Probably many wondered which number is the largest. Of course, we can say that this number will always remain infinity or infinity + 1, but this is unlikely to be the answer that those who ask such a question want to hear. Specific data is usually required. It is interesting not only to imagine an incredibly many abstract things, but to find out what the largest number is called and how many zeros are in it. And we also need examples - what and where in the known and familiar surrounding world there are in such numbers that it would be easier to imagine this set, and knowledge of how such numbers can be written down.
Abstract and concrete
The theoretical numbers are endless - whether it is easy to imagine or absolutely impossible to imagine is a matter of fantasy and desire. But itβs hard not to admit it. There is also another designation that cannot be ignored - this is infinity +1. A simple and ingenious solution to the issue of super-quantities.
Conventionally, all the largest numbers are divided into two groups.
Firstly, these are those that have found application in the notation of the amount of something or used in mathematics to solve specific problems and equations. We can say that they bring concrete benefits.
And secondly, those immeasurably huge quantities that have a place only in theory and abstract mathematical reality - indicated by numbers and symbols, given names in order to simply exist, to exist as a phenomenon, and / or to glorify their discoverer. These numbers do not define anything but themselves, since there is nothing in such quantity that humanity would be aware of.
The largest numbering system in the world
There are two of the most common official systems that define the principle by which large numbers are given names. These systems, recognized in various states, are called American (short scale) and English (long scale of names).
Names in both are formed using the names of Latin numbers, but according to different schemes. To understand each of the systems, it is better to have an idea of ββthe Latin components:
1 unus en
2 duo duo and bis bi- (twice)
3 tres three-
4 quattuor quad
5 quinque quintes
6 sex sex
7 septem septi
8 octo octi
9 novem non-
10 decem dec
The first is adopted, respectively, in the United States, as well as in Russia (with some changes and borrowings from English), in the border with the United States of Canada and in France. Names of quantities are made up of a Latin numeral that shows the power of a thousand, + -lillion is a suffix that indicates an increase. An exception to this rule is only the word "million" - in which the first part is taken from the Latin mille - which means "thousand."
Knowing the Latin ordinal names of numbers, it is easy to calculate how many zeros each has a greater number, named according to the American system. The formula is very simple - 3 * x + 3 (in this case x is a Latin numeral). For example, a billion is a number of nine zeros, a trillion will have twelve zeros, and an octillion will have 27.
The English system is used by a large number of countries. It is used in the UK, in Spain, as well as in many historical colonies of these two states. Such a system gives names to large numbers according to the same principle as the American one, only after a number with an ending - a million, the next (a thousand times large) will be named after the same Latin ordinal numeral, but with an ending - a billion. That is, after a trillion, not a trillion will follow, but a trillion. And then quadrillion and quadrillion.
In order not to get confused in the zeros and names of the English system, there is a formula 6 * x + 3 (suitable for those numbers whose name ends with -illion), and 6 * x + 6 (for those with an ending-billion).
The use of different naming systems has led to the fact that identically named numbers in fact will mean different amounts. For example, a trillion in the American system has 12 zeros, in the English - 21.
The largest of the quantities, the names of which are built on the same principle and which can rightfully refer to the largest numbers in the world, are called as the maximum non-composite numerals that existed among the ancient Romans, plus the suffix - a million, this:
- Vigintillion or 10 63 .
- Centillion or 10,303.
- Million or 10,303.
There are more than a million of numbers, but their names, formed in the manner described earlier, will be compound. In Rome there were no separate words for numbers more than a thousand. For them, a million existed as ten hundred thousand.
However, there are also non-systemic names, as well as non-systemic numbers - their own names are not chosen and compiled according to the rules of the two above methods for generating numerals. These numbers are:
Miriada 10 4
Googol 10 00
Asankheya 10 140
Googolpleks 10 10 100
The second number of Skuse 10 10 10 1000
Mega 2 [5] (in Moser notation)
Megiston 10 [5] (in Moser notation)
Moser 2 [2 [5]] (in Moser notation)
Graham number G63 (in Graham notation)
Stasplex G100 (in Graham notation)
And some of them are absolutely unsuitable for use outside of theoretical mathematics.
Miriada
The word denoting 10000, mentioned in the Dahl dictionary, is outdated and has gone out of circulation as a specific quantity. However, it is widely used to refer to a great many.
Asankheya
One of the iconic and largest numbers of antiquity 10140 is mentioned in the second century BC. e. in the famous Buddhist treatise of the Jaina Sutra. Asankheya comes from the Chinese word asentsi, which means "innumerable." He noted the number of cosmic cycles required to achieve nirvana.
One and eighty zeros
The largest number that has practical application and its own unique, albeit composite, name: one hundred quinquavigintillion or sexvigintillion. It denotes only an approximate number of all the smallest components of our universe. It is believed that zeros should not be 80, but 81.
What is one googol equal to?
The term coined in 38 of the last century by a nine-year-old boy. A number indicating the amount of something equal to 10,100 , ten with one hundred zeros. This is more than the smallest subatomic particles that make up the universe. It would seem, what could be practical application? But it was found:
- scientists believe that itβs in a googol or a year and a half from the moment the Big Bang created our Universe that the massive existing black hole will explode and everything will cease to exist in the form in which it is now known;
- Alexis Lehmer glorified his name with a world record, calculating the root of the thirteenth degree from the largest number - googol - of one hundred.
Planck Values
8.5 x 10 ^ 185 is the number of Planck volumes in the universe. If you write all the numbers without applying the degree, there will be one hundred eighty-five.
Planck volume is the volume of a cube with a face equal to an inch (2.54 cm) in which it is placed near the googol of Planck lengths. Each of them is equal to 0.00000000000000000000000000000616199 meters (otherwise 1.616199 x 10 -35 ). Such small particles and large numbers are not needed in ordinary everyday life, but in quantum physics, for example, for those scientists who work on string theory, such values ββare not uncommon.
Largest prime number
A prime number is one that does not have integer divisors other than one and itself.
2 77 232 917 - 1 is the largest of the prime numbers that we have been able to calculate to date (recorded in 2017). It contains more than twenty-three million digits.
What is googolpleks?
All the same boy from the last century - Milton Sirotta, the nephew of the American Edward Kasner, came up with another successful name for an even larger size - ten in a googol degree. The number received the name "googolplex".
Two numbers of squash
Both the first and second numbers of Skuse are among the largest numbers in theoretical mathematics. Called to set a limit for one of the most complex tasks that have ever existed:
Ξ (x)> Li (x).
The first number of Skuse (Sk1):
number x is less than 10 ^ 10 ^ 10 ^ 36
or e ^ e ^ e ^ 79 (it was later reduced to a fractional number e ^ e ^ 27/4, therefore it is usually not mentioned among the largest numbers).
The second number of Skuse (Sk2):
number x is less than 10 ^ 10 ^ 10 ^ 963
or 10 ^ 10 ^ 10 ^ 1000.
For many years in the Poincare theorem
The number 10 ^ 10 ^ 10 ^ 10 ^ 10 ^ 1,1 denotes the number of years that it takes for everything to repeat and reach the current state, which is the result of random interactions of many small components. Such are the results of theoretical calculations in the Poincare theorem. Simply put: if you have enough time, absolutely everything can happen.
Graham Number
The record holder who fell into the Guinness book in the last century. In the process of mathematical proofs, a large finite number has never been used. Incredibly big. To designate it, one of the special systems for writing large numbers is used - Knuth notation using arrows - and a special equation.
It is expressed in writing as G = f64 (4), where f (n) = 3 β ^ n3. Dedicated by Ron Graham for use in computations concerning the theory of color hypercubes. A number of such a scale that even the Universe cannot accommodate its decimal notation. It is designated as G64 or simply G.
Stasplex
The largest number that has a name. In this way Stanislav Kozlovsky, one of the administrators of the Russian-language version of Wikipedia, immortalized himself, not at all a mathematician, but a psychologist.
Stasplex number = G100.
Infinity and that which is greater than it
Infinity is not just an abstract concept, but an immense mathematical quantity. No matter what calculations with her participation, such as summing, multiplying or subtracting specific numbers from infinity, the result will be equal to it. Probably only when dividing infinity by infinity can one get a unit in the answer. It is known about an infinite number of even and odd numbers at infinity, but there will be about half of the general infinity of both.
No matter how many particles in our Universe, according to scientists, this applies only to a relatively well-known area. If the assumption that the universes are infinite is true, then not only everything is possible, but countless times are possible.
However, not all scientists agree with the theory of infinity. For example, Doron Zilberger, a mathematician from Israel, maintains that numbers will not go on forever. In his opinion, there is a number that is so large that, adding a unit to it, you can get zero.
It is not yet possible to verify or refute this, so the debate about infinity is more philosophical than mathematical.
Methods for fixing theoretical super-quantities
For incredibly large numbers, the number of degrees is so large that using this value is inconvenient. Several mathematicians have developed different systems for displaying such numbers.
Knuth notation using a system of arrow symbols denoting a super degree consisting of 64 levels.
For example, googol is 10 to the hundredth degree, the usual form of record is 10 100 . According to the Knut system, it will be written as 10 β 10 β 2. The larger the number, the more arrows that raise the original number many times to some extent.
Graham's notation is its refinement of the Whip system. To indicate the number of arrows, the numbers G with serial numbers are used:
G 1 = 3 ββ ... ββ 3 (the number of arrows denoting the super degree is 3 ββββ);
G 2 = ββ ... ββ 3 the number of arrows denoting the super degree is equal to G 1 );
And so on to G 63 . It is it that is considered the Graham number and is often written without a serial number.
Steinhaus notation - to indicate the degree of degrees , geometric figures are used, in which this or that number fits. Steinhaus chose the main ones - a triangle, a square and a circle.
The number n in a triangle denotes a number in the degree of this number, in a square - a number in a degree equal to the number in n triangles inscribed in a circle - in a degree identical to the degree of the number inscribed in a square.
Leo Moser, who invented such gigantic numbers as mega and megiston, improved the Steinhaus system by introducing additional polygons and devising a recording method that denotes them using square brackets. He also owns the name megagon, referring to a polygonal geometric figure with a megacount of sides.
One of the largest numbers in mathematics, named after Moser, is considered 2 in a megagon = 2 [2 [5]].