Alright. Its a holiday tomorrow, so I don't have an excuse to write poorly. Sorry for journalling the past two days. I still think its important for there to be a mechanical account of YSP because should another poor soul that doesn't like math that much like me want to take a course on analysis in a prestigious university, he or she should have a resource. My friends probably wouldn't care about whatever I'm learning. I don't even care about what I'm learning. Needless to say, I will provide everything I can for the world to read.
I took the train and the bus by myself today. I don't remember if I drooled on the train. I was lucky to stumble upon a friend on the way, or I might have easily missed my stop. It turns out that I'm the only friend among many who is participating in uninteresting math this summer. I take comfort in that when I go into Multivariable Calculus and Linear Algebra next year, I'll know that nothing can be as bad as proving that x^2 is continuous.
That happened to be the first thing I learned. A function f: R->R is continuous at x(e)R if for all epsilon>0 there exists some delta>0 such that |x-y|<delta -> |f(y)-f(x)|<epsilon. This almost made sense, but our counselors got really excited ("You're gonna have to pull deltas out of your butt!") and started talking about monoids, defined by (delta, #, e) where e is a neutral element such tha a#e=e#a=a. Monoids, are of course associative, just like any other respectable operation except the cross product. Do I really know what I'm talking about? Not a clue. The point was that in the process of completing rationals (Q) to reals (R), analysis comes into play big time. Besides, naturals and integers are just equations (as if the other two sets weren't) and not that topographically interesting. Obviously.
Professor Sally blindly hoisted his prothetic-legged body onto the table. He assigned each of us a coordinate in the lecure room and cut off introduction.
"I have no legs, no eyes, no hair." The class tittered. "But I intend to run. you. to. the. ground."
"Jason!" he shouted. "Write. I will speak."
"ORDERED INTEGRAL DOMAIN." The class jumped to attention. I blinked, hoping that he really was blind so that he couldn't see my careless slouch. "(R,+,*) is a computative ring with 1 if and only if (+,-) are Internal Laws of Composition."
"Give me an example of a c-ring with 1," he demanded of 2-2, the coordinate next to me. The boy failed, as expected. The Professor turned to me.
"Do you know any c-rings?"
"Uh, like 3 times 5 plus 2?" The smart kids who knew real math turned to me.
"Integers," the smart girl hissed.
"Do you know any c-rings with 1?" the Professor demanded again. I decided that I was bad at thinking and caring.
"Do you want an expression?" The smart kids thought about how incredibly stupid I was.
"Integers," the smart girl hissed.
"No," I said firmly. "I don't. Integers?"
"SURE YOU DO," the Professor shouted. "Have you heard of the integers?"
"What? Yeah."
"Do you know the integers?"
"..."
"..."
"Yes." And I promptly fell asleep, ashamed, hoping against all hopes that we would solve some easier modular arithmetic and stop talking about multiplicative cancellation.
I had hot apple cider for lunch. I made $2.50. There is only multiplicative cancellation in n mod m if and only if m is prime. Be sophisticated, baby. An OIDR satisfies WOP if and only if for all S <- R+ and S is non-empty, then S has a smallest element.
Yeah, right.
I ran and turned in the rest of my Consumer Ed homework. UC is very beautiful. Perhap its loveliness will cancel out my nightmarish classroom experiences.
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