week.three

reminder: a1 is due on monday!

on monday, i came in a bit late...haha. i think i'm picking up my first-year habits all over again. i wasn't too sure about the predicate to be proven, in particular what the game round-robin is. but, in a nutshell: p_1 > p_2 > p_3 > p_1 (back to p_1; 3 cycles). another valuable info about the three types induction is that each implies the next in a circular pattern of implication - i.e.: principle of well-ordering => principle of simple induction => principle of complete induction => principle of well-ordering. consequently, is the converse true? yes. i.e.: PWO <=> PSI <=> PCI <=> PWO. this chain of iff equality was a little unclear to me, and is still blurry to me. i hope by reading the text on this topic more than once will somehow explain itself to me.

on wednesday, we discussed the topic "bases larger than zero". in particular, we proved the predicate P(n): 2^n > 10^n. after working through some possible base cases, we concluded that this predicate holds for all n greater than k (that is 5). hence, the base case for the claim, \forall n \in N, 2^n > 10^n, is P(6): 2^6 = 64 > 60 = 10.6, which holds true. within the induction step, we utilized a chain of inequalities to prove that the claim is, in fact, true for all n > 5. this proof, like the stamps proof, was easy to comprehend for me and i find that the structure of the proof in the general case is simple enough to deliver for similar conjecture.

on friday, the problem set #2 was due. i think i did pretty well as far as proof presentation goes. i'm hoping to get a good mark on it. in this class, we considered three different claims about three different topics - equality of a sum, hexagons, and trees. for each, we were given the proof from the beginning and we had to determine whether we dis/agree with each proof. the first two took a little bit of digressing to understand, but the one about the tree threw me off (like always) a little. i'm gonna try to research a bit on different types of trees so i can better understand what each claim about a particular tree means.