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27 January 2009 @ 12:04 am
Ugh, way too much thinking.  

Taking a break from an avalanche of studying to natter on about things.

Thing 1:  I'm ready for my W2, Mr. DeMille.  (I swear I used to never pay attention to these things.)

Thing 2:  When I'm in a state of brain exhaustion, I notice odd things.  Like, for instance, the fact that my doorknob is extremely shiny, as I walk up the stairs to my door.

Thing 3:  school stuff.

Today in Math class, we proved Proof by Induction.  I mean, we proved that it works.  In order to do that, we had to use an Axiom.  Prof:  "An axiom is something that, thank heavens, you won't be asked to prove.  You'll recognize axioms because after reading them, you'll get a strange feeling of 'duh'."  The axiom we used?  The Well Ordering Principle (or axiom):  any non-empty subset of positive integers contains a smallest element.  Yup.  I can see where that would kinda always happen.

After we broke our brains on that proof, we talked about counting.

"Now I need you guys to teach me how to count."  I have never seen any professor who can put a look of more genuine polite bafflement on his face than this guy.  It's vastly entertaining.

The class members looked at each other in mild confusion.  He assured us he was serious.  "You there, show me how to count.  How do you count?"

The girl indicated gamely pointed at someone in the corner of the room and said, "One," and then pointed at someone else and said, "Two..."

"Ah, I see.  Let me give that a try!  One... One... One... Two... Three... Three... Three..."

Naturally there was a chorus of protest.

"Wait, you mean that's not how I count?  What was I doing wrong?"

We told him he was not allowed to give more than one number to each student.  "I'm not?  Why not?  Oh well.  You guys are strict."  Then he wrote the rule up on the board:  'one number per student'.

"Okay, let me try this again.  One... Two... Five... Seventeen... Thirty-three... you're shaking your heads at me again!  What's the deal?"

We informed him with regret that he wasn't allowed to skip any numbers.  He sighed a great big sigh and wrote it on the board, 'no skipping numbers'.

Then he showed a group of students, a group of consecutive numbers, and the lines mapping from one to the other.

It was the quickest and clearest explanation of bijections I've ever been given.

For those of you unfamiliar with the term, that means a function which is both one-to-one (there is only one number in the set of numbers, for each student in the set of students) and onto (each and every number does map to a student, with none left out).

Coincidentally, I just went over bijections in the GRE Math study manual the other day...

We're learning about context-free grammars in Programming Languages, and after the examples, we're trying really hard not to burst into ABBA songs...

If I have time some time soon, I'll post the stuff from my Speech text on the keys to effective listening.  It's good stuff.  (I don't much like the class, but the text has been interesting.)

And in case I didn't mention it, I did just fine on my chapter presentation for Software Design.  And BOY am I glad to have it over with.

Also the Becoming Jane soundtrack is so so pretty, and I'm grateful to my Muddah for alerting me to it.
Current Mood: tiredtired
Current Music: Original Soundtrack - Mrs. Radcliffe
Hunterjjhunter on January 27th, 2009 05:05 pm (UTC)
Math geekery. Yay! :)

(One day, I'll compile a list of bands that use ABCDE - just so I'll have something to fill in when I totally give up while taking bubble exams. ABBA, ACDC, ummm...)
Wiseacreewin on January 27th, 2009 06:04 pm (UTC)
Bwah ha! :)