Till now we have learned two flavors of induction :
1) Simple induction
2) Complete induction
The topics are not really difficult..In fact I seem to like induction... Especially the simple one :)
There you need to define a base case first.. You may as well have several base cases although professor told that you had better get along with as few as you can, preferably just one so that you don't make your proof too long... After that you take inductive step which is actually where all the fun is... You assume that a statement is true for N and then prove that it is also true for N+1 basing your proof on the assumption you made earlier... I don't know why but I just like this step (:
As for the complete induction you don't need the base step at all... As I got it, complete induction uses the assumption that a statement is true for all previous cases to prove the truthfulness of the current case.. For Example you take the current case and decompose it into several smaller cases which are true by your assumption... So this completes your proof...
Anyway soon I will post some examples that I find interesting and worth posting...
1 comment:
Yes, induction is all about building conclusions about larger objects from assumptions about smaller ones. Base cases are only needed if the whole chain of assumptions needs starting points.
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