Indukció

Indukció is a term used in Hungarian to refer to several related concepts in mathematics, physics and logic. In common usage it often denotes the mathematical principle of induction, the physical phenomenon of electromagnetic induction, or inductive reasoning in philosophy and science.

Mathematical induction is a proof technique used to establish that a statement holds for all natural numbers. It involves a base case, showing the statement is true for the initial value, and an inductive step demonstrating that if it holds for one number, it holds for the next. A stronger form, strong induction, assumes the statement for all values up to n to infer it for n+1. A classic example is the formula for the sum 1 + 2 + ... + n = n(n+1)/2. Induction is a method of argument, not a computational rule.

Electromagnetic induction is the generation of an electromotive force in a circuit due to a changing magnetic flux, described by Faraday’s law: emf = - dΦ_B/dt. Lenz’s law provides the direction of the induced current. This phenomenon explains how electric generators, transformers and induction motors operate. It also enables practical techniques such as induction heating and wireless charging, where changing magnetic fields interact with conductors.

Inductive reasoning refers to drawing general conclusions from specific observations. It underpins empirical science but does not guarantee certainty, as future cases may contradict previous ones. The historical problem of induction, discussed by philosophers such as David Hume, highlights the limits of extrapolating from observed instances.

Across domains, indukció reflects the idea of extending a rule, pattern, or cause to broader cases or systems, yielding new results or explanations.