Browse Definitions :
Definition

integer

What is an integer and what are examples of integers?

An integer (pronounced IN-tuh-jer) is a whole number (not a fractional number) that can be positive, negative, or zero.

Examples of integers are: -5, 1, 5, 8, 97, and 3,043.

Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, .09, and 5,643.1.

The set of integers, denoted Z, is formally defined as follows:

Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}

In mathematical equations, unknown or unspecified integers are represented by lowercase, italicized letters from the "late middle" of the alphabet. The most common are p, q, r, and s.

The set Z 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 the list {..., -3, -2, -1, 0, 1, 2, 3, ...} that 356,804,251 and -67,332 are integers, but 356,804,251.5, -67,332.89, -4/3, and 0.232323 ... are not.

The elements of Z can be paired off one-to-one with the elements of N, the set of natural numbers, with no elements being left out of either set. Let N = {1, 2, 3, ...}. Then the pairing can proceed in this way:

integer.gif (1078 bytes)

In infinite sets, the existence of a one-to-one correspondence is the litmus test for determining cardinality, or size. The set of natural numbers and the set of rational numbers have the same cardinality as Z. However, the sets of real numbers, imaginary numbers, and complex numbers have cardinality larger than that of Z.

This was last updated in October 2021

Continue Reading About integer

SearchCompliance
  • ISO 31000 Risk Management

    The ISO 31000 Risk Management framework is an international standard that provides businesses with guidelines and principles for ...

  • pure risk

    Pure risk refers to risks that are beyond human control and result in a loss or no loss with no possibility of financial gain.

  • risk reporting

    Risk reporting is a method of identifying risks tied to or potentially impacting an organization's business processes.

SearchSecurity
  • What is cyber hygiene and why is it important?

    Cyber hygiene, or cybersecurity hygiene, is a set of practices individuals and organizations perform regularly to maintain the ...

  • Pretty Good Privacy (PGP)

    Pretty Good Privacy or PGP was a popular program used to encrypt and decrypt email over the internet, as well as authenticate ...

  • email security

    Email security is the process of ensuring the availability, integrity and authenticity of email communications by protecting ...

SearchHealthIT
SearchDisasterRecovery
  • What is risk mitigation?

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

  • fault-tolerant

    Fault-tolerant technology is a capability of a computer system, electronic system or network to deliver uninterrupted service, ...

  • synchronous replication

    Synchronous replication is the process of copying data over a storage area network, local area network or wide area network so ...

SearchStorage
  • direct access

    In computer storage, direct access is the process of reading and writing data on a storage device by going directly to where the ...

  • kibi, mebi, gibi, tebi, pebi and exbi

    Kibi, mebi, gibi, tebi, pebi and exbi are binary prefix multipliers that, in 1998, were approved as a standard by the ...

  • holographic storage (holostorage)

    Holographic storage is computer storage that uses laser beams to store computer-generated data in three dimensions.

Close