# Is principal of mathematical induction an example of inductive or deductive reasoning?

Is principal of mathematical induction an example of inductive or deductive reasoning according to wikipedia it says it is deductive as it is just a mathematical proof but according to the definition of inductive reasoning it should be inductive instead of deductive. Can someone help?

• What is the difference between induction and deduction? – parsiad Oct 9 '16 at 15:45
• Induction means going particular to general and deduction means general to particular. – Matt Oct 9 '16 at 15:48
• I'm not sure what that means, but I would recommend, since I assume this is for the purpose of building intuition, to pick whichever speaks best to you. – parsiad Oct 9 '16 at 15:48

If $P$ is some property of natural numbers, and $(i)$ $P$ holds of $1$, and $(ii)$ for every $n$, if $P$ holds of $n$ then $P$ holds of $n+1$; then $P$ holds for all natural numbers.
Note that in order to use this, we need to prove both parts. It's not enough to observe "$P$ holds of $1$, $P$ holds of $2$, $P$ holds of $3$, therefore $P$ always holds;" the whole "meat" of induction is the induction step, which is the part where you prove that $P(n)$ implies $P(n+1)$ for every $n$.