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

SearchCompliance

  • PCAOB (Public Company Accounting Oversight Board)

    The Public Company Accounting Oversight Board (PCAOB) is a Congressionally-established nonprofit that assesses audits of public ...

  • cyborg anthropologist

    A cyborg anthropologist is an individual who studies the interaction between humans and technology, observing how technology can ...

  • RegTech

    RegTech, or regulatory technology, is a term used to describe technology that is used to help streamline the process of ...

SearchSecurity

  • Advanced Encryption Standard (AES)

    The Advanced Encryption Standard, or AES, is a symmetric block cipher used by the U.S. government to protect classified ...

  • identity theft

    Identity theft, also known as identity fraud, is a crime in which an imposter obtains key pieces of personally identifiable ...

  • spear phishing

    Spear phishing is an email-spoofing attack that targets a specific organization or individual, seeking unauthorized access to ...

SearchHealthIT

SearchDisasterRecovery

  • 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.

  • disaster recovery as a service (DRaaS)

    One approach to a strong disaster recovery plan is DRaaS, where companies offload data replication and restoration ...

SearchStorage

  • CIFS (Common Internet File System)

    CIFS (Common Internet File System) is a protocol that gained popularity around the year 2000, as vendors worked to establish an ...

  • GlusterFS (Gluster File System)

    GlusterFS (Gluster File System) is an open source distributed file system that can scale out in building-block fashion to store ...

  • virtual memory

    Virtual memory is a memory management capability of an OS that allows a computer to compensate for physical memory shortages by ...

SearchSolidStateStorage

  • Tier 0

    Tier 0 (tier zero) is a level of data storage that is faster, and perhaps more expensive, than any other level in the storage ...

  • PCIe SSD (PCIe solid-state drive)

    A PCIe SSD (PCIe solid-state drive) is a high-speed expansion card that attaches a computer to its peripherals.

  • SSD caching

    SSD caching, also known as flash caching, is the temporary storage of data on NAND flash memory chips in a solid-state drive so ...

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