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Mathematical induction can be informally illustrated by reference to the sequential effect of falling dominoes. [1] [2]Mathematical induction is a method for proving that a statement () is true for every natural number, that is, that the infinitely many cases (), (), (), (), … all hold.
Faraday's law of induction (or simply Faraday's law) is a law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (emf). This phenomenon, known as electromagnetic induction , is the fundamental operating principle of transformers , inductors , and many types of electric ...
Aluminium ring moved by electromagnetic induction, thus demonstrating Lenz's law. Experiment showing Lenz's law with two aluminium rings on a scales-like device set up on a pivot so as to freely move in the horizontal plane. One ring is fully enclosed, while the other has an opening, not forming a complete circle.
The earliest form of mathematics was phenomenological. For example, if someone could draw a reasonable picture, or give a convincing description, then that met all the criteria for something to be described as a mathematical “fact”. On occasion, analogical arguments took place, or even by “invoking the gods”. The idea that mathematical ...
The induction, bounding and least number principles are commonly used in reverse mathematics and second-order arithmetic. For example, I Σ 1 {\displaystyle {\mathsf {I}}\Sigma _{1}} is part of the definition of the subsystem R C A 0 {\displaystyle {\mathsf {RCA}}_{0}} of second-order arithmetic.
The extension of the above considerations confirms that where B is to H, and where J is to ρ, then it necessarily follows from Gauss's law and from the equation of continuity of charge that E is to D i.e. B parallels with E, whereas H parallels with D. Engineering diagram of Boltzmann's Bicykel. Boltzmann's Bicykel model of electromagnetic ...
Foundational mathematics: Giuseppe Peano: Planck's law: Electromagnetism: Max Planck: Poincaré–Bendixson theorem: Mathematics: Henri Poincaré and Ivar Otto Bendixson: Poincaré–Birkhoff–Witt theorem: Mathematics: Henri Poincaré, George David Birkhoff, and Ernst Witt: Poincaré–Hopf theorem: Mathematics: Henri Poincaré and Heinz Hopf ...
In set theory, -induction, also called epsilon-induction or set-induction, is a principle that can be used to prove that all sets satisfy a given property. Considered as an axiomatic principle, it is called the axiom schema of set induction. The principle implies transfinite induction and recursion.