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Hooray for Mathematics!
Apr. 10th, 2005 10:37 amI'm still working on writing a short paper titled "Geometric Transformation Groups and Invariant Properties." I'll write today's sermon when I'm done with it, if I can pick a topic.
Also, I've recently been rereading parts of my old analysis textbook, Real Mathematical Analysis by Charles Chapman Pugh. I hadn't realized how awesome it was the first time I read it, probably because I didn't actually read much of it. First of all, the section about Cantor sets is called "Cantor Set Lore." And check out this excerpt:
73 Corollary: A Cantor set is homeomorphic to its own Cartesian square, C~CxC.
Proof: It is enough to check that CxC is a Cantor space. It is. See Exercise 109.
The fact that a non-trivial space is homeomorphic to its own Cartesian square is disturbing, is it not?
Is that awesome or what? Man, I love this guy's writing style. Never before have I heard a result in mathematics called "disturbing." (For those of you who are completely lost by those above three lines, Pugh is right: it is kinda disturbing.)
Anyway. Shower, laundry, then back to essay.
-=-Barnabas
Also, I've recently been rereading parts of my old analysis textbook, Real Mathematical Analysis by Charles Chapman Pugh. I hadn't realized how awesome it was the first time I read it, probably because I didn't actually read much of it. First of all, the section about Cantor sets is called "Cantor Set Lore." And check out this excerpt:
73 Corollary: A Cantor set is homeomorphic to its own Cartesian square, C~CxC.
Proof: It is enough to check that CxC is a Cantor space. It is. See Exercise 109.
The fact that a non-trivial space is homeomorphic to its own Cartesian square is disturbing, is it not?
Is that awesome or what? Man, I love this guy's writing style. Never before have I heard a result in mathematics called "disturbing." (For those of you who are completely lost by those above three lines, Pugh is right: it is kinda disturbing.)
Anyway. Shower, laundry, then back to essay.
-=-Barnabas
