Hmmm well-ordering...

This week we learned more on induction and saw some false induction proofs...Also we found the connection between WOP, SIP, and CIP...

The thing is that Well-Ordering Principle seems a bit tricky to me...I understand the theorem that every non-empty set has got a least element and all that, but I didn't understand the example of round-robin tournament... Basically because I don't know the rules of a domino tournament, I don't know what happens when a player beats another player and in what order do players play...so I felt lost on that example... :S Sooo today when I was doing my assignment the question# 3 gave me a hard time but in the end I think I understood that by WOP if you can always find an element which is a bit less than the element already in the set it creates a contradiction..Is that right? :)

Everything else is quite clear... 

First weeks of classes...

Soooo...The second week of classes is about to end but it already feels like I have been studying for ages :) 

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...