## inductionA method of reasoning by which one infers a generalization from a series of instances. Say there is a hypothesis H that contains the variable
n, which is a whole number. To prove by induction that H
is true for every value of n is a two-step process: (1) prove that
H is true for n = 1; (2) prove that H being true
for n = k implies that H is true for n
= k + 1. This is sufficient because (1) and (2) together imply
that H is true for n = 2, which, from (2), then implies
H is true for n = 3, which implies H is true
for n = 4, and so on. H is called an inductive hypothesis.
Some philosophers don't accept this kind of proof,
because it may take infinitely many steps to prove something; however, most
mathematicians are happy to use it. ## Related category• LOGIC | |||||

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