Browse Definitions :
Definition

natural number

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, denoted N, can be defined in either of two ways:

N = {0, 1, 2, 3, ...}

N = (1, 2, 3, 4, ...}

In mathematical equations, unknown or unspecified natural numbers are represented by lowercase, italicized letters from the middle of the alphabet. The most common is n, followed by m, p, and q. In subscripts, the lowercase i is sometimes used to represent a non-specific natural number when denoting the elements in a sequence or series. However, i is more often used to represent the positive square root of -1, the unit imaginary number.

The set N, whether or not it includes zero, is a denumerable set. Denumerability refers to the fact that, even though there might be an infinite number of elements in a set, those elements can be denoted by a list that implies the identity of every element in the set. For example, it is intuitive from either the list {1, 2, 3, 4, ...} or the list {0, 1, 2, 3, ...} that 356,804,251 is a natural number, but 356,804,251.5, 2/3, and -23 are not.

Both of the sets of natural numbers defined above are denumerable. They are also exactly the same size. It's not difficult to prove this; their elements can be paired off one-to-one, with no elements being left out of either set. In infinite sets, the existence of a one-to-one correspondence is the litmus test for determining cardinality, or size. The set of integers and the set of rational numbers has the same cardinality as N. However, the sets of real numbers, imaginary numbers, and complex numbers have cardinality larger than that of N.

See also: integer, rational number, real number, imaginary number, complex number

This was last updated in March 2019

Continue Reading About natural number

SearchCompliance

SearchSecurity

  • cyber attack

    A cyber attack is any attempt to gain unauthorized access to a computer, computing system or computer network with the intent to ...

  • backdoor (computing)

    A backdoor is a means to access a computer system or encrypted data that bypasses the system's customary security mechanisms.

  • post-quantum cryptography

    Post-quantum cryptography, also called quantum encryption, is the development of cryptographic systems for classical computers ...

SearchHealthIT

SearchDisasterRecovery

  • risk mitigation

    Risk mitigation is a strategy to prepare for and lessen the effects of threats faced by a business.

  • call tree

    A call tree is a layered hierarchical communication model that is used to notify specific individuals of an event and coordinate ...

  • Disaster Recovery as a Service (DRaaS)

    Disaster recovery as a service (DRaaS) is the replication and hosting of physical or virtual servers by a third party to provide ...

SearchStorage

  • cloud SLA (cloud service-level agreement)

    A cloud SLA (cloud service-level agreement) is an agreement between a cloud service provider and a customer that ensures a ...

  • NOR flash memory

    NOR flash memory is one of two types of non-volatile storage technologies.

  • RAM (Random Access Memory)

    RAM (Random Access Memory) is the hardware in a computing device where the operating system (OS), application programs and data ...

Close