Common Examples of Uncountable Sets

Not all infinite sets are the same. One way to distinguish between these sets is by asking if the set is countably infinite or not. In this way, we say that infinite sets are either countable or uncountable. We will consider several examples of infinite sets and determine which of these are uncountable.​ Countably Infinite We begin by ruling out several examples of infinite sets. Many of the infinite sets that we would immediately think of are found to be countably infinite. This means that they can be put into a one-to-one correspondence with the natural numbers. The natural numbers, integers, and rational numbers are all countably infinite. Any union or intersection of countably infinite sets is also countable. The Cartesian product of any number of countable sets is countable. Any subset of a countable set is also countable. Uncountable The most common way that uncountable sets are introduced is in considering the interval (0, 1) of real numbers. From this fact, and the one-to-one function f( x ) bx a. it is a straightforward corollary to show that any interval (a, b) of real numbers is uncountably infinite. The entire set of real numbers is also uncountable. One way to show this is to use the one-to-one tangent function f ( x ) tan x. The domain of this function is the interval (-π/2, π/2), an uncountable set, and the range is the set of all real numbers. Other Uncountable Sets The operations of basic set theory can be used to produce more examples of uncountably infinite sets: If A is a subset of B and A is uncountable, then so is B. This provides a more straightforward proof that the entire set of real numbers is uncountable.If A is uncountable and B is any set, then the union A U B is also uncountable.If A is uncountable and B is any set, then the Cartesian product A x B is also uncountable.If A is infinite (even countably infinite) then the power set of A is uncountable. Two other examples, which are related to one another are somewhat surprising. Not every subset of the real numbers is uncountably infinite (indeed, the rational numbers form a countable subset of the reals that is also dense). Certain subsets are uncountably infinite. One of these uncountably infinite subsets involves certain types of decimal expansions. If we choose two numerals and form every possible decimal expansion with only these two digits, then the resulting infinite set is uncountable. Another set is more complicated to construct and is also uncountable. Start with the closed interval [0,1]. Remove the middle third of this set, resulting in [0, 1/3] U [2/3, 1]. Now remove the middle third of each of the remaining pieces of the set. So (1/9, 2/9) and (7/9, 8/9) is removed. We continue in this fashion. The set of points that remain after all of these intervals are removed is not an interval, however, it is uncountably infinite. This set is called the Cantor Set. There are infinitely many uncountable sets, but the above examples are some of the most commonly encountered sets.

California Politics And Government A Practical Approach

The book, California Politics and Government: A practical Approach, helps students understand the government and politics. It describes the principles used in the state government and the relevance of these to the nowadays students and the future ones. The book has clear examples and explanations that help the students understand the California politics. It includes budgetary politics and policies, California law and court cases, government regulations, policymaking and elections in terms of political parties and interest groups. It addresses the economic, educational, immigration and social issues and theireffecton the politics. Students are able to familiarize with the public policy coverage; hence, make a connection between the effects and practical applications of legislation and the government. The first chapter of the book is an introduction to the economy, politics and people of California. It encompasses the economy, politics and demography of the state for the past, present and the future. The edition features updated demographic information of the state from the census that took place in 2010. The chapter explains the state’s transition from colonization to rebellion and statehood. It discusses California’s past, including the great depression, political turmoil, infrastructure, workingmen’s party and World War II. The growth, reform and progressive change of the state to what it is today is also highlighted in the book. California previously faced budget deficitsShow MoreRelatedThe Rise and Fall of the Electric Car Essay1192 Words   |  5 Pagesâ€Å"Fro-Joy†, â€Å"everything in life is somewhere else, and you get there in a car†, which could not be any truer (White). The first minute and nineteen seconds of the film, Who Killed the Electric Car, reported that â€Å"two million new cars are sold in California each year† (Who). 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I regard Mosca as a classic exponent of democratic elitismRead MoreHousing Discrimination : Improve Housing Quality For The Poor By Outlawing Source Of Income Discrimination2239 Words   |  9 Pagesconditions, and lower quality education than wealthier Americans (United States Government Accountability Office, 2007). Additionally, and more importantly to the purposes of this report, the poor are more likely to experience homelessness or live in inadequate housing. The National Alliance to End Homelessness (2016) estimates that over 500 thousand people were homeless on any given night in 201 5. The federal government, recognizing this issue exists, has responded by allocating â€Å"50 billion in housing

Evaluation Approach And Methodological Framework - 1554 Words

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Chopin VS Thurber and Relationships - 2545 Words

In the stories â€Å"The Secret Life of Walter Mitty† by James Thurber (Clugston, sec. h1.1) and â€Å"The Story of an Hour† by Kate Chopin (Clugston, sec. h2.1) escapism is a similar theme with in both these stories, yet there is a slight variance in how each of these authors place these characters into their escape from reality, relationships, and everyday chaos. In each of these stories the author shows the characters escaping the realities of the relationship, one through Walter Mitts’ daydreams, and the other through one brief hour when Louise Mallard pictures her new life of freedom. Through the use of characterization, imagery, point of view and setting these authors bring in the element of escapism to each story. In the short story â€Å"The†¦show more content†¦h2.1). In this stanza it paints a portrait of her going back in time to try and recollect what love was about with her husband and was it silent or restless. B. two white slender hands(Clugston, sec. h2.1) is a clue to the reader that her character is gentle as well as a lady and should be treated as so, however the lines(Clugston, sec. h2.1) as described by the narrator show she’s hiding many deep feelings. When someone is filled with recession the chance to escape their stress and hurt would be welcomed. In â€Å"The Secret Life of Walter Mitty the use of imagery give the reader a illustrative description of the daydreams he is having while allowing the reader to have a vivid picture of the goings-on around him. The imagery of his wife’s consistent nagging is brought into focus allowing the reader to identify with Walter concerning his wife s overbearing and scrutinizing ways. In â€Å"The Story of An Hour† imagery gives the reader a feel of almost relief along with the use of our senses such as taste, smell, sight and sounds to set a stage the tragedies yet to come. Deneau suggests this story may be a reflection of a sexual experience. In both of these cases an escape from the true reality is possible. (1) Secret Life of Walter Mitty A. In the stanzas â€Å"not so fast! You’re driving too fast!† said Mrs. Mitty. â€Å"What are you driving so fast for?† (Clugston, sec. h1.1),these lines give the reader a picture of both Mr. Mitty and Mrs. Mitty driving

Shadow Kiss Chapter 8 Free Essays

string(105) " With her out of the way, I moved off to the side, hoping to assist Eddie – but there was no need\." Eight FOR THE NEXT FEW DAYS, I followed Christian around without incident. And as I did, I found myself growing more and more impatient. For one thing, I was discovering that a lot of being a guardian was waiting around. We will write a custom essay sample on Shadow Kiss Chapter 8 or any similar topic only for you Order Now I’d always known that, but the reality was harder than I’d realized. Guardians were absolutely essential for when Strigoi decided to attack. But those Strigoi attacks? They were generally rare. Time could pass – years could pass – without a guardian ever having to engage in any sort of conflict. While my instructors certainly wouldn’t make us wait that long during this exercise, they nonetheless wanted to teach us patience and how important it was not to slack just because there’d been no danger in a while. We were also being held to the strictest conditions a guardian could be in: always standing and always being formal. More often than not, guardians who lived with Moroi families behaved casually in their homes and did ordinary things like reading or watching TV – while still staying perfectly aware of any threats. We couldn’t always expect that, though, so we had to practice the hard way while in school. My patience level didn’t do so well with all this waiting, but my frustration was more than just restlessness. I was desperate to prove myself, to make amends for not having reacted when Stan attacked. I’d had no further Mason sightings and had decided that what I’d seen really had been fatigue- and stress-induced. That made me happy, because those were much better reasons than being crazy or inept. But certain things were not making me happy. When Christian and I met up with Lissa after class one day, I could feel worry and fear and anger radiating off of her. It was only the bond that clued me in, though. To all outside appearances, she looked fine. Eddie and Christian, who were talking about something with each other, didn’t notice a thing. I moved close and put an arm around her as we walked. â€Å"It’s okay. Everything’s going to be okay.† I knew what was bothering her. Victor. We’d decided that Christian – despite his willingness to â€Å"take care of things† – probably wasn’t the best choice to go see about us getting into Victor’s trial. So Lissa had played diplomat the other day and very politely spoken to Alberta about the possibility of us testifying. Alberta had told her, equally politely, that it was out of the question. â€Å"I figured if we just explained things – why it was so important – they’d let us go,† she murmured to me. â€Å"Rose, I can’t sleep. †¦ I just keep thinking about it. What if he gets loose? What if they really set him free?† Her voice trembled, and there was an old vulnerability there that I hadn’t seen in a long time. That sort of thing usually set off my warning bells, but this time, it triggered a weird rush of memories, of times past when Lissa had depended on me so much. I was happy to see how strong she’d become and wanted to make sure she stayed that way. I tightened my arm, hard to do while still walking. â€Å"He won’t get loose,† I said fiercely. â€Å"We’ll get to court. I’ll make sure of it. You know I’d never let anything happen to you.† She leaned her head against my shoulder, a small smile on her face. â€Å"That’s what I love about you. You have no idea how you’ll get us to court, but you still push forward anyway to make me feel better.† â€Å"Is it working?† â€Å"Yes.† The worry still lurked in her, but her amusement dampened its effects a little. Plus, despite her teasing me about my bold promise, my words really had reassured her. Unfortunately, we soon found out that Lissa had other reasons to be frustrated. She was waiting for the medication to fade from her system and allow her full access to her magic. It was there – we could both sense it – but she was having trouble touching it. Three days had passed, and nothing had changed for her. I felt for her, but my biggest concern was her mental state – which thus far had stayed clear. â€Å"I don’t know what’s going on,† she complained. We had almost reached the commons. Lissa and Christian had plans to watch a movie. I half-wondered how difficult it would be for me to watch the movie and be on alert. â€Å"It seems like I should be able to do something, but I still can’t. I’m stuck.† â€Å"That might not be a bad thing,† I pointed out, moving away from Lissa so I could scan the path ahead. She shot me a rueful look. â€Å"You’re such a worrier. I thought that was my job.† â€Å"Hey, it’s my job to look out for you.† â€Å"Actually, it’s my job,† said Eddie, in a rare show of joking. â€Å"Neither of you should be worrying,† she argued. â€Å"Not about this.† Christian slipped his arm around her waist. â€Å"You’re more impatient than Rose here. All you need to do is – â€Å" It was d? ¦j? ¤ vu. Stan leapt out from a copse of trees and reached for Lissa, wrapping his arm around her torso and jerking her toward him. My body responded instantly, no hesitation whatsoever as I moved to â€Å"save† her. The only problem was that Eddie had responded instantly too, and he was closer, which put him there ahead of me. I circled, trying to get in on the action, but the way the two were squaring off blocked me from being effective. Eddie came at Stan from the side, fierce and swift, pulling Stan’s arm away from Lissa with a strength nearly powerful enough to rip it out of the socket. Eddie’s wiry frame often hid how muscular he really was. Stan’s hand caught the side of Eddie’s face, nails digging in, but it was enough so that Lissa could wriggle free and run to join Christian behind me. With her out of the way, I moved off to the side, hoping to assist Eddie – but there was no need. You read "Shadow Kiss Chapter 8" in category "Essay examples" Without missing a beat, he grabbed Stan and threw him down to the ground. Half a breath later, Eddie’s practice stake was poised right above Stan’s heart. Stan laughed, genuinely pleased. â€Å"Nice job, Castile.† Eddie withdrew the stake and helped his instructor up. With the action gone, I could now see how bruised and blotched Stan’s face was. Attacks for us novices might be few and far between, but our guardians were picking fights daily during this exercise. All of them were taking a lot of abuse, but they handled it with grace and good humor. â€Å"Thank you, sir,† said Eddie. He looked pleased but not conceited. â€Å"I’d be faster and stronger if I were Strigoi, of course, but I swear, you could have rivaled one with your speed there.† Stan glanced at Lissa. â€Å"You okay?† â€Å"Fine,† she said, face aglow. I could sense that she’d actually enjoyed the excitement. Her adrenaline was running high. Stan’s smiling face disappeared as he turned his attention on me. â€Å"And you – what were you doing?† I stared, aghast at his harsh tone. It was what he’d said last time too. â€Å"What do you mean?† I exclaimed. â€Å"I didn’t freeze or anything this time! I was ready to back him up, looking for a chance to join in.† â€Å"Yes,† he agreed. â€Å"That’s exactly the problem. You were so eager to get a punch in that you forgot that you had two Moroi behind you. They might as well have not existed as far as you were concerned. You’re out in the open, and you had your back to them.† I strode forward and glared at him, unconcerned about propriety. â€Å"That is not fair. If we were in the real world and a Strigoi attacked, you cannot tell me that another guardian wouldn’t jump in and do everything they could to take that Strigoi down as quickly possible.† â€Å"You’re probably right,† Stan said. â€Å"But you weren’t thinking about eliminating the threat efficiently. You weren’t thinking about your exposed Moroi. You were thinking about how quickly you could do something exciting and redeem yourself.† â€Å"Wh-what? Aren’t you making a few leaps there? You’re grading me on what you think was my motivation. How can you be sure what I’m thinking?† I didn’t even know half the time. â€Å"Instinct,† he replied mysteriously. He took out a small pad of paper and made some notes on it. I narrowed my eyes, wishing I could see through the notepad and discern what he was writing about me. When he finished, he slipped the pad back in his coat and nodded at all of us. â€Å"See you later.† We watched him walk across the snowy grounds toward the gym where dhampirs trained. My mouth was hanging open, and I couldn’t even get any words out at first. When did it end with these people? I was getting burned again and again on stupid technicalities that had nothing to do with how I’d actually perform in the real world. â€Å"That was not even fair. How can he judge me on what he thinks I was thinking?† Eddie shrugged as we continued our journey toward the dorm. â€Å"He can think whatever he wants. He’s our instructor.† â€Å"Yeah, but he’s going to give me another bad mark! Field experience is pointless if it can’t really show how we’d do against Strigoi. I can’t believe this. I’m good – I’m really good. How on earth can I be failing this?† Nobody had an actual answer for that, but Lissa noted uncomfortably, â€Å"Well†¦ whether he was fair or unfair, he had one thing right: You were great, Eddie.† I glanced over at Eddie and felt bad that I was letting my own drama take away from his success. I was pissed off – really pissed off – but Stan’s wrongness was my problem to deal with. Eddie had performed brilliantly, and everyone praised him so much on the walk back that I could see a blush creeping over his cheeks. Or maybe that was just the cold. Regardless, I was happy for him. We settled into the lounge, pleased to find no one else had claimed it – and that it was warm and toasty. Each of the dorms had a few of these lounges, and all were stocked with movies and games and lots of comfy chairs and couches. They were only available for student use at certain times. On weekends, they were pretty much open the whole time, but on weekdays, they had limited hours – presumably to encourage us to do our homework. Eddie and I assessed the room and made a plan, then took up our positions. Standing against the wall, I eyed the couch Lissa and Christian were sprawled out upon with considerable envy. I’d thought the movie would distract me from being on alert, but actually, it was my own churning feelings that kept my mind spinning. I couldn’t believe Stan had said what he’d said. He’d even admitted that in the heat of battle, any guardian would be trying to get into the fight. His argument about me having ulterior, glory-seeking motives was absurd. I wondered if I was in serious danger of failing this field experience. Surely, so long as I passed, they wouldn’t take me from Lissa after graduation? Alberta and Dimitri had spoken like this was all just an experiment to give Lissa and me new training, but suddenly, an anxious, paranoid part of me began to wonder. Eddie was doing a great job of protecting her. Maybe they wanted to see how well she could work with other guardians. Maybe they were worried that I was only good at protecting her and not other Moroi – I’d let Mason die, after all, right? Maybe the real test here was to see if I needed to be replaced. After all, who was I, really? An expendable novice. She was the Dragomir princess. She would always have protection – and it didn’t have to be me. The bond was pointless if I ultimately proved incompetent. Adrian’s entrance put my frantic paranoia on hold. He slipped into the darkened room, winking as he flounced into an armchair near me. I had figured it was only a matter of time before he would surface. I think we were his only entertainment on campus. Or maybe not, judging from the strong smell of alcohol around him. â€Å"Are you sober?† I asked him when the movie ended. â€Å"Sober enough. What have you guys been up to?† Adrian hadn’t visited my dreams since the one in the garden. He’d also laid off on some of his outrageous flirting. Most of his appearances with us were to work with Lissa or to ease his boredom. We recapped our encounter with Stan for him, playing up Eddie’s bravery and not mentioning my dressing-down. â€Å"Nice work,† said Adrian. â€Å"Looks like you got a battle scar too.† He pointed to the side of Eddie’s face where three red marks glared back at us. I remembered Stan’s nails hitting Eddie during the struggle to free Lissa. Eddie lightly touched his cheek. â€Å"I can barely feel it.† Lissa leaned forward and studied him. â€Å"You got that protecting me.† â€Å"I got that trying to pass my field experience,† he teased. â€Å"Don’t worry about it.† And that’s when it happened. I saw it seize her, that compassion and undeniable urge to help others that so often filled her. She couldn’t stand to see pain, couldn’t stand to sit by if she could do something. I felt the power build up in her, a glorious and swirling feeling that made my toes tingle. I was experiencing how it affected her. It was fire and bliss. Intoxicating. She reached out and touched Eddie’s face†¦. And the marks vanished. She dropped her hand, and the euphoria of spirit faded from both of us. â€Å"Son of a bitch,† breathed Adrian. â€Å"You weren’t kidding about that.† He peered at Eddie’s cheek. â€Å"Not a goddamned trace of it.† Lissa had stood up and now sank back to the couch. She leaned her head back against it and closed her eyes. â€Å"I did it. I can still do it.† â€Å"Of course you can,† said Adrian dismissively. â€Å"Now you have to show me how to do it.† She opened her eyes. â€Å"It’s not that easy.† â€Å"Oh, I see,† he said in an exaggerated tone. â€Å"You grill me like crazy about how to see auras and walk in dreams, but now you won’t reveal your trade secrets.† â€Å"It’s not a ‘won’t,'† she argued. â€Å"It’s a ‘can’t.'† â€Å"Well, cousin, try.† Then suddenly he raked his nails across his hand and drew blood. â€Å"Jesus Christ!† I yelped. â€Å"Are you insane?† Who was I kidding? Of course he was. Lissa reached out and held his hand, and just like before, she healed the skin. Elation filled her, but my mood suddenly dropped without any real cause. The two of them launched into a discussion I couldn’t follow, using standard magical terms as well as some terms I was pretty sure they’d invented on the spot. Judging from Christian’s face, it looked like he didn’t understand either, and it soon became clear that Adrian and Lissa had forgotten us in their zeal over the mystery of spirit. Christian finally stood up, looking bored. â€Å"Come on, Rose. If I wanted to listen to this, I’d be back in class. I’m hungry.† Lissa glanced up. â€Å"Dinner’s not for another hour and a half.† â€Å"Feeder,† he said. â€Å"I haven’t had mine today.† He planted a kiss on Lissa’s cheek and then left. I followed alongside him. It had started snowing again, and I glared at the flakes accusingly as they drifted down around us. When it had first started snowing in early December, I’d been excited. Now this white stuff was getting pretty damned old. As it had a few nights ago, though, being out in such harsh weather defused my mood a little, the cold air kind of snapping me out of it. With each step closer to the feeders, I felt myself calming down. A â€Å"feeder† was what we called humans who volunteered to be regular sources of blood for Moroi. Unlike Strigoi, who killed the victims they drank from, Moroi took only small quantities each day and didn’t have to kill the donor. These humans lived for the high they got from vampire bites and seemed perfectly happy to spend their lives that way and separate from normal human society. It was weird but necessary for Moroi. The school usually had a feeder or two in the Moroi dorms for overnight hours, but for most of the day, students had to go to the commons to get their daily fix. As I continued walking, taking in the sights of white trees, white fences, and white boulders, something else white in the landscape caught my attention. Well, it wasn’t white exactly. There was color – pale, washed-out color. I came to an abrupt halt and felt my eyes go wide. Mason stood on the other side of the quad, nearly blending in with a tree and a post. No, I thought. I’d convinced myself that this was over, but there he was, looking at me with that sorrowful, phantom face. He pointed, off toward the back of campus. I glanced that way but again had no clue what to look for. Turning back to him, I could only stare, fear twisting within me. An icy-cold hand touched the side of my neck, and I spun around. It was Christian. â€Å"What’s up?† he asked. I looked back to where I’d seen Mason. He was gone, of course. I squeezed my eyes shut a moment and sighed. Then, turning back to Christian, I kept walking and said, â€Å"Nothing.† Christian usually always had some witty stream of comments whenever we were together, but he was silent as we made the rest of our journey. I was consumed with my own thoughts and worries about Mason, so I had little to say either. This sighting had only lasted a few seconds. Considering how hard it was to see out there, it seemed more than likely that he’d been a trick of the eye, right? I tried to convince myself of this for the rest of the walk. When we entered the commons and escaped the cold, it finally hit me that something was amiss with Christian. â€Å"What’s wrong?† I asked, trying not to think about Mason. â€Å"Are you okay?† â€Å"Fine,† he said. â€Å"The way you just said that proves you aren’t fine.† He ignored me as we went to the feeders’ room. It was busier than I’d expected, and all of the little cubicles that feeders sat in were filled with Moroi. Brandon Lazar was one of them. As he fed, I caught a glimpse of a faded green bruise on his cheek and recalled that I never had found out who had beaten him up. Christian checked in with the Moroi at the door and then stood in the waiting area until he was called. I racked my brain, trying to figure out what could have caused Christian’s bad mood. â€Å"What’s the matter? Didn’t you like the movie?† No answer. â€Å"Grossed out by Adrian’s self-mutilation?† Giving Christian a hard time was a guilty pleasure. I could do this all night. No answer. â€Å"Are you – Oh.† It hit me then. I was surprised I hadn’t thought of this before. â€Å"Are you upset that Lissa wanted to talk magic with Adrian?† He shrugged, which told me all I needed to know. â€Å"Come on, she doesn’t like magic more than she likes you. It’s just this thing with her, you know? She spent all these years thinking she couldn’t do real magic, and then found out she could – except it was this wacky, completely unpredictable kind. She’s just trying to understand it.† â€Å"I know,† he said tightly, staring across the expansive room without actually focusing on any of the people. â€Å"That’s not the problem.† â€Å"Then why †¦Ã¢â‚¬  I let my words fade as another revelation hit me. â€Å"You’re jealous of Adrian.† Christian fixed his ice-blue eyes on me, and I could tell I’d hit the mark. â€Å"I’m not jealous. I’m just – â€Å" † – feeling insecure over the fact that your girlfriend is spending a lot of time with a rich and reasonably cute guy whom she might like. Or, as we like to call it, jealous.† He turned away from me, clearly annoyed. â€Å"The honeymoon might be over between us, Rose. Damn it. Why are these people taking so long?† â€Å"Look,† I said, shifting my stance. My feet hurt after so much standing. â€Å"Didn’t you listen to my romantic speech the other day about being in Lissa’s heart? She’s crazy about you. You’re the only one she wants, and believe me, I can say that with 100 percent certainty. If there was anyone else, I’d know.† The hint of a smile crossed his lips. â€Å"You’re her best friend. You could be covering for her.† I scoffed. â€Å"Not if she were with Adrian. I assure you, she has no interest in him, thank God – at least not romantically.† â€Å"He can be persuasive, though. He knows how to work his compulsion†¦Ã¢â‚¬  â€Å"He’s not using it on her, though. I don’t even know if he can – I think they cancel each other out. Besides, haven’t you been paying attention? I’m the unfortunate object of Adrian’s attention.† â€Å"Really?† asked Christian, clearly surprised. Guys were so oblivious to this sort of stuff. â€Å"I know he flirts – â€Å" â€Å"And shows up in my dreams uninvited. Seeing as I can’t get away, it gives him the perfect chance to torture me with his so-called charm and attempt to be romantic.† He turned suspicious. â€Å"He shows up in Lissa’s dreams too.† Shoot. Shouldn’t have mentioned the dreams. What had Adrian said? â€Å"Those are instructional. I don’t think you need to worry.† â€Å"People wouldn’t stare if she showed up at some party with Adrian.† â€Å"Ah,† I said. â€Å"So this is what it’s really about. You think you’re going to drag her down?† â€Å"I’m not that good †¦ at those kinds of social things,† he admitted in a rare show of vulnerability. â€Å"And I think Adrian’s got a better reputation than me.† â€Å"Are you joking?† â€Å"Come on, Rose. Drinking and smoking aren’t even in the same league as people thinking you’re going to turn Strigoi. I saw the way everyone acted when she took me to dinners and stuff at the ski lodge. I’m a liability. She’s the only representative from her family. She’s going to spend the rest of her life tied up with politics, trying to get in good with people. Adrian could do a lot more for her than I could.† I resisted the urge to literally shake some sense into him. â€Å"I can see where you’re coming from, but there’s one flaw in your airtight logic. There’s nothing going on with her and Adrian.† He looked away and didn’t say anything else. I suspected his feelings went beyond her simply being with another guy. As he’d even admitted, he had a whole tangle of insecurity about Lissa. Being with her had done wonders for his attitude and sociability, but at the end of the day, he still had trouble dealing with coming from a â€Å"tainted† family. He still worried he wasn’t good enough for her. â€Å"Rose is right,† an unwelcome voice said behind us. Preparing my best glare, I turned around to face Jesse. Naturally, Ralf lurked nearby. Jesse’s assigned novice, Dean, stood watch at the doorway. They apparently had a more formal bodyguard relationship. Jesse and Ralf hadn’t been in line when we arrived, but they’d apparently wandered up and heard enough to piece together some of our conversation. â€Å"You’re still royal. You have every right to be with her.† â€Å"Wow, talk about a turnaround,† I said. â€Å"Weren’t you guys just telling me the other day how Christian was about to turn Strigoi at any moment? I’d watch your necks, if I were you. He looks dangerous.† Jesse shrugged. â€Å"Hey, you said he was clean, and if anyone knows Strigoi, it’s you. Besides, we’re actually starting to think that rebellious Ozera nature is a good thing.† I eyed him suspiciously, assuming there must be some trick here. Yet he looked sincere, like he really was convinced Christian was safe. â€Å"Thanks,† said Christian, a slight sneer curling his lips. â€Å"Now that you’ve endorsed me and my family, I can finally get on with my life. It’s the only thing that’s been holding me back.† â€Å"I’m serious,† said Jesse. â€Å"The Ozeras have been kind of quiet lately, but they used to be one of the strongest families out there. They could be again – especially you. You’re not afraid to do things that you aren’t supposed to. We like that. If you’d get over your antisocial bullshit, you could make the right friends and go far. Might make you stop worrying so much about Lissa.† Christian and I exchanged glances. â€Å"What are you getting at?† he asked. Jesse smiled and cast a covert glance around us. â€Å"Some of us have been getting together. We’ve formed a group – sort of a way for those of us from the better families to unite, you know? Things are kind of crazy, what with those Strigoi attacks last month and people not knowing what to do. There’s also talk about making us fight and finding new ways to hand out the guardians.† He said it with a sneer, and I bristled at hearing guardians described like objects. â€Å"Too many non-royals are trying to take charge.† â€Å"Why is that a problem if their ideas are good?† I demanded. â€Å"Their ideas aren’t good. They don’t know their place. Some of us have started thinking of ways to protect ourselves from that and look out for each other. I think you’d like what we’ve learned to do. After all, we’re the ones who need to keep making decisions, not dhampirs and nobody Moroi. We’re the elite. The best. Join us, and there are things we could do to help you with Lissa.† I couldn’t help it. I laughed. Christian simply looked disgusted. â€Å"I take back what I said earlier,† he told them. â€Å"This is what I’ve been waiting for my whole life. An invitation to join your tree house club.† Ralf, big and lumbering, took a step forward. â€Å"Don’t screw with us. This is serious.† Christian sighed. â€Å"Then don’t screw with me. If you really think I want to hang out with you guys and try to make things even better for Moroi who are already spoiled and selfish, then you’re even stupider than I thought you were. And that was pretty stupid.† Anger and embarrassment filled both Jesse and Ralf’s faces, but mercifully, Christian’s name was called just then. He seemed considerably cheered as we walked across the room. Nothing like a confrontation with two assholes to make you feel better about your love life. Christian’s assigned feeder tonight was a woman named Alice, who was the oldest feeder on campus. Most Moroi preferred young donors, but Christian, being the twisted person he was, liked her because she was kind of senile. She wasn’t that old – sixties – but too many vampire endorphins over her life had permanently affected her. â€Å"Rose,† she said, turning her dazed blue eyes on me. â€Å"You aren’t usually with Christian. Have you and Vasilisa had a fight?† â€Å"Nope,† I said. â€Å"Just getting a change of scenery.† â€Å"Scenery,† she murmured, glancing at a nearby window. Moroi kept windows tinted to block out light, and I doubted a human could see anything. â€Å"The scenery is always changing. Have you noticed that?† â€Å"Not our scenery,† said Christian, sitting beside her. â€Å"That snow’s not going anywhere. Not for a few months.† She sighed and gave him an exasperated look. â€Å"I wasn’t talking about the scenery.† Christian gave me an amused smile, then leaned over and sank his teeth into her neck. Her expression grew slack, all talk of scenery or whatever she’d meant forgotten as he drank from her. I lived around vampires so much that I didn’t even think about their fangs half the time. Most Moroi were actually pretty good at hiding them. It was only in moments like these that I remembered the power a vampire had. Usually, when I watched a vampire feed, I was reminded of when Lissa and I had run away from the Academy, and I’d let her feed off of me. I’d never reached the crazy addiction levels of a feeder, but I had enjoyed the brief high. I used to want it in a way I could never admit to anybody. In our world, only humans gave blood. Dhampirs who did it were cheap and humiliated. Now, when I watched a vampire drink, I no longer thought about how good the high felt. Instead, I flashed back to that room in Spokane where Isaiah, our Strigoi captor, had fed off of Eddie. The feelings that stirred up in me were anything but good. Eddie had suffered horribly, and I hadn’t been able to do anything except sit there and watch. Grimacing, I turned away from Christian and Alice. When we left the feeders’ room, Christian looked more vibrant and upbeat. â€Å"The weekend’s here, Rose. No classes – and you get your day off.† â€Å"No,† I said, having almost forgotten. Damn it. Why did he have to remind me? I was almost starting to feel better after the Stan incident. I sighed. â€Å"I have community service.† How to cite Shadow Kiss Chapter 8, Essay examples

Change, Development and Progress free essay sample

The same is true for a nation. A nation or a country is doomed unless there is a constant change taking place which moulds the lives of the countrymen and takes the country forward. This process of change has to be catalysed by the powers that govern the nation. In our country, successive democratically elected governments have put the country on the path of progress since independence. Today as a nation we can boast that we are in a position which probably in the furthest of imagination nobody could even dream of when we Just attained independence in 1947. As our president Dr. Abdul Kalam has mentioned that by 2020 he dreams of an India which will be recognized as one of the most powerful nations of the world. The specific areas where the nation has made tremendous progress are extensive industrialization, massive growth in agricultural production resulting in self-sufficiency in food grains and remarkable growth in nfrastructure sector specially power and roadways. We will write a custom essay sample on Change, Development and Progress or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page The industrialization of our country took giant strides with the setting up of the huge steel plants in the public sector, which the then Prime Minister Shri Jawaharlal Nehru described as The temples of modern India. The heavy engineering industry also took giant leaps in the post independence era. Oil, mining,cement and metal industries also progressed significantly. The industrial scenario in the country has undergone a sea change in the last one decade. Liberalisation of economy has exposed the Indian industries to lobal competition. The management of industries is increasingly shifting from the government to the private sector. Indian industries are having a trying time to meet global standards in terms of quality and cost. They have to benchmark their production against the best in the world. The oil exploration industry has to be given a major thrust as a substantial portion of our crude oil requirements is met through imports, which means heavy drain of foreign exchange from the exchequer. The Indian refineries are not only augmenting their capacity, but also producing better uality fuel as well as lubricating base oil through state-of-the-art refining technology. The agricultural sector has witnessed a major revolution and today we can proudly say that we are in a position to generate surplus food grain for export after feeding one billion hungry mouths in our country. This is a commendable achievement, which has been made possible through the Green Revolution with major change being brought about by improved irrigation, and mechanized agricultural techniques. The Indian farmer today is a happy and ontended person and his smile is bringing happiness to millions of Indian homes because our economy is primarily agrarian and we cannot afford to be entirely dependent on the vagaries of nature for our economic progress though, even today, to a considerable extent, our GDP is related to a good monsoon. The Golden Quadrangle Project has now made travel by highways much faster and comfortable. The Highways Authority of India has erected carpet like smooth become much better and bumpy roads are now a thing of the past in most parts of the country. The world has now become a global village. Unprecedented developments have taken place in the area of communication. Gone are the days when speed of communication was a factor of distance. Now, communication is the most important tool available to the human civilization and our country is no exception. Cell phones have now penetrated to remotest corners of the country and computers have revolutionized access to information and mails now travel at the click of a mouse. Change, development and progress are now the buzz words which govern the destiny of our nation.

Bouyancy and displacement Essay Example For Students

Bouyancy and displacement Essay Ships do not sink because of displacement; the ship moves more water than the ship actually weighs. Archimedes Principle: Any object wholly or partly immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object. Density is mass of a unit volume of a material substance, expressed as kilograms per cubic meter in MKS or SI units. Density offers a convenient means of obtaining the mass of a body from its volume or vice versa; the mass is equal to the volume multiplied by the density, while the volume is equal to the mass divided by the density. The weight of a body, which is usually of more practical interest than its mass, can be obtained by multiplying the mass by the acceleration of gravity. Tables that list the weight per unit volume of substances are also available; this quantity has various titles, such as weight density, specific weight, or unit weight. D = mass/volumeDisplacement is distance moved by a particle or body in a specific direction. It is a vector quantity, possessing both magnitude and direction. The distance traveled by the point depends on the path that it follows; it will be equal to the magnitude of the displacement only if the path is straight. In mechanics, it is freque ntly necessary to distinguish between the distance that a point movesor through which a force actsand the displacement of the point or the force. The purpose of this experiment was to make an object buoyant by adding a sufficient amount of extra volume to displace the water necessary. My hypothesis was that the additional amount of displacement needed would be .54 liters. The needed amount of displacement was found by first finding the difference between the mass and displacement. The solution was the difference in mass and the weight of the water being moved. This solution was divided by the density of the salt water at Seaquarium, which was 1.03 kilograms. The materials that were needed to conduct this experiment was a concrete or lead object, a scale to weigh the object, string, empty bottles, sea water, a graduated cylinder for measuring the water accurately, and buckets filled with sea water. The procedure followed to perform the experimentation is as follows:1.Choose a concrete or lead object and weigh it on a scale. The unit of the scale was pounds. It s mass was 2.7 pounds. 2.To find the weight of the object in ounces, the whole number of the weight was multiplied by 16 and then add the decimal. Then the solution was divided by 16. To convert the weight from ounces to kilograms, 2.44 was divided by 2.2. 3.To obtain the volume of the object, a bucket was filled with sea water .The inside of the bucket was marked with a marker where the water reached. Then the object was placed into to the bucket to see how much the water would rise. When the object was taken out, the water height reduced. 4.Using a graduated cylinder in liters, we measured how much water it took to reach the original point. This is the volume of the object. We converted it into liters by dividing by 1000. 5.Displacement was calculated by multiplying the objects volume by the density of the seawater..65 x 1.03 = .6695 Liters To find the extra amount of displacement needed was found by finding the difference between the mass and displacement. The solution was the difference in mass and the weight of the water being moved. This solution was divided by the density of the salt water at Seaquarium, which was 1.03 kilograms. The extra displacement needed was .54 liters of water, which was added to a 1-liter bottle. .ucc8a2a67903e5742f14b0677893bb384 , .ucc8a2a67903e5742f14b0677893bb384 .postImageUrl , .ucc8a2a67903e5742f14b0677893bb384 .centered-text-area { min-height: 80px; position: relative; } .ucc8a2a67903e5742f14b0677893bb384 , .ucc8a2a67903e5742f14b0677893bb384:hover , .ucc8a2a67903e5742f14b0677893bb384:visited , .ucc8a2a67903e5742f14b0677893bb384:active { border:0!important; } .ucc8a2a67903e5742f14b0677893bb384 .clearfix:after { content: ""; display: table; clear: both; } .ucc8a2a67903e5742f14b0677893bb384 { display: block; transition: background-color 250ms; webkit-transition: background-color 250ms; width: 100%; opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #95A5A6; } .ucc8a2a67903e5742f14b0677893bb384:active , .ucc8a2a67903e5742f14b0677893bb384:hover { opacity: 1; transition: opacity 250ms; webkit-transition: opacity 250ms; background-color: #2C3E50; } .ucc8a2a67903e5742f14b0677893bb384 .centered-text-area { width: 100%; position: relative ; } .ucc8a2a67903e5742f14b0677893bb384 .ctaText { border-bottom: 0 solid #fff; color: #2980B9; font-size: 16px; font-weight: bold; margin: 0; padding: 0; text-decoration: underline; } .ucc8a2a67903e5742f14b0677893bb384 .postTitle { color: #FFFFFF; font-size: 16px; font-weight: 600; margin: 0; padding: 0; width: 100%; } .ucc8a2a67903e5742f14b0677893bb384 .ctaButton { background-color: #7F8C8D!important; color: #2980B9; border: none; border-radius: 3px; box-shadow: none; font-size: 14px; font-weight: bold; line-height: 26px; moz-border-radius: 3px; text-align: center; text-decoration: none; text-shadow: none; width: 80px; min-height: 80px; background: url(https://artscolumbia.org/wp-content/plugins/intelly-related-posts/assets/images/simple-arrow.png)no-repeat; position: absolute; right: 0; top: 0; } .ucc8a2a67903e5742f14b0677893bb384:hover .ctaButton { background-color: #34495E!important; } .ucc8a2a67903e5742f14b0677893bb384 .centered-text { display: table; height: 80px; padding-left : 18px; top: 0; } .ucc8a2a67903e5742f14b0677893bb384 .ucc8a2a67903e5742f14b0677893bb384-content { display: table-cell; margin: 0; padding: 0; padding-right: 108px; position: relative; vertical-align: middle; width: 100%; } .ucc8a2a67903e5742f14b0677893bb384:after { content: ""; display: block; clear: both; } READ: Brave New World vs 1984 Essay6.The object was tested by putting it in the ocean to see if it floats. 7.Recalculated the air needed to make the object float. Added and subtracted water. The result of the experiment was that the object actually needed 4.39 liters of water to float in the seawater. We also used a bigger bottle. In conclusion, the hypothesis was incorrect. 4.39 Liters of water were necessary to make the object buoyant. The percentage error from our hypothesis was 45%. Bibliography:science discivery text bookpages 9-190