CSC165 SLOG Week5

What’s something new I learned this week?

• Proof using contrapositive : when the reverse direction is easier to prove than the original.

          General idea: Instead of proving P => Q, prove ¬Q => ¬P (equivalent to P => Q)
          When it’s not easy to prove P => Q,  try proving ¬Q => ¬P

• Proof using contradiction : a special case of contrapositive

           P => Q, with implicit P : sometimes it is not clear what P is, for example : “If every common            sense is true, then Q”, contrapositively, “if not Q, then something in common sense is                      false”, i.e. if not Q, then it will contradict with some common sense. When the assumptions              are implicit, try   assuming ¬Q, and see whether it leads somewhere, hunting for a                             contradiction.

• Proof for existence 

          direct proof of the existential : find a single example.

• Proof about a sequence
• With multiple quantifiers, zoom into smaller and smaller part of the statement, layer by layer.
• One proof may consist of several different structures

What’s something that frustrated and challenged me this week?

I did't do quite well as I thought in Assignment1, and I think i could improved a lot later on

How confident do you feel about material covered this week?

I thought I understood the material pretty well.

How does course material relate to other classes or interests?

The proof material is kind of like what I met in MAT137 class, though I didn't study the proof structure then. And I think the structure I'm learning is helpful and essential for further math proofs.

How did your tutorial/test/assignment go this week?

I'd like to address assignment1 question4 and the proving sstructure the TA mentioned in this week's tutorial.
Direct Proof Structure: 1) domain assumption 2) assume the antecedent  3) show consequent  4) close assumptions