Can someone please, briefly yet very clearly explain to me what Induction is all about?
I am so very confused!
Hey, so this might come a bit late but this was the way I was taught it:
Mathematical Induction (which actually used to be in the methods course a while ago) is like a set of dominoes. The set, usually natural numbers, goes 1,2,3,.... So you have your first domino, second domino, third domino, etc etc.
For the theorem to work, the first domino has to fall, which is why you test for n=1, P(1). Now, lets assume a domino, say at k place, falls and knocks over the (k+1) domino. So you want to prove the k+1 domino does fall iff the domino before it, k, falls. This is why we prove P(k+1) using P(k).
And then, since we all know how dominoes work, we have proved the first one falls, knocks over the next one, which knocks over the one after that and so on and so forth hence proving the theory with mathematical induction.
Just do a lot of practise questions and you'll be fine!! It's just the inequality proofs that require a bit more thought..
Home
Help
Search
Login
