Browse Definitions :
Definition

aleph

In mathematics, aleph, the first letter of the Hebrew alphabet, in its uppercase form ( ) denotes numbers representing the sizes of infinite set s. Such numbers are known as transfinite cardinal number s, or transfinite cardinals.

The smallest transfinite cardinal is , called aleph null or aleph nought. This is the cardinality of (the number of elements in) the set of natural number s. It is also the cardinality of the set of integer s and the set of rational number s. This number is denumerable, in the sense that the elements of any set with cardinality can be entirely defined by writing a list, or at least the first few elements of a list. For example, the set of integers can be listed as {0, 1, -1, 2, -2, 3, -3, ...}. Although it is not possible to completely write out this list, its elements are implied by the continuation symbol (...).

The cardinality of the set of real number s is larger than . The real numbers cannot be denoted by any sort of list. This was proven by the German mathematician Georg Cantor (1845-1918), and produced the counterintuitive result that some infinities are larger than others.

See Mathematical Symbols .

This was last updated in September 2005

Continue Reading About aleph

Start the conversation

Send me notifications when other members comment.

Please create a username to comment.

-ADS BY GOOGLE

Dateiendungen und Dateiformate

Gesponsert von:

SearchCompliance

SearchSecurity

  • time-based one-time password (TOTP)

    A time-based one-time password (TOTP) is a temporary code, generated by an algorithm, for use in authenticating access to ...

  • Security Operations Center (SOC)

    A security operations center (SOC) is a command center facility for a team of IT professionals with expertise in information ...

  • incident response team

    An incident response team is a group of IT professionals in charge of preparing for and reacting to any type of organizational ...

SearchHealthIT

SearchDisasterRecovery

  • disaster recovery team

    A disaster recovery team is a group of individuals focused on planning, implementing, maintaining, auditing and testing an ...

  • cloud insurance

    Cloud insurance is any type of financial or data protection obtained by a cloud service provider. 

  • business continuity software

    Business continuity software is an application or suite designed to make business continuity planning/business continuity ...

SearchStorage

  • storage class memory (SCM)

    Storage class memory (SCM) is a type of NAND flash that includes a power source to ensure that data won't be lost due to a system...

  • Hadoop as a service (HaaS)

    Hadoop as a service (HaaS), also known as Hadoop in the cloud, is a big data analytics framework that stores and analyzes data in...

  • blockchain storage

    Blockchain storage is a way of saving data in a decentralized network which utilizes the unused hard disk space of users across ...

Close