Week3: Well Ordering

This week's topic was focused on well-ordering. First of all, the concept of well-ordering was introduced and proved. Then we had some examples on proving some statements using well-ordering.

The concept of well-ordering was new to me. And I was a little bit confused about the concept at the lecture. Though I can understand all the examples, It wasn't clear to me what exactly the concept of well-ordering is. Furthermore, I didn't know for which part of the examples, the principle of well-ordering was applied.

My approach to find out the answer was to read the text book and lecture notes. After doing the reading and looking back at all the examples. I just realized that all I need to remember about the principle of well-ordering is that "Every none empty subset of N has a smallest element." Just that!

Also I wanted to ask some of my classmates. But at that time, I simply didn't know and hadn't talked to anybody. So I realized that maybe the first step that I should do was try to be brave and speak out and make more friends.

This week's tutorial was focused on Complete Induction. Though the questions on the hand out were not hard. I had difficulty to finish the quiz in time, because I wanted to add some creativity and try a new method rather than the one presented by the TA. But later I regretted that I should try my creativity work after class, not during the quiz!

Quiz 1 was returned this week. Though I got full mark, I made a mistake in the predicate.
My predicate looked like this:
P(n): For all n belongs to N, blah blah....
Here I shouldn't use "for all", it made the predicate too strong.

My lecture notes are as follows: