Integers

Numbers are an abstract concept. They are a quantitative characteristic of objects and there are real, rational, negative, whole and fractional, and also natural.

The natural series is usually used in an account in which number designation naturally occurs. Acquaintance with the account begins in the earliest childhood. What kid escaped ridiculous oddities, in which elements of a natural account were used? "One, two, three, four, five ... A bunny came out for a walk!" Or "1, 2, 3, 4, 5, 6, 7, 8, 9, 10, the king decided to hang me ..."

For any natural number one can find another, greater than it. This set is usually denoted by the letter N and should be considered infinite in the direction of increasing. But the beginning of this set is - this unit. Although there are French natural numbers, many of which also include zero. But the main distinguishing features of both sets are the fact that they do not include either fractional or negative numbers.

The need for the recalculation of a variety of subjects arose in prehistoric times. Then the notion of "natural numbers" was supposedly formed. Its formation occurred throughout the entire process of changing the worldview of man, the development of science and technology.

However, primitive people could not yet think abstractly. It was difficult for them to understand what the commonality of the concepts "three hunters" or "three trees" is. Therefore, when specifying the number of people used one definition, and when specifying the same number of items of another kind - a completely different definition.

And the number series was extremely short. It was attended only by numbers 1 and 2, and ended with the notion of "a lot", "herd", "crowd", "pile".

Later, a more progressive account was formed, already broader. It is interesting that there were only two numbers - 1 and 2, and the following numbers were obtained by adding.

An example of this is the information that has come down to us about the numerical series of the Australian tribe of the Murray River. They 1 denoted the word "Enza", and 2 - the word "patted". The number 3 therefore sounded like "petted-Enza", and 4 - already as "patted-pecked".

Most people recognized the standard of the fingers. Further development of the abstract concept of "natural numbers" went along the path of using notches on a stick. And then there was a need to designate a dozen other signs. Ancient people our way out - began to use another wand, on which were made notches, denoting tens.

The possibilities in reproducing numbers have greatly expanded with the advent of writing. At first, the numbers were depicted by lines on clay tablets or papyrus, but other icons were gradually used to record large numbers. So there were Roman numerals.

Significantly later appeared Arabic numerals, which opened the possibility of writing numbers with a relatively small set of characters. Today it is not difficult to write down such huge numbers as the distance between the planets and the number of stars. It is only necessary to learn to use degrees.

Euclid in the 3rd century BC in the book "Beginnings" establishes the infinity of a numerical set of primes. And Archimedes in Psamyte reveals the principles for constructing the names of arbitrarily large numbers. Almost until the middle of the 19th century people did not need a clear formulation of the concept of "natural numbers". The definition was required with the advent of an axiomatic mathematical method.

And in the seventies of the 19th century George Cantor formulated a clear definition of natural numbers based on the notion of a set. And today we already know that natural numbers are all integers, from 1 to infinity. Little children, making their first step in acquaintance with the queen of all sciences - mathematics - begin to study these numbers.