Browse Definitions:
Definition

mathematical induction

Mathematical induction is a a specialized form of deductive reasoning used to prove a fact about all the elements in an infinite set by performing a finite number of steps. 

In order for mathematical induction to work with an infinite set, that set must be denumerable, meaning that a one-to-one correspondence must exist between the elements of the set in question and the set of positive integers. In other words, it must be possible to express the set in the form an implied list of discrete elements such as {1, 2, 3, 4, ...}.

Consider a denumerably (also called countably) infinite set X with elements x1, x2, x3, x4, and so on. In order to prove a proposition about all the elements of X, we begin by proving that the proposition holds true for x1, the first element in the set X. Then we must prove that if the proposition holds true for some arbitrary element xn in X (where n is a positive integer), then the proposition also holds true for the next element xn+1 in set X. If we can do both of these two things successfully using deductive reasoning, we create an infinite chain of true statements by rigorous logical implication, proving the proposition true for all of the elements in X.

The first explicit formalization of the induction principle was composed by the French mathematician Blaise Pascal in 1665. Mathematical induction should not be confused with inductive reasoning. The former principle is mathematically rigorous (meaning that the conclusions are logically certain), but the latter methodology deals with probability and allows for some uncertainty.

This was last updated in June 2013

Start 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.

-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