CSC165 - Week Five and Six - Test & Proof

Did not create a blog post cuz there was a test,

Tests are always like bombs, right?

We talked about all kinds of proofs, but that's not the focus...

The test is.

Okay, the test wasn't that hard, it feels more like a 'welcome to university, see? you can do well' test, the class average is at 80%+, which is a very generous mark, even when compared to some of my high school tests *cough* that averaged at 60%.

Proofs are the primary indicator of the rigorous part of mathematics and computer science theories, they are the foundation to every theorem we use today. In a short sentence, Proofs are to be written in a completely sealed format, variables are declared and initialized in the front, assumptions are made, deductions are written indented after the assumption, the structure of proof can be easily related to...

REDDIT!

Like every discussion thread, a proof looks like a completed indented block.

We also learned contrapositive proofs and proofs by contradiction, and touched on limit.

Contrapositive proof:

Biggest hint to contrapositive proof: contrapositive and original is equivalent

wtf is that a hint? Yes, that means proving contrapositive equals to proving original, ... Oh yea cause they are the same. When proving contrapositive is easier than proving the original, using contrapositive proof is a really smart approach.

Proof by contradiction:

This is harder to comprehend compared to other proofs, basically in this one P => Q you assume Q to be false, then by smart manipulation you get Q is true, which contradicts Q is false, which means Q must be true.

Proof something is false == proving its negation to be true, using above methods.

Limits:

Greek..

epsilons and deltas are like nightmares that never goes away, we defined limit in a rigorous sense, for every little distance to f(x), there must be a little range from x that if x is inside that range, f(x) is inside its boundary.

To prove limit, we have to write out the actual delta epsilon equations, and by manipulating the epsilon part, we seek to get ourselves some delta, so that we can see how small the delta should be so that epsilon is satisfied, usually the value of delta is related to epsilon.