Week 5: Week of Proofs

This week I did my first term test and found myself still poor in identifying true or false in multiple quantifiers.

The second question part(a) of Question 2 from the test confuses me. Can I say that the negation of S1 is correct because if we pick m=n-1, then m+n=-1, given that p is natural number, in the case m+n cannot be p, so the negation of S1 is true.??? I'm not sure about my answer.

Week 5 is basically a proof week.Larry showed us the examples of different proofs.

Learned:


proof using contrapositive: 
instead of proving P => Q,
prove ¬Q => ¬P

note: sometimes the reverse direction is easier to prove(try the contrapositive when stuck)

proof using contradiction:
when P is implicit, try to assume NOT Q, hunt for a contradiction

proof for existence:
to proof "there exists some...", we need to pick a suitable example(number)


proof about a sequence:
pick a number for i that works
negate the consequence for contraposiitive

This week, while browsing some of my classmates' slogs, I found one very helpful and conclusive. Since he is from the other section, I feel I can learn more from following his slog: http://timothylock.me/sLOG/

Coincidentally, I find we are both confused about choosing ε, δ. Based on his slog, Prof Heap presented function codes to explain, while Prof Larry used real-life examples(which I like more since they are easier to understand for me).