Noun
mathematical induction (countable and uncountable, plural mathematical inductions)
(mathematics) A method of proof which, in terms of a predicate P, could be stated as: if
P
(
0
)
{\displaystyle P(0)}
is true and if for any natural number
n
≥
0
{\displaystyle n\geq 0}
,
P
(
n
)
{\displaystyle P(n)}
implies
P
(
n
+
1
)
{\displaystyle P(n+1)}
, then
P
(
n
)
{\displaystyle P(n)}
is true for any natural number n.
Mathematical induction, one of various methods of proof of mathematical propositions, based on the principle… Source: Internet
Suppose that we wish to prove a statement about an n-ary operation implicitly defined from a binary operation, using mathematical induction on n. In this case it is natural to take 2 for the induction basis. Source: Internet
It is not difficult to turn this argument into a proof (by mathematical induction ) of the binomial theorem. Source: Internet
Complete induction is equivalent to ordinary mathematical induction as described above, in the sense that a proof by one method can be transformed into a proof by the other. Source: Internet
Joel E. Cohen proposed the following argument, which purports to prove by mathematical induction that all horses are of the same color: citation. Source: Internet
The ninth, final axiom is a second order statement of the principle of mathematical induction over the natural numbers. Source: Internet