EducationSecondary education and schools

What is the largest number? The largest and smallest number

When a man was just learning to count, he had enough fingers to determine that two mammoths walking around a cave are less than a herd after a mountain. But as soon as he realized what a positional number (when a number has a specific place in a long row), he began to wonder: what next, what is the largest number?
Since then, the best minds have begun to look for how to calculate such quantities, and most importantly, what sense to impart to them.

Ellipsis at the end of the series

When schoolchildren are introduced to the original concept of natural numbers, an ellipsis is judiciously placed at the edges of a series of numbers and explains that the largest and smallest number is a meaningless category. There is always the possibility of adding one to the largest number, and it will not be the greatest anymore. But progress would not have been possible if there had not been those who wanted to find meaning where it should not be.

The infinity of the numerical series, apart from the frightening and indefinite philosophical significance, created purely technical difficulties. It was necessary to look for the notation for very large numbers. At first this was done separately for the main language groups, and with the development of globalization, words appeared that called the largest number, generally accepted throughout the world.

Ten, one hundred, one thousand

In each language, for numbers of practical importance, a proper name is found.

In Russian, first of all, this is a range from zero to ten. Up to a hundred further numbers are called or based on them, with a slight change of roots - "twenty" (two to ten), "thirty" (three to ten), etc., or are compound: "twenty-one," fifty-four ". Exception - instead of "fourteen" we have a more convenient "forty".

The largest two-digit number - "ninety-nine" - has a compound name. Further from its own traditional names - "one hundred" and "one thousand", the rest are formed from the right combinations. A similar situation in other common languages. It is logical to think that the established names were given to the numbers and figures with which most ordinary people dealt. Even a thousand heads of cattle could be imagined by an ordinary peasant. With a million it was more difficult, and confusion began.

Million, quintillion, decillion

In the mid-fifteenth century, the Frenchman Nicolas Szuke in order to designate the largest number, proposed a system of naming on the basis of numerals from the generally accepted Latin among scientists. In Russian, they underwent some modification for the convenience of pronunciation:

  • 1 - Unus - un.
  • 2 - Duo, Bi (double) - duo, bi.
  • 3 - Tres - three.
  • 4 - Quattuor - quad.
  • 5 - Quinque - quint.
  • 6 - Sex - sexties.
  • 7 - Septem - septi.
  • 8 - Octo - octi.
  • 9 - Novem - noni.
  • 10 - Decem - deci.

The basis of the names should be -illion, from "million" - "big thousand" - i.e. 1,000,000 - 1000 ^ 2 - A thousand in a square. This word, to mention the largest number, was first used by the famous sailor and scientist Marco Polo. So, a thousand in the third degree became a trillion, 1000 ^ 4 is a quadrillion. Another Frenchman, Pelletier, proposed for numbers that Shyuke called "a thousand million" (10 ^ 9), "a thousand bilions" (10 ^ 15) And so on, use the ending "billiards". It turned out that 1,000,000,000 is a billion, 10 ^ 15 - billiards, unit with 21 zero - trilliard and so on.

The terminology of French mathematicians has been used in many countries. But gradually it became clear that 10 ^ 9 In some works they began to be called not a billion, but a billion. And in the United States adopted a system by which the ending -illion received degrees of not a million, like the French, but thousands. As a result, today there are two scales in the world: "long" and "short". To understand what number is meant by a name, for example, a quadrillion, it is better to specify the degree to which the number is raised. If in the 15th, it is a "short" scale adopted in the USA, Canada, the United Kingdom and a number of other countries in Including in Russia (true, we have 10 ^ 9 - not a billion, but a billion), if in 24 - it is "long", adopted in most regions of the world.

Tredcillillion, vigintilliard and milleillion

After the last decimal digit is used, and the decillion is formed - the largest number without complex word formations - 10 ^ 33 on a short scale, the combinations of the necessary prefixes are used for the following digits. Complex compound names of the type Tredcillion-10 ^ 42, quindecillion - 10 ^ 48, etc. are obtained. Incomplete, the Romans received their own names: twenty - viginti, one hundred - centum and one thousand - mille. Following the rules of Shyuke, you can forever create monster names. For example, the number 10 ^ 308760 is called ducentuil-duomilongong-nong-one-year-oldion.

But these constructions are of interest only to a limited number of people - they are not used in practice, and even these values are not tied even to theoretical problems or theorems. It is for purely theoretical constructions that gigantic numbers are intended, sometimes they receive very sonorous names or are called by the author's surname.

Darkness, legion, asankheya

The question of huge numbers was also worried about "precomputer" generations. Slavs had several number systems, in some they reached huge heights: the largest number - 10 ^ 50. The names of numbers from the height of our time seem to be poetry, but in all of them there was a practical meaning, only historians and linguists know: 10 ^ 4 - "darkness", 10 ^ 5 - "legion", 10 ^ 6 - "leodr", 10 ^ 7 - a raven, a raven, 10 ^ 8 - a "deck".

No less beautiful by the name of the number of asaṃkhyeya is mentioned in Buddhist texts, in ancient Chinese and ancient Indian collections of sutras. The quantitative value of the number of asankheya researchers is given as 10 ^ 140. For those who understand it, it is full of divine meaning: it is so many cosmic cycles that the soul must go to purify itself of all the bodily accumulated during the long path of rebirth, and reach the blissful state of nirvana.

Гугол, гуголплекс

Mathematician from Columbia University (USA) Edward Kasner from the beginning of 1920 began to think about large numbers. In particular, he was interested in a sonorous and expressive title for a beautiful number of 10 ^ 100. Once he was walking with his nephews and told them about this number. Nine-year-old Milton Sirotta proposed the word googol - googol. Uncle received from his nephews and a bonus - a new number, which they explained as follows: a unit and as many zeros as you can write until you get tired. The name was Gugolplex. After reflection, Kashner decided that this would be the number 10 ^ googol.

Sense in such numbers Kashner saw more pedagogical: science then did not know anything in such quantity, and to future mathematicians, on their example, he explained what the largest number can keep from infinity.

The smart idea of the small geniuses of naming was appreciated by the founders of the company to promote a new search engine. The domain googol was busy, and the letter o fell out, but a name appeared, for which the ephemeral number could ever become real - so much will its stock cost.

The number of Shannon, the number of Skewes, the meson, megiston

Unlike physicists who periodically come across restrictions imposed by nature, mathematicians continue their way towards infinity. The fan of the chess game Claude Shannon (1916-2001) filled the meaning with the number 10 ^ 118 - just as many variants of positions can arise within 40 moves.

Stanley Skewes from South Africa was involved in one of seven tasks on the list of "Millennium Problems" - the Riemann hypothesis. It concerns the search for a regularity in the distribution of prime numbers. In the course of his argument, he used first the number 10 ^ 10 ^ 10 ^ 34, designated by him Sk 1 , and then 10 ^ 10 ^ 10 ^ 963 - the second Skewes number - Sk 2 .

To operate with such numbers, even the usual recording system is not suitable. Hugo Steinhaus (1887-1972) suggested using geometric figures: n in the triangle is n to the power of n, n is squared - n in n triangles, n in the circle is n in n squares. He explained this system by the example of mega-2 numbers in a circle, a meson - 3 in a circle, megiston - 10 in a circle. So it is difficult to designate, for example, the largest two-digit number, but it became easier to operate colossal quantities.

Professor Donald Knuth proposed an arrow notation in which re- elevation was indicated by an arrow borrowed from the practice of programmers. Gugol in this case looks like 10 ↑ 10 ↑ 2, and gugolplex - 10 ↑ 10 ↑ 10 ↑ 2.

Graham Number

Ronald Graham (born 1935), an American mathematician, in the course of his investigation of the Ramsey theory related to hypercubes-multidimensional geometric bodies-introduced special numbers G 1 -G 64 , with which he indicated the boundaries of the solution, where the upper limit was the largest multiple, his name. He calculated even the last 20 digits, and the initial values were the following values:

- G 1 = 3 ↑↑↑↑ 3 = 8.7 x 10 ^ 115.

- G 2 = 3 ↑ ... ↑ 3 (number of arrows of super-degree = G 1 ).

- G 3 = 3 ↑ ... ↑ 3 (number of arrows of super-degree = G 2 ).

...

- G 64 = 3 ↑ ... ↑ 3 (number of super-degree arrows = G 63 )

G 64 , simply denoted by G, and is the largest number in the world used in the course of mathematical calculations. It is listed in the record book. It is practically impossible to imagine its scale, considering that the entire volume of a universe known to man, expressed in the smallest unit of volume (a cube with a Planck length edge (10 -35 m)) is expressed by the figure 10 ^ 185.

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