Mathematical induction is traditionally defined as a mathematical method, or a type of a mathematical proof, which is used when the necessity to prove that in the following expression: “(fg)’ = f’g + fg’”, “for every integer n >= 1, the derivative of f(x) = xn is f'(x) = nxn – 1’” (The technique of proof by induction, n. d., para. 1).
It is believed that the principle of mathematical induction was suggested by Plato in ca. 370 BC (Mathematical induction, n. d., para. 4). To be more exact, Plato mentions the concept of mathematical induction in his Parmenides. However, speaking of the person that first introduced the term, one must give credit to Euclid and his proof of the fact that the “numbers of primes are infinite” (Mathematical induction, n. d., para. 4).
Bhaskara, as the creator of the so-called “cyclic method” (Mathematical induction, n. d., para. 4) can also be mentioned among the range of people that worked on the problem of mathematical induction and its use as a means of solving mathematical problems.
Speaking of the actual application of the aforementioned method to the process of problem-solving in mathematics, mathematical induction is used widely in two realms, which are mathematical logic and computer science. In the latter, mathematical induction manifests itself as recursion, a method that is used to split a complex problem into a range of smaller and simpler ones. In the former, induction helps solve the propositional logic problems (Mathematical induction, n. d.a, p. 3).
In fact, mathematical induction is used as a form of “rigorous deductive reasoning” (Mathematical induction, n. d., para. 3). It should also be kept in mind that mathematical induction is not applicable for inductive reasoning, which, in its turn, is defined as a form of non-rigorous reasoning in mathematics.
Reference List
Mathematical induction. Web.
Mathematical induction. Web.
The technique of proof by induction. Web.