Mathematical knowledge is quite peculiar. This AOK is the only one that explores its own information, that is to say it doesn’t use any other AOK to carry out contributions which expand its information.
Both deductive and inductive knowledge are used to expand knowledge. Although deductive knowledge is the mostly used, inductive knowledge is also useful.
It is a method that goes from particular to general, so it is always used when talking about series, for example. In this mathematical area we start with few numbers and suppose a general formula is followed by all the terms in the series. We’re not completely sure about it, since numbers don’t need to follow this rule and maybe in infinity numbers follow a different pattern or don’t follow it at all. However, it is the way from which mathematicians solve this problems since there are no other previous facts from which we can deduce the series.
This way, we prove by deduction an inductive fact.
In conclusion, in an AOK based in reasoning, inductive knowledge is used when there’s no possibility to use deductive knowledge because of the lack of specific information. However, there’s a deductive methodology.