# Natural numbers

**Natural numbers** arise naturally when counting objects: 1, 2, 3... Natural because they were designated (modeled) by real undivided objects: people, animals, things... The notion of a natural number arose, as we have seen, back in prehistoric times. They have two main functions: the first - the characteristics of the number of objects, and the second - the characteristics of the order of objects placed in a row. In accordance with these functions, the concepts of ordinal number (first, second, etc.) and quantitative number (one, two, etc.) arose. In the first case, the series of natural numbers begins with unity, in the second case it starts from zero. In the overwhelming majority of Russian sources, the first approach has traditionally been adopted, that is, zero is not considered a natural number. The second approach is found in some foreign authors. Long and hard mankind has reached the first level of generalization of numbers. Hundred centuries it took to build the shortest natural numbers from number one to infinity: 1, 2,...

An important role played by natural numbers was noted by the Greek mathematician Nicomach of Geraz. He spoke about the natural, that is, the natural series of numbers: "With the help of these signs you can write any number". But the trouble is that the Hellenes did not have a successful system to denote natural numbers. Instead of numbers, the Greeks used letters; position system for writing large numbers they did not know.

It is believed that the term "natural numbers" was first used by the Roman statesman, philosopher, author of works on mathematics and music theory Anitius Manlius Torquat Severin Boethius (480-524). The notion of natural numbers in modern understanding was consistently used also by the outstanding French mathematician, philosopher-educator D'Alembert (1717-1783).

Finally, we quote one statement by the German mathematician Kronecker (1823-1891): "God created natural numbers, everything else is the work of human hands".

The set of all natural numbers is usually denoted by the symbol *N* (from the Latin naturalis - natural). The set of natural numbers is infinite, since for any natural number *n* there is a positive integer greater than *n*.