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mathematical induction

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in⋅duc⋅tion

  [in-duhk-shuhn]
–noun
1. the act of inducing, bringing about, or causing: induction of the hypnotic state.
2. the act of inducting; introduction; initiation.
3. formal installation in an office, benefice, or the like.
4. Logic.
a. any form of reasoning in which the conclusion, though supported by the premises, does not follow from them necessarily.
b. the process of estimating the validity of observations of part of a class of facts as evidence for a proposition about the whole class.
c. a conclusion reached by this process.
5. Also called mathematical induction. Mathematics. a method of proving a given property true for a set of numbers by proving it true for 1 and then true for an arbitrary positive integer by assuming the property true for all previous positive integers and applying the principle of mathematical induction.
6. a presentation or bringing forward, as of facts or evidence.
7. Electricity, Magnetism. the process by which a body having electric or magnetic properties produces magnetism, an electric charge, or an electromotive force in a neighboring body without contact. Compare electromagnetic induction, electrostatic induction.
8. Embryology. the process or principle by which one part of the embryo influences the differentiation of another part.
9. Biochemistry. the synthesis of an enzyme in response to an increased concentration of its substrate in the cell.
10. an introductory unit in literary work, esp. in an early play; prelude or scene independent of the main performance but related to it.
11. Archaic. a preface.
Origin:
1350–1400; ME induccio(u)n < L inductiōn- (s. of inductiō). See induct, -ion

Related forms:
in⋅duc⋅tion⋅less, adjective
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2009.
Cite This Source Link To mathematical induction
mathematical induction  
n.  Induction.
The American Heritage® Dictionary of the English Language, Fourth Edition
Copyright © 2009 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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Medical Dictionary

Main Entry: in·duc·tion
Pronunciation: in-'d&k-sh&n
Function: noun
1 : the act of causing or bringing on or about<induction of labor>; specifically : the establishment of the initial state of anesthesia often with an agent other than that used subsequently to maintain the anestheticstate
2 : the process by which an electrical conductor becomes electrified when near a charged body, by which a magnetizable body becomes magnetized when in a magnetic field or inthe magnetic flux set up by a magnetomotive force, or by which an electromotive force is produced in a circuit by varying the magnetic field linked with the circuit
3 a : arousalof a part or area (as of the retina) by stimulation of an adjacent part or area b : the sum of the processes by which the fate of embryonic cells is determined and morphogeneticdifferentiation brought about —in·duct /in-'d&kt/ transitive verb
Merriam-Webster's Medical Dictionary, © 2002 Merriam-Webster, Inc.
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Medical Dictionary

induction in·duc·tion (ĭn-dŭk'shən)
n.

  1. The process of initiating or increasing the production of an enzyme or other protein at the level of genetic transcription.

  2. The period from the first administration of anesthesia to the establishment of a depth of anesthesia adequate for surgery.

  3. The change in form or shape caused by the action of one tissue of an embryo on adjacent tissues or parts, as by the diffusion of hormones.

  4. A modification imposed upon the offspring by the action of environment on the germ cells of one or both parents.

  5. The generation of electromotive force in a closed circuit by a varying magnetic flux through the circuit.

The American Heritage® Stedman's Medical Dictionary
Copyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company.
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Science Dictionary
induction   (ĭn-dŭk'shən)  Pronunciation Key 


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    1. The process of deriving general principles from particular facts or instances.

    2. A conclusion reached by this process. See Note at deduction.

    3. The creation of a voltage difference across a conductive material (such as a coil of wire) by exposing it to a changing magnetic field. Induction is fundamental to hydroelectric power, in which water-powered turbines spin wire coils through strong magnetic fields. It is also the working principle underlying transformers and induction coils.

    4. The generation of an electric current in a conductor, such as a copper wire, by exposing it to the electric field of an electrically charged conductor.

    5. The building up of a net electric charge on a conductive material by separating its charge to create two oppositely charged regions, then bleeding off the charge from one region.

    1. The creation of a voltage difference across a conductive material (such as a coil of wire) by exposing it to a changing magnetic field. Induction is fundamental to hydroelectric power, in which water-powered turbines spin wire coils through strong magnetic fields. It is also the working principle underlying transformers and induction coils.

    2. The generation of an electric current in a conductor, such as a copper wire, by exposing it to the electric field of an electrically charged conductor.

    3. The building up of a net electric charge on a conductive material by separating its charge to create two oppositely charged regions, then bleeding off the charge from one region.


The American Heritage® Science Dictionary
Copyright © 2002. Published by Houghton Mifflin. All rights reserved.
Cite This Source
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