Friday, July 5, 2013

YSP Day 4: Fields

I woke up still bitterly terrified of my parent, but I had an 800 page Chronicles of Narnia in my backpack with a 16 pack of Trident Strawverry Kiwi gu, so I was prepared to face my trials. I did so by falling asleep, a few chapters into Creating Narnia.

I stepped into the barn, previously drawn in Day 2, only to find that there was homework assigned yesterday, not that I could have proved that the set generated by the ordered integral domain of well ordered positive elements was also isomorphic.

I learned more from this morning's summary than I did from the entire lecture yesterday. Apparently, we've been learning structures. We started with a commutative ring with 1. "Atta baby," Professor Sally would crow. After C-ring with 1, we went into integral domains, the difference being that ID's have multiplicative cancellation, whatever that means. Ordered integral domains are.. ordered. I chewed through another three pieces of gum.

Now fields, fields are integral domains, c-rings with 1 with multiplicative inverses. They are transitive, symmetric, and reflexive, just like congruent triangles. I checked my phone for the 5th time. What a lonely class this was after all.

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