Friday, October 19, 2007

My first proof

It's nothing to be proud of. We took the first part of our test on Wednesday, and I had never successfully done a proof by myself before. This was reflected in my grade. I have a chance to pass though, so I am devoting this weekend to logic. This tiny, baby proof is just the first step. We have a lot of grades in this class, so hopefully this test won't hurt me too much. Right now I'm trying to keep my goals within reach. I have two hours until practice (our last practice this season) and I plan on using them for studying.


Emily said...

What was the proof?

Here are some basic logic tips:
1) Whenever you see a conjunction, break it up. It's like unwrapping a present and it's almost always more useful when it's broken down into chunks.
2) If you're doing quantifiers, keep in mind that universal statements are almost always conditionals and existentials are almost always conjunctions
3) If you have absolutely no idea how to proceed, try reductio: assuming the opposite of what you are trying to prove and showing that it leads to a contradiction
4) If there's a disjunction ("or") in the premises, you'll probably need to do an or-out proof: show that each disjunct leads to the conclusion. E.g. if you have P v Q and you want to show R, you're going to have to show P-->R and Q --> R.

Bill said...

What excellent advice. I am going to follow these tips in every phase of my life.

Greg said...

My God, it sounds like Harry Potter. "Reductio!" Emily shouted, gesturing with a flourish at the ogre. He fit into the cauldron nicely, after that.

Emily said...

Reductio is actually a little bit like Riddiculus, the charm they use on Boggarts. Reducio turns your opponent into a logical contradiction! What an excellent spell that would be!

lily said...

oh. my. god. emily, WHY didn't you just TELL me you were a witch? You KNOW I would have been okay with it!
I guess you didn't tell me because I would have insisted that you solve all my problems magically. Nah, you mathmagician folk are best left alone.

“What a shame,” sighed the Dodecahedron. “They’re so very useful. Why, did you know that if a beaver two feet long with a tail a foot and a half long can build a dam twelve feet high and six feet wide in two days, all you would need to build Boulder Dam is a beaver sixty-eight feet long with a fifty-one-foot tail?”

“Where would you find a beaver that big?” grumbled the Humbug as his pencil point snapped.

“I’m sure I don’t know,” he replied, “but if you did, you’d certainly know what to do with him.”

“That’s absurd,” objected Milo, whose head was spinning from all the numbers and questions.

“That may be true,” he acknowledged, “but it’s completely accurate, and as long as the answer is right, who cares if the question is wrong? If you want sense, you’ll have to make it yourself.”
The Phantom Tollbooth / Juster, Norton / Ch.14