The act or process of reasoning from a part to a whole, from particulars to generals, or from the individual to the universal; also, the result or inference so reached.
(mathematical) a method of proving a general truth affirming that every one of a set of mathematical objects (e.g. the natural numbers) has a certain property (e.g. has exactly one prime factorisation). The method depends upon their being a systematic way of constructing all the elements of the set by starting with one of a finite set of basis elements and repeatedly applying a finite number of constructions (for the natural numbers the basis is the number 0, and the method of construction is addition of 1). An inductive proof then consists of a proof that the basis elements each have the required property and a proof that the construction, when applied to elements having the property, will yield an element also having the property. Mathematical induction is in fact a kind of deduction. It is also called structural induction. (scientific) scientific induction is the process of concluding empirical generalisation s from particular instances, where this is not deductively sound because not all possible instances are premises
An inference from a set of propositions, or premises, that support the truth of another proposition, or conclusion, with a certain degree of probability or likelihood.