Natural number
Definition
A Natural number is a number that occurs commonly and obviously in nature. As such, it is a whole, non-negative number. The set of natural numbers is often denoted by the symbol 'N' in mathematics.
Origins
The concept of natural numbers dates back to ancient times, where they were used for counting and ordering. The earliest recorded use of natural numbers was by the ancient Sumerians, who developed a counting system based on the number 60. This system is still in use today in our measurement of time and angles.
Properties
Natural numbers have several distinct properties that set them apart from other number sets. These include:
- Closure: The set of natural numbers is closed under addition and multiplication. This means that if you add or multiply any two natural numbers, the result is always another natural number.
- Well-Ordering: Every non-empty set of natural numbers contains a least element. This property is known as the well-ordering principle and is fundamental to many proofs in number theory.
- Induction: The principle of mathematical induction is a method of proof specifically designed for natural numbers. It involves proving a base case, and then proving that if the statement holds for one natural number, it also holds for the next.
Applications
Natural numbers have a wide range of applications in various fields. In mathematics, they are used in number theory to study the properties of integers. In computer science, natural numbers are used in counting loops and recursive algorithms. In physics, they are used to quantify the number of particles or quantum states.
See Also
