# Natural numbers

numbers - is an abstract concept.They are the quantitative characteristics of the object, and there are real, rational, negative integers and fractions, as well as natural.

Natural number commonly used in the analysis, which arise naturally indicate the number.Meeting with the score begins in early childhood.What a funny kid escaped schitalok, which just use the natural elements of the account?"One, two, three, four, five ... Bunny 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 can be found another, more of it.This set is usually denoted by the letter N, and should be considered as infinite in the direction of increasing.But at the start of this set is a - is a unit.Although there are French natural numbers, the set including also zero.But the main distinguishing features and that, and the other set is the fact that they do not belong to any fractions or negative numbers.

need for recalculation variety of subjects originated in prehistoric times.Then presumably formed the concept of "natural numbers".Its formation took place throughout the process of change in a person's world, science and technology development.

However, primitive man could not even think abstractly.He was hard to understand, what is the common notions of "three hunters" or "three trees".Therefore, when you specify the number of people to use a single definition, but if you specify the same number of objects of a different kind - a completely different definition.

And numerical series was very short.In it there were only numbers 1 and 2, and ended with the account the concept of "a lot", "flock", "crowd", "heap".

later formed a more progressive bill, has wider.An interesting fact is that there were only two numbers - 1 and 2 and the following numbers were obtained already added.

example of this were the extant information on the numerical number of the Australian tribe the Murray River.They have 1 represents the word "Enza" and 2 - the word "petcheval."Number 3 so sounded like "petcheval-Enza" and 4 - is as "petcheval-petcheval."

majority of the peoples of the standard account acknowledged fingers.Further development of the abstract concept of "natural numbers" has gone the way of the use of notches on a stick.And there stood the need for designation of a dozen other characters.Ancient people, our way - began to use another wand, which made notches, indicating the tens.

Opportunities in playing numbers are extremely expanded with the advent of writing.Initially, the number of dashes portrayed on clay tablets or papyrus, but gradually began to use other icons for writing large numbers.So there were the Roman numerals.

Much later came the Arabic numerals, which opened up the possibility of writing numbers is relatively small set of characters.Today is not difficult to write such a huge number, the distance between the planets and the number of stars.It is necessary to learn to use the powers.

Euclid in the 3rd century BC in the book "Elements" infinite sets numerical set of primes.And Archimedes in the "dogs" reveals principles for building names arbitrarily large numbers.Almost until the middle of the 19th century, the people did not get up the need for a clear formulation of the concept of "natural numbers".Determining needed with the advent of the axiomatic mathematical method.

And in the 70s of the 19th century Georg Cantor formulated a clear definition of the natural numbers, based on the notion of a set.And now we know that the natural numbers - it's all integers from 1 to infinity.Young children making their first step in getting acquainted with the queen of all sciences - mathematics - are beginning to study these numbers.