Ampoliros said:Induction is used in some math proofs but I think it can be tricky. A small flaw in logic can cause you lots of headache - one of our classes spent a few minutes debunking the professors inductive proof that any size group had all the same age, because it follows the proper inductive pattern:
-Prove true for base case (One person has the same age as himself)
-Assume true for any case n. (cant really argue against that.)
-Show that this implies that it is true for the n+1 case (its hard to do this, but basically he said for any group n+1 you could form some groups of size n which according to the assumption all have the same age, so they all have the same age.)
The logical problem of this occurs between n=1 and n=2, because there's nothing that says a group of two individuals - the induction breaks down there.
So, it works. But you need to be careful
yes, i remember going over the very same example in some of my math classes. but that's a flaw in the use of induction, not a flaw in induction itself. the point is, there is indeed a serious field of human knowledge that uses inductive proofs.
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