# Induction

Also known as mathematical induction or finite induction, this affirms that to prove that a certain property P holds for all natural numbers, it suffices to show that P(l) is true and that P(k + 1) is true whenever P(k) is true.

Intuitively, one can think of this in terms of climbing a ladder, where proving P(l) corresponds to getting on the ladder, and proving P(k + 1) from P(k) corresponds to taking the (k + l)th step; once one knows how to move from one step of the ladder to the next, it is possible, in principle, to reach any step of the ladder.

There is an equivalent form of this principle, sometimes called complete induction, in which the inductive hypothesis above is replaced by the stronger assumption that P(j) is true for all integers j less than or equal to k; this latter form of induction is often simpler to apply in practice.

Also see: uniformity of nature, inductivism, Goodman’s paradox, WELL-ORDERING PRINCIPLE

## Philosophy

• Inductive reasoning, in logic, inferences from particular cases to the general case

## Biology and chemistry

• Labor induction (birth/pregnancy)
• Induction chemotherapy, in medicine
• Induction period, the time interval between cause and measurable effect
• Inductive cleavage, in organic chemistry
• Inductive effect, the redistribution of electron density through molecular sigma bonds
• Induced stem cells, stem cells derived from somatic, reproductive, pluripotent or other cell types by deliberate epigenetic reprogramming
• Asymmetric induction, the formation of one specific stereoisomer in the presence of a nearby chiral center
• Cellular differentiation, the process where a cell changes from one cell type to another
• Enzyme induction and inhibition, a process in which a molecule induces the expression of an enzyme
• Morphogenesis, the biological process that causes an organism to develop its shape
• Regulation of gene expression, the means by which a gene product is either induced or inhibited

## Computing and mathematics

• Backward induction in game theory and economics
• Epsilon-induction, a kind of transfinite induction
• Grammar induction, in computing
• Induced representation, in representation theory
• Inductive bias, in computing
• Inductive probability, in computing
• Inductive programming, in computing
• Inductive set, in mathematics
• Mathematical induction, a method of proof in the field of mathematics
• Parabolic induction, a method of constructing group representations
• Rule induction, in computing
• Statistical induction, also known as statistical inference
• Strong induction, or complete induction, a variant of mathematical induction
• Structural induction, a generalization of mathematical induction
• Transfinite induction, a kind of mathematical induction
• Word-sense induction, in computing

## Physics

• Electromagnetic induction in physics and engineering
• Electrostatic induction in physics and engineering
• Forced induction, with combustion engines
• Induction cooker, which uses induction heating for cooking
• Induction equation, in physics
• Induction generator, in electricity
• Induction heating, the process of heating an electrically conducting object
• Induction plasma, in physics
• Induction regulator, in electricity
• Induction shrink fitting, in electricity
• Inductive amplifier, in electronics
• Inductive coupling, in electricity
• Inductive pump, in engineering
• Inductive sensor, in electronics

## Other uses

• Induction (play), an opening scene in a play
• Induction (teachers), a stage in teacher training
• Induction cut, a haircut
• Induction day, U.S. Naval Academy
• Inductive reasoning aptitude, an aptitude or personality characteristic
• Collective Induction, in psychology
• Price Induction, a French company that manufactures turbofan engines
• Hypnotic induction, process to establish the state required for hypnosis
• Formal admission into a learned society or hall of fame

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