What is the biggest number?

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What is the biggest number?
What is the biggest number?
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Probably, many have wondered what is the largest number. Of course, one can say that such a 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. Usually specific data is required. It is interesting not just to imagine an incredibly large amount of something abstract, but to find out what the name of the largest number is and how many zeros are in it. And we also need examples - what and where in the known and familiar surrounding world is in such quantity that it is easier to imagine this set, and knowledge of how such numbers can be written.

Abstract and concrete

Theoretical numbers are endless - whether it's easy to imagine or absolutely impossible to imagine - a matter of fantasy and desire. But it's hard not to admit it. There is also another designation that cannot be ignored - this is infinity +1. Simple and ingenioussolution of the issue of supermagnitudes.

Conventionally, all the largest numbers are divided into two groups.

Firstly, these are those that have found application in the designation of the amount of something or were used in mathematics to solve specific problems and equations. We can say that they bring specific 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 be, exist as a phenomenon, or / and glorify their discoverer. These numbers do not define anything but themselves, as there is nothing in such quantity that would be known to mankind.

Different numbers - not very big

Notation systems for the largest numbers in the world

There are two most common official systems that determine the principle by which names are given with large numbers. These systems, recognized in various states, are called American (short scale) and English (long scale names).

The 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 understanding of the Latin components:

1 unus en-

2 duo duo- and bis bi- (twice)

3 tres three-

4 quattuor quadri-

5 quinque quinti-

6 sex sexty-

7 septem septi-

8 octo octo-

9 novem noni-

10 decem deci-

First accepted,respectively, in the United States, as well as in Russia (with some changes and borrowings from English), in Canada bordering the United States and in France. The names of the quantities are made up of the Latin numeral, which indicates the power of a thousand, + -llion is a suffix denoting an increase. The only exception to this rule is 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 count how many zeros each larger number has, named according to the American system. The formula is very simple - 3x + 3 (in this case, x is a Latin numeral). For example, a billion is a number with nine zeros, a trillion would have twelve zeros, and an octillion would have 27.

In a man's head

The English system is used by a large number of countries. It is used in Great Britain, 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 - million, the next (a thousand times larger) will be named after the same Latin ordinal number, but with an ending - billion. That is, after a trillion, not a quadrillion, but a trillion will follow. And then a quadrillion and a quadrillion.

In order not to get confused in the zeros and the names of the English system, there is a formula 6x+3 (suitable for those numbers whose name ends in -million), and 6x+6 (for those with the ending -billion).

The use of different naming systems has led tothe same named numbers in fact will mean a different amount. For example, a trillion in the American system has 12 zeros, in the English system it has 21.

The largest of the quantities, whose names are built on the same principle and which can rightfully refer to the largest numbers in the world, are called as the maximum non-compound numbers that existed among the ancient Romans, plus the suffix -llion, this is:

  • Vigintillion or 1063.
  • Centillion or 10303.
  • Millionion or 103003.

There are more than a million numbers, but their names, formed in the way described earlier, will be composite. In Rome, there were no separate words for numbers over 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 chosen and compiled not according to the rules of the above two ways of forming the names of numerals. These numbers are:

Myriad 104

Google 1000

Asankheyya 10140

Googleplex 1010100

Second Skewes number 1010 10 1000

Mega 2[5] (in Moser notation)

Megiston 10 [5] (in Moser notation)

Moser 2[2[5]] (in Moser notation)

G63 Graham number (in Graham notation)

Stasplex G100 (in Graham notation)

And some of them are still absolutely unsuitable for use outside of theoretical mathematics.

Myriad

The word for 10000, mentioned in Dahl's dictionary,obsolete and out of circulation as a specific value. However, it is widely used to refer to the great multitude.

Asankheya

Numbers in a spiral

One of the iconic and largest numbers of antiquity 10140 is mentioned in the second century BC. e. in the famous Buddhist treatise Jaina Sutra. Asankheya comes from the Chinese word asengqi, which means "innumerable". He noted the number of cosmic cycles required to reach nirvana.

One and eighty zeros

The largest number that has a practical application and its own unique, albeit compound name: one hundred quinquavigintillion or sexvigintillion. It denotes only an approximate number of all the smallest components of our Universe. There is an opinion that zeros should not be 80, but 81.

What is one googol equal to?

A term coined in 1938 by a nine-year-old boy. A number denoting the amount of something, equal to 10100, ten followed by one hundred zeros. This is more than the smallest subatomic particles that make up the universe. It would seem, what could be the practical application? But it was found:

  • scientists believe that exactly in a googol or one and a half googol years from the moment the Big Bang created our Universe, the most massive black hole in existence will explode, and everything will cease to exist in the form in which it is now known;
  • Alexis Lemaire made his name famous with a world record by calculating the thirteenth root of the largest number - a googol - with a hundred digits.

Planck values

8, 5 x 10^185 is the number of Planck volumes in the universe. If you write all the numbers without using a degree, there will be one hundred and eighty-five.

Planck's volume is the volume of a cube with a face equal to an inch (2.54 cm), which fits about a googol of Planck lengths. Each of them is equal to 0.0000000000000000000000000000616199 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 ​​\u200b\u200bare not uncommon.

The largest prime number

Lots of numbers

A prime number is something that has no integer divisors other than one and itself.

277 232 917− 1 is the largest prime number that could be calculated to date (recorded in 2017). It has over twenty-three million digits.

What is a "googolplex"?

The same boy from the last century - Milton Sirotta, the nephew of the American Edward Kasner, came up with another good name to denote an even larger value - ten to the power of a googol. The number was named "googolplex".

Two Skuse numbers

Both the first and second Skewes numbers are among the largest numbers in theoretical mathematics. Called to set the limit for one of the toughest challenges ever:

"π(x) > Li(x)".

First Skuse number (Sk1):

number x is less than 10^10^10^36

or e^e^e^79 (laterwas reduced to a fractional number e^e^27/4, so it is usually not mentioned among the largest numbers).

Second Skuse number (Sk2):

number x is less than 10^10^10^963

or 10^10^10^1000.

For many years in the Poincaré theorem

Time and numbers

The number 10^10^10^10^10^1, 1 indicates the number of years that it will take for everything to repeat itself and reach the current state, which is the result of random interactions of many tiny components. Such are the results of theoretical calculations in Poincaré's theorem. To put it simply: if there is enough time, absolutely anything can happen.

Graham's number

A record holder who got 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 denote it, one of the special systems for writing large numbers is used - Knuth notation using arrows - and a special equation.

Written as G=f64(4), where f(n)=3↑^n3. Highlighted by Ron Graham for use in calculations concerning the theory of colored hypercubes. A number of such a scale that even the Universe cannot contain its decimal notation. Referred to as G64 or simply G.

Stasplex

The largest number that has a name. Stanislav Kozlovsky, one of the administrators of the Russian-language version of Wikipedia, immortalized himself in this way, not at all a mathematician, but a psychologist.

Stasplex number=G100.

Numbers, numbers, numbers

Infinityand more than her

Infinity is not just an abstract concept, but an immense mathematical quantity. Whatever calculations with her participation are made - summation, multiplication or subtraction of specific numbers from infinity - the result will be equal to her. Probably, only when dividing infinity by infinity can one be obtained in the answer. It is known about an infinite number of even and odd numbers in infinity, but the total infinity of both of them will be about half.

No matter how many particles in our Universe, according to scientists, this applies only to a relatively known area. If the assumption of the infinity of universes is correct, then not only everything is possible, but an uncountable number of times.

However, not all scientists agree with the theory of infinity. For example, Doron Silberger, an Israeli mathematician, takes the position that numbers will not continue indefinitely. In his opinion, there is a number that is so large that by adding one to it, you can get zero.

It is still impossible to verify or disprove this, so the debate about infinity is more philosophical than mathematical.

Methods of fixing theoretical supervalues

Mathematician among equations and numbers

For incredibly large numbers, the number of degrees is so large that it is inconvenient to use this value. Several mathematicians have developed different systems for displaying such numbers.

Knuth's notation using the system of symbols-arrows denoting the superdegree, consistingof 64 levels.

For example, a googol is 10 to the hundredth power, the usual notation is 10100. According to the Knuth system, it will be written as 10↑10↑2. The larger the number, the more arrows that raise the original number many times to any power.

Graham's notation is an extension of Knuth's system. To indicate the number of arrows, G numbers with serial numbers are used:

G1=3↑↑…↑↑3 (the number of arrows indicating superdegree is 3 ↑↑↑↑);

G2=↑↑…↑↑3 the number of arrows denoting superdegree is G1);

And so on until G63. It is it that is considered the Graham number and is often written without a serial number.

Steinhouse notation – To indicate the degree of degrees, geometric figures are used, into which one or another number fits. Steinhouse chose the main ones - a triangle, a square and a circle.

The number n in a triangle denotes a number to the power of this number, in a square - a number to the power equal to the number in n triangles, inscribed in a circle - to the power identical to the power of the number inscribed in the square.

Leo Moser, who invented such giant numbers as mega and megiston, improved the Steinhouse system by introducing additional polygons and inventing a way to write them, using square brackets. He also owns the name megagon, referring to a polygonal geometric figure with a mega number of sides.

One of the biggest numbers in mathematics,named after Moser, counts as 2 in megagon=2[2[5]].

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