second number of Skusza, J. Skews were introduced in the same article to designate the number for which Riman's hypothesis is not valid. SK2 is 1010. 10103 , that is, 1010 101000 .
As you understand the more degrees, the harder it is to understand which of the numbers is more. For example, looking at the number of Skusz, without special calculations, it is almost impossible to understand which of these two numbers is more. Thus, for super-high numbers, it becomes inconvenient to use degrees. Moreover, you can come up with such numbers (and they are already invented), when the degrees are simply not climbed into the page. Yes, that on the page! They will not fit, even in a book, the size of the whole universe! In this case, the question arises how to record them. The problem, as you understand, are solvable, and mathematics have developed several principles for recording such numbers. True, every mathematician who asked this problem came up with his way of recording, which led to the existence of several not related to each other, methods for recording numbers - these are notations of Knuta, Conway, Steinhause, etc.
Consider the notation of the Hugo Roach (H. Steinhaus. Mathematical Snapshots., 3rd EDN. 1983), which is pretty simple. Stein House offered to record large numbers inside geometric figures - triangle, square and circle:
Steinhauses came up with two new super-high numbers. He called the number - Mega, and number - Megiston.
Mathematics Leo Moser finalized the notation of the wallhause, which was limited by the fact that if it was required to record numbers a lot more Megiston, difficulties and inconvenience occurred, since it had to draw a lot of circles one inside the other. Moser suggested not circles after squares, and pentagons, then hexagons and so on. He also offered a formal entry for these polygons so that the numbers can be recorded without drawing complex drawings. Notation by Mosel looks like that:
Thus, according to the notation of Mosel, Steinhouse mega is recorded as 2, and Megstone as 10. In addition, Leo Moser proposed to call a polygon with the number of sides to mega-megaagon. And suggested the number "2 in the megagon", that is 2. This number became known as Moser (Moser "s Number) or just like moser.
But Moser is not the largest number. The largest number ever used in mathematical proof is the limit value known as graham number(Graham "S Number), first used in 1977 in the proof of one assessment in the Ramsey theory. It is associated with bichromatic hypercubs and cannot be expressed without a special 64-level system of special mathematical symbols introduced by the whip in 1976.
Unfortunately, the number recorded in the notation of the whip cannot be translated into a record on the Mosel system. Therefore, this system will have to explain. In principle, it also has nothing complicated. Donald Knut (yes, yes, this is the same whip that wrote the "Art of Programming" and created the TeX editor) invented the concept of a superpope, which offered to record the arrows directed upwards
In general, it looks like this:
I think everything is clear, so let us return to the number of Graham. Graham proposed the so-called G-numbers:
The number G63 began to be called number Graham(It is often simple as G). This number is the largest number in the world in the world and entered even in the "Guinness Book of Records". A, here is that the number of Graham is greater than the number of Mosel.
P.S.To bring the great benefit to all mankind and become famous in the centuries, I decided to come up with and name the biggest number. This number will be called ostasks And it is equal to the number G100. Remember it and when your children will ask what the world's largest number, tell them that this number is called ostasks
So there are numbers more than graham? There are, of course, to start there are the number of Graham. As for the meaningful number ... Well, there are some devilish complex areas of mathematics (in particular, areas known as combinatorics) and informatics in which there are even large numbers than the number of Graham. But we almost reached the limit of what can be reasonably and understood.
Child today asked: "What is the name of the largest number in the world?" The question is interesting. We climbed into the Internet and here on the first line of Yandex found a detailed article in LJ. Everything is described in detail. There are two numbers name systems: English and American. And, for example, quadrillion in English and American systems are completely different. The biggest not a constituent number is
Milleillion \u003d 10 in 3003 degrees.
The son as a result came to a completely reasonable introduction that it is possible to count endlessly.
The original is taken by W. ctac in the biggest number in the world
As a child, I was tormented by a question that exists
the largest number and I got out of this stupid
the question is almost all in a row. Upon learning Number
million, I asked if there is a number more
million. Billion? And more than a billion? Trillion?
And more trillion? Finally, someone was intelligent,
who explained to me that the question is stupid, since
just just add to the very
a large number of one, and it turns out that it
never was the biggest way exist
the number is even more.
And here, after many years, I decided to ask another
question, namely: what is the most
a large number that has its own
name? Good, now there is an Internet and puzzle
they can be patient search engines that are not
will call my questions idiot ;-).
Actually, I did it, and that's what as a result
found out.
| Number | Latin name | Russian console |
| 1 | Unus | An- |
| 2 | duo. | duo- |
| 3 | Tres. | three- |
| 4 | quattuor | quadry |
| 5 | QUINQUE | quint |
| 6 | Sex | sexti |
| 7 | septem. | septic |
| 8 | Octo. | octic |
| 9 | novem. | non- |
| 10 | Decem. | deci- |
There are two numbers name systems -
american and English.
The American system is pretty
simply. All the names of large numbers are built as:
at the beginning there is a Latin ordinal number,
and at the end, suffix is \u200b\u200badded to it.
The exception is the name "Million"
which is the name of the number of a thousand (lat. mille)
and magnifying suffix -illion (see table).
So it turns out the numbers - 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 among the recorded by
american system, it is possible by a simple formula
3 · X + 3 (where X is Latin numeral).
English name system most
distributed in the world. She enjoyed, for example, in
Great Britain and Spain, as well as in most
former English and Spanish colonies. Names
numbers in this system are built like this: so: to
latin numerical add suffix
-Lion, the next number (1000 times more)
it is based on the principle - the same
latin numerical, but suffix - -lilliard.
That is, after a trillion in the English system
trilliard goes, and only then quadrillion, for
whom the quadrillard follows, etc. Thus
way, kvadrillion in English and
american systems are quite different
numbers! Find out the number of zeros among
recorded in the English system and
ending suffix -illion can
formula 6 · x + 3 (where X is Latin numeral) and
according to the formula 6 · X + 6 for the numbers ending on
-Lilliard.
From the English system in the Russian language
only the number of billion (10 9), which is still
it would be more correct to call as it is called
americans - Billion, as we have accepted
it is the American system. But who we have
the country does something according to the rules! ;-) By the way,
sometimes in Russian consumes the word
trilliard (you can make sure about it
running search B. Google or Yandex) and it means, judging by
everything, 1000 trillion, i.e. quadrillion.
In addition to the numbers recorded with Latin
prefixes on the American or England system,
famous and so-called non-systemic numbers,
those. numbers that have their own
names without any Latin prefixes. Such
numbers there are several, but I Read more about them
i'll tell you a little later.
Let's go back to the record with Latin
numeral. It would seem that they can
write numbers to abstractness, but it is not
quite like that. Now I will explain why. Let's see for
beginning as numbers from 1 to 10 33:
| Name | Number |
| Unit | 10 0 |
| Ten | 10 1 |
| One hundred | 10 2 |
| One thousand | 10 3 |
| Million | 10 6 |
| Billion | 10 9 |
| Trillion | 10 12 |
| Quadrillion | 10 15 |
| Quintillion | 10 18 |
| Sextillion | 10 21 |
| Septillion | 10 24 |
| Octillion | 10 27 |
| Quintillion | 10 30 |
| Decillion | 10 33 |
And now, the question arises, and what's next. what
there for Decillion? In principle, you can, of course,
with the help of combining consoles to generate such
monsters like: Andecilion, Douodecillion,
treadsillion, QuintorDecyllion, Quendecyllion,
sexillion, septemberion, octodeticillion and
newdecyllion, but it will already be composite
names, and we were interested in
own names numbers. Therefore, their own
names on this system, in addition to the above, still
can only get three
- Vigintillion (from Lat. viginti. —
twenty), Centillion (from Lat. centum. - one hundred) and
milleilla (from Lat. mille - one thousand). More
thousands of own names for numbers in Romans
there was no (all numbers more than a thousand they had
composite). For example, a million (1,000,000) Romans
called decies Centena Milia., that is, "Ten hundred
thousand. "And now, in fact, Table:
Thus, according to a similar number of the number
more than 10,3003, who would have
own, incompening name get
impossible! But nevertheless, the number is more
milleillion is known - these are the most
intimated numbers. Let's tell you finally, about them.
| Name | Number |
| Miriada | 10 4 |
| Gugol. | 10 100 |
| Asankhaya | 10 140 |
| Googolplex | 10 10 100 |
| The second number of Skusza | 10 10 10 1000 |
| Mega | 2 (in the notation of Moser) |
| Megiston | 10 (in the notation of Mosel) |
| Moser | 2 (in the notation of Moser) |
| Graham number | G 63 (in the Graham Notation) |
| Ostasks | G 100 (in Graham Notation) |
The smallest such number is miriada
(it is even in the Dala dictionary), which means
hundred hundred, that is - 10,000. The word is, however,
outdated and practically not used, but
it is curious that the word is widely used
"Miriada", which means not at all
a certain number, and countless, unpleasant
many of something. It is believed that the word Miriad
(eng. Myriad) came to European languages \u200b\u200bfrom the ancient
Egypt.
Gugol. (from the English. Googol) is the number ten in
a hundredth of the degree, that is, a unit with a hundred zeros. ABOUT
"Google" first wrote in 1938 in the article
"New Names in Mathematics" in the January issue of the magazine
Scripta Mathematica American Mathematics Edward Casner
EDWARD KASNER). According to him, call "Gugol"
a large number suggested his nine-year-old
milton Sirotta nephew (Milton Sirotta).
Well-known this number was due to
named after him, search engine Google . note that
"Google" is a trademark, and googol - a number.
In the famous Buddhist treatise Jaina-Sutra,
100 g. BC, meets the number asankhaya
(from whale. asianz - innumerable), equal to 10 140.
It is believed that this number is the number
space cycles required for gaining
nirvana.
Googolplex (eng. googolplex.) - the number is also
invented by Castner with his nephew and
meaning a unit with google zeros, that is, 10 10 100.
Here's how Kasner himself describes this "Opening":
Words of Wisdom Are Spoken by Children At Least Asiss AS by Scientists. The Name.
"Googol" WAS Invented by A Child (Dr. Kasner "S Nine-Year-Old Nephew) Who Was
aSKED TO THINK UP A NAME FOR A VERY BIG NUMBER, NAMELY, 1 WITH A HUNDRED ZEROS AFTER IT.
He Was Very Certain That This Number Was Not Infinite, And Theraefore 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.
Even greater than the googolplex number - the number
Skuse (Skewes "Number) was proposed by Skews in 1933
year (Skewes. J. London Math. SOC. 8
, 277-283, 1933.) when
proof of hypothesis
Rimanna concerning prime numbers. It
means e.in degree e.in degree e.in
degree 79, that is, E E E 79. Later,
Riel (Te Riele, H. J. J. "On the Sign of the Difference P(x) -li (x). "
Math. Comput. 48
, 323-328, 1987) reduced the number of Skusza to E E 27/4,
which is approximately 8,185 · 10 370. Clear
the matter is that the value of the number of Skusza depends on
numbers e.then it is not a whole, so
we will not consider it, otherwise I would have to
remember other insignificant numbers - the number
pi, number E, number of Avogadro, etc.
But it should be noted that there is a second number
Skusza, which in mathematics is indicated as SK 2,
which is even more than the first number of Skuse (SK 1).
The second number of SkuszaIt was introduced by J.
Skusom in the same article for the designation of the number, to
which is the hypothesis of Rimena fair. SK 2.
equal to 10 10 10 10 3, that is 10 10 10 1000
.
As you understand the more degrees,
the hard to understand which of the numbers is more.
For example, looking at the number of Skusza, without
special calculations are almost impossible
understand which of these two numbers is more. Thus
for super-high numbers to use
degnese becomes uncomfortable. Moreover, you can
come up with such numbers (and they are already invented) when
the degrees of degrees simply do not fit on the page.
Yes, that on the page! They will not fit, even in the book,
the size of the whole universe! In this case, gets up
the question is how to record them. Problem how you
understand solvable and mathematics developed
several principles for recording such numbers.
True, every mathematician who wondered this
the problem came up with his way of recording that
led to the existence of several not related
with each other, ways to write numbers is
notation Knuta, Konveya, Steinhaus, etc.
Consider the notation of the Hugo Roach (H. Steinhaus. Mathematical
Snapshots., 3rd EDN. 1983), which is pretty simple. Stein
howes offered to record large numbers inside
geometric figures - triangle, square and
circle:
Steinhauses came up with two new superbral
numbers. He called the number - Mega, and number - Megiston.
Mathematics Leo Moser finalized notation
Stenhause, which was limited by the fact that if
required to record numbers a lot more
megiston, difficulties and inconvenience arose, so
how I had to draw a lot of circles one
inside the other. Moser offered after squares
do not draw circles, and pentagons, then
hexagons and so on. He also suggested
formal entry for these polygons,
so that you can write numbers without drawing
complex drawings. The notation of Moser looks like this:
Thus, according to the notation of Moser
steinhauzovsky mega is recorded as 2, and
megston like 10. In addition, Leo Moser offered
call a polygon with the number of sides to equal
mega - Megagon. And offered the number "2 in
Megagon ", that is 2. This number has become
known as Moser number (Moser "s Number) or just
as moser.
But Moser is not the largest number. The largest
the number ever used in
mathematical proof is
limit value known as graham number
(Graham "S Number), first used in 1977 in
proof of one assessment in the Ramsey theory. It
associated with bichromatic hypercubes and not
can be expressed without a special 64-level
systems of special mathematical symbols,
introduced by the whip in 1976.
Unfortunately, the number recorded in the notation of the whip
cannot be transferred to a record on the MOGER system.
Therefore, this system will have to explain. IN
the principle in it is also nothing complicated. Donald
Knut (yes, yes, this is the same whip that wrote
"Art of Programming" and created
tex editor) invented the concept of a superpope,
which suggested burn arrows,
directed up:
In general, it looks like this:
I think that everything is clear, so let's return to the number
Graham. Graham proposed the so-called G-numbers:
The number G 63 began to be called number
Graham (It is often simple as G).
This number is the largest known in
the world is the number and entered even in the "Book of Records
Guinis ". Ah, that's what the number of Graham is greater than the number
Moser.
P.S. To bring great benefits
all mankind and become famous in the centuries, I
decided to come up and call the biggest
number. This number will be called ostasks and
it is equal to the number G 100. Remember it and when
your children will ask what is the biggest in
world number, tell them that this number is called ostasks.
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