Okay, so my girlfriend was supposed to come over to my house today because I was going to go take her to a movie. She lives about 20 minutes away, and the movie we were supposed to see started at 4:15, which was in about 40 minutes. I figured "cool, I'll just read SICP while I wait".
So I'm reading SICP, and having a pretty damn good time. Anyway, she finally does show up, except she's crying as she walks into my room. Instead of doing the right thing by comforting her, I half-focus on my book and her. She starts telling me her cat died, and just as she was getting into it, I get into a rather interesting topic on the nature of time in concurrent systems.
Holy shit. I stare into my book in wonder, yelling "holy shit, YES", interrupting her mid-story. She sobs more, and she starts to yell "You don't even ****ing care! YOU JUST WANT TO READ YOUR ****ING BOOK!" I'm still looking at my book, still focusing on figure 3.29, when she walks over, and tosses the book against the wall. I run over and pick up my SICP hoping that she hadn't damaged it, and quickly noticed that a lot of the pages are now loose and fall out as I pick it up. My SICP and my hopes of becoming an EXPERT PROGRAMMER, gone forever.
I start screaming every obscenity I know, and started flailing my arms around. I didn't know she was behind me, and apparently I backhanded her in the face while I was being a dumbass and swinging my fists around. She yells out "**** YOU", and runs out of my house in tears.
What have I done? I've ****ed up so badly, and I need to know how to approach her. I don't want a read of SICP to be responsible for ruining my best relationship ever. Help me guys
Since the 5th century BC, beginning with Greek mathematician Zeno of Elea in the West and early Indian mathematicians in the East, mathematicians had struggled with the concept of infinity. Especially notable is the work of Bernard Bolzano in the first half of the 19th century. Modern understanding of infinity began in 1867–71, with Cantor's work on number theory. An 1872 meeting between Cantor and Richard Dedekind influenced Cantor's thinking and culminated in Cantor's 1874 paper.
A different form of "infinity" are the ordinal and cardinal infinities of set theory. Georg Cantor developed a system of transfinite numbers, in which the first transfinite cardinal is aleph-null (leph_0), the cardinality of the set of natural numbers. This modern mathematical conception of the quantitative infinite developed in the late nineteenth century from work by Cantor, Gottlob Frege, Richard Dedekind and others, using the idea of collections, or sets.
The work of analysts such as Henri Lebesgue demonstrated the great mathematical utility of set theory, which has since become woven into the fabric of modern mathematics. Set theory is commonly used as a foundational system, although in some areas category theory is thought to be a preferred foundation.
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Anonymous2013-08-31 22:27
For example, Cohen's construction adjoins additional subsets of the natural numbers without changing any of the cardinal numbers of the original model. Forcing is also one of two methods for proving relative consistency by finitistic methods, the other method being Boolean-valued models.
The much stronger axiom of determinacy, or AD, implies that every set of reals is Lebesgue measurable, has the property of Baire, and has the perfect set property (all three of these results are refuted by AC itself). ZF + DC + AD is consistent provided that a sufficiently strong large cardinal axiom is consistent (the existence of infinitely many Woodin cardinals).
Morphisms can have any of the following properties. A morphism f : a → b is a:
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Anonymous2013-09-01 2:13
Identity: for every object X, there exists a morphism idX : X → X called the identity morphism on X, such that for every morphism f : A → B we have idB ∘ f = f = f ∘ idA.
Power sets: The power set functor P : Set → Set maps each set to its power set and each function f : X o Y to the map which sends U \subseteq X to its image f(U) \subseteq Y. One can also consider the contravariant power set functor which sends f : X o Y to the map which sends V \subseteq Y to its inverse image f^{-1}(V) \subseteq X.
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Anonymous2013-09-01 10:34
If X and Y are disjoint, addition is given by the union of X and Y. If the two sets are not already disjoint, then they can be replaced by disjoint sets of the same cardinality, e.g., replace X by X×{0} and Y by Y×{1}.
|X| + |Y| = | X ∪ Y|.
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Anonymous2013-09-01 11:20
\int_{a}^{b} \, f(t)\ dt \ = \infty means that f(t) does not bound a finite area from a to b