Browse Definitions:
Definition

real number

A real number is any element of the set R, which is the union of the set of rational numbers and the set of irrational numbers. In mathematical expressions, unknown or unspecified real numbers are usually represented by lowercase italic letters u through z. The set R gives rise to other sets such as the set of imaginary numbers and the set of complex numbers. The idea of a real number (and what makes it "real") is primarily of interest to theoreticians. Abstract mathematics has potentially far-reaching applications in communications and computer science, especially in data encryption and security.

If x and z are real numbers such that x < z, then there always exists a real number y such that x < y < z. The set of reals is "dense" in the same sense as the set of irrationals. Both sets are nondenumerable. There are more real numbers than is possible to list, even by implication.

The set R is sometimes called the continuum because it is intuitive to think of the elements of R as corresponding one-to-one with the points on a geometric line. This notion, first proposed by Georg Cantor who also noted the difference between the cardinalities (sizes) of the sets of rational and irrational numbers, is called the Continuum Hypothesis. This hypothesis can be either affirmed or denied without causing contradictions in theoretical mathematics.

See an introduction to real numbers and subsets:

This was last updated in February 2016

Continue Reading About real number

Join the conversation

3 comments

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.

ANO PUBA ANG REAL NUMBER
Cancel
what is the set of real no
Cancel
plz help me what is the set of real no

Cancel

-ADS BY GOOGLE

File Extensions and File Formats

Powered by:

SearchCompliance

  • smart contract

    A smart contract, also known as a cryptocontract, is a computer program that directly controls the transfer of digital currencies...

  • risk map (risk heat map)

    A risk map, also known as a risk heat map, is a data visualization tool for communicating specific risks an organization faces. A...

  • internal audit (IA)

    An internal audit (IA) is an organizational initiative to monitor and analyze its own business operations in order to determine ...

SearchSecurity

SearchHealthIT

SearchDisasterRecovery

  • incident management plan (IMP)

    An incident management plan (IMP), sometimes called an incident response plan or emergency management plan, is a document that ...

  • crisis communication

    Crisis communication is a method of corresponding with people and organizations during a disruptive event to provide them with ...

  • Zerto

    Zerto is a storage software vendor that specializes in enterprise-class business continuity and disaster recovery in virtual and ...

SearchStorage

  • SSD write cycle

    An SSD write cycle is the process of programming data to a NAND flash memory chip in a solid-state storage device.

  • data storage

    Data storage is the collective methods and technologies that capture and retain digital information on electromagnetic, optical ...

  • hard disk

    A hard disk is part of a unit -- often called a disk drive, hard drive or hard disk drive -- that stores and provides relatively ...

SearchSolidStateStorage

  • hybrid hard disk drive (HDD)

    A hybrid hard disk drive is an electromechanical spinning hard disk that contains some amount of NAND Flash memory.

Close