Browse Definitions:

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


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.

what is the set of real no
plz help me what is the set of real no



File Extensions and File Formats


  • 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 ...

  • pure risk (absolute risk)

    Pure risk, also called absolute risk, is a category of threat that is beyond human control and has only one possible outcome if ...


  • cloud ecosystem

    A cloud ecosystem is a complex system of interdependent components that all work together to enable cloud services.

  • cloud services

    Cloud services is an umbrella term that may refer to a variety of resources provided over the internet, or to professional ...

  • uncloud (de-cloud)

    The term uncloud describes the action or process of removing applications and data from a cloud computing platform.


  • federated identity management (FIM)

    Federated identity management (FIM) is an arrangement that can be made among multiple enterprises to let subscribers use the same...

  • cross-site scripting (XSS)

    Cross-site scripting (XSS) is a type of injection security attack in which an attacker injects data, such as a malicious script, ...

  • firewall

    In computing, a firewall is software or firmware that enforces a set of rules about what data packets will be allowed to enter or...




  • bad block

    A bad block is an area of storage media that is no longer reliable for storing and retrieving data because it has been physically...

  • all-flash array (AFA)

    An all-flash array (AFA), also known as a solid-state storage disk system, is an external storage array that uses only flash ...

  • volume manager

    A volume manager is software within an operating system (OS) that controls capacity allocation for storage arrays.


  • hybrid hard disk drive (HDD)

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