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 2017

Continue Reading About natural number

Join the conversation

1 comment

Send me notifications when other members comment.

By submitting you agree to receive email from TechTarget and its partners. If you reside outside of the United States, you consent to having your personal data transferred to and processed in the United States. Privacy

Please create a username to comment.

I understand now
Cancel

-ADS BY GOOGLE

File Extensions and File Formats

Powered by:

SearchCompliance

SearchSecurity

  • copyright

    Copyright is a legal term describing ownership of control of the rights to the use and distribution of certain works of creative ...

  • keylogger (keystroke logger or system monitor)

    A keylogger, sometimes called a keystroke logger or system monitor, is a type of surveillance technology used to monitor and ...

  • password

    A password is an unspaced sequence of characters used to determine that a computer user requesting access to a computer system is...

SearchHealthIT

SearchDisasterRecovery

  • business continuity plan (BCP)

    A business continuity plan (BCP) is a document that consists of the critical information an organization needs to continue ...

  • call tree

    A call tree -- sometimes referred to as a phone tree -- is a telecommunications chain for notifying specific individuals of an ...

  • mass notification system (MNS)

    A mass notification system is a platform that sends one-way messages to inform employees and the public of an emergency.

SearchStorage

  • CompactFlash card (CF card)

    A CompactFlash card (CF card) is a memory card format developed by SanDisk in 1994 that uses flash memory technology to store ...

  • email archiving

    Email archiving (also spelled e-mail archiving) is a systematic approach to saving and protecting the data contained in email ...

  • RAID (redundant array of independent disks)

    RAID (redundant array of independent disks) is a way of storing the same data in different places on multiple hard disks to ...

SearchSolidStateStorage

  • M.2 SSD

    An M.2 SSD is a solid-state drive (SSD) that conforms to a computer industry specification written for internally mounted storage...

  • NVMe (non-volatile memory express)

    NVMe (non-volatile memory express) is a host controller interface and storage protocol to enable a solid-state drive to use the ...

  • SSD RAID (solid-state drive RAID)

    SSD RAID (solid-state drive RAID) is a methodology commonly used to protect data by distributing redundant data blocks across ...

SearchCloudStorage

  • RESTful API

    A RESTful application program interface breaks down a transaction to create a series of small modules, each of which addresses an...

  • cloud storage infrastructure

    Cloud storage infrastructure is the hardware and software framework that supports the computing requirements of a private or ...

  • Zadara VPSA and ZIOS

    Zadara Storage provides block, file or object storage with varying levels of compute and capacity through its ZIOS and VPSA ...

Close