Let φ : G -> G' be an isomorphism of a group <G, *> with a group <G', *'>. Write out a proof to convince a skeptic that if G is cyclic, then G' is cyclic.Other than the terminology, I'm as lost as you are at this point. I may be able to explain what the question wants, but I can by no means prove it. Thus, I present the following argument.
This question is question 42. Clearly, the answer is the inverse of The Life, Universe, and Everything, or (Life, Universe, Everything)-1. After all, f-1(f(x)) = x, so the answer to the question is clearly the question of the inverse of the answer. Or something. To simplify, we can write the answer to 42 as (Death, Universe-1, Nothing). However, what is the inverse of the universe? One is immediately tempted to say either "a point" or "the multiverse." However, neither of these answers suffice. It's much like asking, "What is the opposite of a dog?" No, the answer's not cat. The answer is not-dog. Clearly, a cat is more like a dog than a not-dog is.
However, the question was not, "What is the opposite of the universe?" but rather, "What is the inverse of the universe?" If we look at the universe additively, the answer is the negative universe. This can't be correct because the universe contains equal amounts of matter and anti-matter, thus the negative universe is the same as the universe. If we look at the universe multiplicitively, we see that the inverse of the universe is (1/universe). Which leads us to a slightly different question, "What is 1 divided by the universe?" Let us explore this more deeply.
One is the concept of unity. There is only one universe, by definition. Thus, if I were to find a number to accurately describe the universe, it would clearly have to be 1, correct? But, I already showed that the negative universe = the universe, and the only number that has this property is zero. Thus, I can safely say that the numerical form of the universe is zero. Thus, 1/the universe is the same as 1/0, which is undefined. However, the limit as n approaches 0 of 1/n is infinity. But the universe is infinite (If it's not, into what is it expanding?). How can both the universe and the inverse of the universe be infinite? So the numerical value of the universe is not zero, as I had thought. Nor is it infinity, because the inverse is also infinite.
Because there is no known number d such that d and 1/d are both infinite, I find this the perfect time to introduce the much-needed concept of counterfeit numbers. Clearly, the universe is a counterfeit number. Because counterfeit numbers are produced only through division by zero, the inverse of all counterfeit numbers is zero.
Therefore the correct answer to the original question is (Death, 0, Nothing). However, zero and nothing are the same. However, because taking the inverse of counterfeit numbers is not a one-to-one operation, the universe and everything are not necessarily equivalent. This is a topic to be explored at another time.
I had just finished printing off my Faust paper for World Lit through Film when I heard a knock on the apartment door. Cynic yelled "It's open" or "Come in" or something similar, and indeed the door opens. I am fairly certain I know who it is, so I go out to the living room.
"Ah, I see I did find the right place," said a familiar voice. Cynic looked up from his repose to see who was speaking, because he recognized the voice as well. He looked over, and I could see the gears turning for a moment before he recognized who had just walked in to the Ice Cave.
"Dr. Baas," said Cynic in a very, very surprised tone. "What are you doing here?" At this point, I reached out and took the papers from this school's premier computer science prof. He had come down to our apartment to give me the papers I needed to grade.
Having fulfilled the purpose of his visit, Dr. Baas stayed around for a minute or two, inquiring where Cynic was this morning. I knew full well that he had consciously slept through his 8 AM class. That is, he made a conscious decision the previous night to remain unconscious during the first half-hour or so of his 8 AM class. Got it? Good. Baas then asked us what we had in the fridge. Sadly, we have nothing, and we told him so. So after a couple of minutes of general merriment, Dr. Baas went out the door, got on his bicycle, and rode away.
On the way to SAGA, Cynic and I decided that we should definitely start stocking our fridge with food (keeping under lock and key so that this one doesn't get ahold of it) and invite profs down to the Ice Cave. Clearly, we ought to drag Solganick back one night after WLTF. Or possibly drag Watson back next week. Now there's an idea...
Since I've been rather silent for some time, I figure I should relate an almost amusing story. Last Wednesday, I was sitting in physics lab, working on things as I should have, wearing this shirt. Normally, when I wear this shirt, people ask me what 127.0.0.1 is, I explain it to them, and they catch the reference. But this being LeTourneau, I can't expect this every time. A fellow student sees my shirt, and says, "Alright. 127.0.0.1 is localhost, right?"
"Yes," I reply.
"Okay." He has a confused look on his face. "So what's the shirt mean?"
At this point, I'm rather astonished. "You know, 'There's no place like home, there's no place like home, there's no place like home?'"
"Oh, right. I just wasn't associating that with that." Clearly.
Only at LeTourneau, I hope. I'm fairly certain I'm wrong, but I can hope.
Ever wondered why I'm getting an English minor?
The internet is a wonderful place. For example, when was the last time you saw a bookstore on vacation? Hm? I rest my case.
Tomorrow I have three classes for a total of just under five hours in class. I only have homework for two of them, but I've already finished that. No point in starting my homework for Thursday; after all, I want to maintain some semblance of college norms. I figure most of this will change when I have tests to study for and projects to complete, but for now, I am free. Even next week, I'm beginning a "tutoring" session (essentially a TI session, except that it goes on my grading timecard) for Baas' data structures students next Monday, and I will hopefully be getting a reply from the guy I'm supposed to be tutoring one-on-one sometime soon. But I suppose I'll go ahead and go through my schedule for the benefit of those who care.
CAPA hates me, and wants me to die,'Nuff said. Almost. The class should be interesting, but difficult. My lab is with Ruby at 2:35 on Wednesdays. Lecture with Dr. Forringer.
But I hate it, so that's alright.
Oh, CAPA hates me, and wants me to die,
But I hate it, so everything's fine.
So I'm reading through the American Lit reading for tomorrow. Oh, my. The American Indians do indeed have some entertaining stories. Take this passage from "A Tale of the Sky World." This account describes one aspect of creation. At this moment in the story, the only humans on the Earth are a woman and her daughter.
Before long the young daughter gave signs that she was about to become a mother. Her mother reproved her, saying that she had violated the injunction not to face the east, as her condition showed that she had faced the wrong way while digging potatoes... When the days of her delivery were at hand, she overheard twins within her body in a hot debate as to which should be born first and as to the proper place of exit, one declaring that he was going to emerge through the armpit of his mother, the other saying that he would emerge in the natural way.
Ever wondered why I'm getting an English minor?
Indeed, it's been quite a while. But, as Wheeler (among others around the Ice Cave) are trying to get me to post, I suppose I'll give in. Peer pressure and all that, you know? So here you are. Enjoy it while it lasts, because, knowing me, it will be the last you hear of me in quite some time. But that's just how it goes.
Last month, I read Wil Wheaton's Just a Geek. I saw this book and thought it might be interesting to read, because no one's seen Wil in years. But, I didn't really want to pay money for it because I figured that he was just a washed-up celebrity trying to get some money off his fame. But somewhere or another, I stumbled across his blog. Much to my surprise, this guy is an amazing writer. He's witty, even downright hilarious in places, and many of his stories get you to empathize with him. It's strange, but I feel like I can call him Wil even though I've never seen the guy.
Most of the book is excerpts from his blog, though he explains most of the backstory and his feelings when he was writing it. Most of the book is not about Star Trek, though obviously he has to deal with the subject more than once. Most of the book is actually about proving the Voice of Prove to Everyone that Quitting Star Trek wasn't a Mistake wrong and about silencing the Voice of Self-Doubt. It's about his struggles as an actor, trying to provide for and spend time with his family, and eventually finding that his other great talent is writing.
While this is Wil's story, and probably doesn't have any major life lessons in it, it does have some well-written message in it. Though he also has some purely entertaining stories as well. Most of the stories he has from the set of Star Trek are highly entertaining. As an appendix, he includes his interview from Slashdot, where one guy asked him, "When you were on the set of TNG, did you ever find yourself running into the automatic doors when there was no one there to open them for you?" So Wil relates the story of a time when,
"Patrick [Stewart, i.e. Jean-Luc Picard] is going on and on about the Prime Directive or something and there is a loud CRASH! from the turbolift. We all turn around to look, and the doors open slowly (like the FX guy is scared to open the door), and Jonathan [Frakes, William Riker] is on the floor. I think it was Michael Dorn who was in the turbolift with him, and he is standing over him, just pointing and laughing."Maybe it's just me, but the thought of Michael Dorn, in all his Klingon garb, pointing and laughing at anything is absurdly amusing.
Wil also relates the joys of blogging, learning HTML, PHP, and Linux. He also admits that he has been a Trekkie all his life, is interested in sci-fi of all sorts, and is generally an all-around geek, hence the title. The only thing I had a problem with was he sometimes seemed to lay it on a little thick, as though he felt he had to prove to his audience that he was indeed a geek. The story has two major climaxes, in the chapters titled, "A Sort of Homecoming," and "The Wesley Dialogues." In the first, he realizes that even though he believed Star Trek ruined his acting career, he actually loved the show and all the people on it. In "The Wesley Dialogues," he finally overcomes his self-doubt, accepts his lot, and moves on. All in all, Just a Geek is an excellent book, and I recommend it to just about everyone. If you like Star Trek: TNG, or Star Trek, or, you know, life, you should definitely come borrow this book. If you can't seem to separate Wesley Crusher from Wil Wheaton, you should most certainly borrow this book.
So there. A post.