Here it is, tell me who is wrong... A definition of Induction and Deduction in a general science field: Inductive approach- To understand something through obsevation with no prior knowledge and concluding at the end of your observations. Deductive approach- To understand something through reasoning using prior knowledge and observing results of experiments using your hypothesis. A definition of Inductive proof and Deductive proof in mathemetics: Inductive proof- To proof a mathemetical statement by using an assumption and verifying that the assumption is correct. Deductive proof- To proof a mathemetical statement by using a series of algebraic rules in order to change the form of one side of the equals sign into the other side and thereby proof an identity. Now these are not quoted, just digested from what I understood in both subjects. Aren't they contradictions? If you use an assumption then it is a deductive approach whilst if you just follow a path using algebra and observation of how the form changes until you arrive to your answer then it is inductive. Am I wrong? Or is it inductive because you have no pre defined knowledge and are observing the results given by an assumption whilst the other is deductive because you are using predefined mathematical proofs?