natural numbers

natural numbers
 
In mathematics, there are two consensus on the set of natural numbers. The first is the definition according to the traditional mathematician, ie the set of positive integers not zero {1, 2, 3, 4, ...}. While the second definition by logicians and computer scientists, is the set of zero and positive integers {0, 1, 2, 3, ...}. Natural numbers is one of the most simple mathematical concepts and includes the first concept to be learned and understood by humans, and some studies have shown several species of monkeys can also be caught.

Naturally, if the natural numbers are the first type of numbers used to count, count, etc.. Deeper properties of natural numbers, including related to prime numbers, are studied in number theory. For advanced mathematics, natural numbers can be used to sort and define a set of properties of matter.

Each number, for example number 1, is an abstract concept that can not be captured by the human senses, but it is universal. One way to introduce the concept of the set of all natural numbers as an abstract structure is through Peano axioms (for illustration, see Peano arithmetic).

The concept of numbers more general and wider needs further discussion, even sometimes requires a depth of logic to understand and define. For example, the mathematical theory, the set of all rational numbers can be built in stages, starting from the set of original numbers.