Limit Inferior and Superior Analysis problem

I'm guessing this is more of an issue of understanding the definitions and how they work but I am completely lost from what my professor has told us of these two things.
https://imgur.com/a/VaWPchy

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πŸ‘€︎ u/Soulgiver831
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A problem concerning limits superior/inferior

Consider the function f(x) where:

f(x) = x when x is rational

f(x) = 0 when x is irrational.

Find limsup(f(x)) and liminf(f(x)) as x approaches a for: a = 0, a = -1, a = 2.

My answers were:

a = 0: limsup(f(x))=0 (correct), liminf(f(x))=0 (correct)

a = -1: limsup(f(x))=-1 (incorrect, should be 0), limsup(f(x))=-1 (correct)

a = 2: limsup(f(x))=2 (correct), liminf(f(x))=2 (incorrect, should be 0)

Why were some of these incorrect? All values of a are rational. Any help is appreciated.

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[Analysis] Find every limit superior and limit inferior

.. for sequence {n*cos((pi*n)/2)}

I assumed that cos(pi*n) = (-1)^n, and n = 2k, so:

2kcos(pi*2k/2) = 2kcos(pi*k) = 2k*(-1)^(2k) = 2k; limn->inf = +inf, therefore it's a limit superior.

I am not sure what to do next. I tried to apply the same steps for n = 2k-1;

(2k-1)(cos((pi(2k-1))/2) = (2k-1)(cos(pi(k - 1/2))) = ... ???

And it didn't work out since I can't find the limit. I also stuck doing this while looking at its definition.

Any tips how to work it out? Are my steps correct?

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A few questions on limit inferior and superior
  1. Show that lim sup(-x_n) = -(lim inf (x_n))
  2. If lim x_n exists, show that lim sup x_n = lim inf x_n = lim x_n
  3. For any sequence x_n in the reals, show that lim inf x_n <= lim sup x_n
  4. Let a_n and b_n be bounded sequences of the reals. Show that lim sup (a_n b_n) <= (lim sup a_n) (lim sup b_n)

I know the reasoning behind all these. I just stuck on how to show it formally. Thanks in advance!

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The Lightning Network - We explain the motivation behind the creation of LN and why its scaling characteristics are superior, potentially resulting in a transformational improvement. We look at LNs limitations, including the downside of inferior security blog.bitmex.com/the-light…
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Why I swear by Fidelity's superior fills and price improvements. The limit order was set right at the mid price and filled instantly. Good luck getting that on your 'free' brokerage.
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A little behind the scenes of a short film my girlfriend and I made. Wanted to have the camera at a great height to make me feel inferior and powerless. If you want to check the short, check first comment Don't let the budget limit your work and be careful! reddit.com/gallery/n3k0e9
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This man is the greatest gamer to ever scratch the surface of our planet, we will never see anyone quiet like him. His paradigms of prosperity are vastly superior and exceeds the limits at which can be concocted from the inner depths of our simple human feeble little brains.
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So Sasuke's Amenotejikara Vs Minato's Flying Raijin Which Is Superior & Best ?? Amenotejikara Works In Limited Range But Can Teleport Anything (Living/Non Living) Without Markings !! Flying Ragin Can Teleport Anywhere No Range Limit Instant, But Requires Markings !! Which ability will you choose ?
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Nonexistent islands of Lake Superior at the border of Canada and the USA, from the 1755 map of North America by Dr. John Mitchell: "A Map of the British and French Dominions in North America. With the Roads, Distances, limits, and Extent of the Settlements" Isle Royale is real, most others are not. reddit.com/gallery/pbzwin
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I propose we get rid of the inferior M320 grenade lobber. And get the superior chainsaw bayonet.
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ads for TV screens and computer displays show you how superior the details and colors are.. on your supposedly inferior screen that just can't achieve that.
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β€œWhen one limits one self to human labels one is trapping the mind to inferior paradigms and the illusory self.” - Lord_Zeath
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Yes guys, only Canadians are morally superior to us inferior Americans… and yes, all 300+ million of us think the same reddit.com/gallery/raegiv
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All 14 black Democrat lawmakers in Mississippi Senate walk out in protest over bill to ban teaching that "any race is superior or inferior" and curb critical race theory in schools dailymail.co.uk/news/arti…
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Chihiro and Mondo Swap because I was inspired by u/BRRTAI after commenting on his Kaede/Shuichi swap and thus using my inferior photoshop skills I present to you this despair or hope (whichever gives you an orgasm)-inducing art which I shall use as a stepping stone for hope. 300 character limit done
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Hitler was brilliant at brainwashing the German people into thinking they were racially superior, and this was a common attitude held by many Germans at the time. However, did any Jews also come to believe Hitler aswell and belive that they were racially inferior and deserved their treatment?

Hitler was known to be an extremely persuasive and charasmatic speaker, and could seemingly convince the German people of anything. And so, did he manage to convince some Jews that they were racially inferior and deserved how they were treated?

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This dock is off-limits to inferior sequels
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SOUNDWAVE SEZ: DRS and HODL, Superior; Day-trading GME through brokerage "to pick up more shares", Inferior.
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The superior weight limit measurement
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Question about the superior and inferior border of the superficial inguinal ring

Hi,

I'm learning anatomy in Latin and for anulus inguinalis superficialis we are taught that margo superior is crus mediale and margo inferior is crus laterale.

Margo medialis which is ligamentum reflexum makes sense.

I don't understand what a crus mediale/laterale is. Could anyone kindly explain this.

Thank you

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Peter R. Rizun: "BTC is realizing that Lightning cannot solve the high-fee problem and that a block-size limit increase is needed for another growth cycle. But once bigger blocks are discussed seriously, BCH will gain further credibility as its scaling roadmap is recognized as superior." twitter.com/peterrizun/st…
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[Michael David Smith] β€œThe superior man blames himself. The inferior man blames others.”-Don Shula β€œHey, dipshit, make your fucking kicks! I’m the head ball coach, I’ll kick you whenever the fuck I want.”-Urban Meyer twitter.com/michaeldavsmi…
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Seekers superior dream inferior
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Beijing is clearly inferior to Moscow (during the USSR or now) when it comes to propaganda - even with superior resources and technology.

https://preview.redd.it/twje7a0k9r081.png?width=601&format=png&auto=webp&s=1fea7b6fc7611f85f23a869ae2c430f2df27de31

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DAE have mood swings from when you feel happy and superior to feeling inferior and ugly compared to everyone else and a loser (15m)

Like sometimes especially during the night at my house I have a big ego and I feel like I am popular and everyone likes me and I have so many friends and that I am very handsome but when I go to school this immediately goes away and I feel lonely depressed and I start to even contemplate suicide when I see how many friends other people have and I feel like I am nobody’s favorite person and that I am just annoying everyone Like I joke around with my friends when texting them on Instagram during the night but as soon as I go to school I just feel like I was annoying them and that they don’t really like me at all and that nobody likes me nor respects me and I view myself as superior at night but then as school I view myself as inferior to everyone

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So, if Liquid was the ''Superior'' clone and Solidus the ''perfect mix'', does that means Solid Snake even tho he is the inferior he is in fact the strongest of all 3 brothers?

Pretty sure he beat the living shit out of Liquid in MGS1, played a big role in the fall of Solidus in MGS2 and defeated Ocelot in MGS4 for not mention all the staff from the old games. But the fact that he is still named the inferior after all this kinda bugs me out, he clearly outmatched all of his brothers.

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Sports fans of Reddit: You have a 30 word limit to try and convince everyone why your sport is superior. What do you say?
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Eros is Superior. Gabriela is inferior.
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[OC] The [Superior Quality], the [Inferior Quality] and the [Aesthetically Displeasing]

Station Security scuttled into what was once a dining establishment. The furniture, bolted down as per regulation in the event of loss of gravity, was a total write-off. There were dents in the duralloy bar and the floor was stained with more than spilled drinks. However, the place was deserted save for the owner and proprietor of the establishment, who was behind the bar typing into a datapad.

"Took you long enough." the proprietor grumbles, most of his attention still on the datapad. A delicate claw tapping into it, feathers bristled and disheveled. His beak was completely closed, probably to avoid the smell. "I gave you a heads up to cut this off before it got out of control, then again when everything went to Void and back. You were still nearly ten micro-time-units too slow."

"Where is the perpetrator?" the chief of the enforcer squad asks

"Void if I know. Dragged the other one out. You are stepping on the trail. Once they leave my establishment, it isn't my problem anymore."

"What happened?" The chief of the enforcer squad, the proprietor decided, was what some of his human patrons would call a 'numpty', given the state of disassembly in general.

The barkeep warbles a whistle of irritation, then looks up from the datapad. "Humans have a saying 'too little, too late'. I find it appropriate for the situation. But for paperwork's sake, and by station regulation, I will asist." Feathers ruffle in his species version of a shrug "Where should I begin?"

"Start just before your first call, when the lone human entered." The sole remaining light fixture cast a glare off of the well polished chitin of the security enforcers as it made a gesture with the second manipulator limbs to indicate the seriousness of the request.

"All right. So, how much do you know about humans and human behavior and social structure? Trust me, it's relevant."

"Humans are a bipedal heavy-gee predator species, capable of extreme feats of strength when provoked, and a metabolism that neutralizes or renders ineffective most tranqs. Hell, if the regs are to be believed, they can shrug of an electrical neural disruptor! As far as behavior and social structure, I'm not a xenopsychologist, I'm a security grunt."

"Okay, so I've been serving humans for around five revolutions now, and I've picked up on many of their mannerisms and social behavior structure. They're not just predators, they're *pack* predators. They also consider this location to be far enough outside their normal

... keep reading on reddit ➑

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[16M] too many simps and pedos. Not enough soundwave. SOUNDWAVE SUPERIOR, HUMANS INFERIOR reddit.com/gallery/piftjr
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What is the practical limit of a superior ranks authority ?

In the the civilian world, an employee can just quit if asked to do something they strongly disagree with. Not so in the military I gather.

Can a Major or some similar rank tell some enlisted type , "Go get a shovel and dig me a 10x10 and 55 meter deep pit over by that tree" because he feels like it?

Can a superior rank just order a lesser rank to turn over private property? IE "Give me your PS5 private."

Can General say "Go defuse that unexploded bomb Colonel" knowing the Colonel has no training in such an area ?

And what about an officer killing his own men in combat for refusing orders, like happened several times in world war 1 when soldiers refused to go over the top in the trenches ?

If the service member refuses and says "yeah, Im not going to do that sir" What would happen to them?

Thanks for reading and have a nice day.

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"I am superior. You are inferior!" I LOVED THIS SCENE!!! It is hard not to simultaneously love and hate Madam Yu here. I like donghua better for this scene tho. She trashed that b**** with zidian! v.redd.it/dhgminmobxm71
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How is the idea of "superior and inferior cultures", morally speaking, generally seen by anthropologists?

So, it was pretty common in the past for empires to justify colonization by calling their victims savages, retrograde and stuff like that, right? An impression that I've got is that, for that reason, any accusation of inferiority of a culture's morality is generally seen as colonialist due to the historical correlation.

But at the same time, we cannot criticize our own culture and wish for it to change unless we give ourselves the right to evaluate and judge cultures different from our own, can we? I mean, if I cannot say that rape culture in South Africa and arranged marriage and caste systems in India are bad, even worse than they are in our (here focusing on English speaking countries though I'm from Brazil, so maybe just "western culture" though I know that's some BS oversimplification) culture/s, then what criticism can I give to patriarchy in my culture? Any moral standard which allows one to criticize one's own culture and wish for it to change must allow for criticism of any culture. One consequence of that is that some cultures are going to be morally superior or inferior to others if we accept that criticizing culture in moral grounds is acceptable.

At the same time, I've heard that some degree of "methodological cultural relativism" is necessary for proper, less biased analysis of historical and current societies. As in, first you just study a society in its own terms and merely describe it factually, and if there is to be any judgement it must come after the descriptive analysis or you risk biasing your extraction of facts from the investigation, as well as the interpretation of any facts extracted.

So I wanted to ask... how exactly is it that moral judgement of cultures tends to be treated by anthropology/by anthropologists? What are the more common viewpoints on this and ways of doing it, if it is to be done at all?

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While one person hesitates because he feels inferior, the other is busy making mistakes and becoming superior. - Dr. Henry C. Link[1920x1080]
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β€œFarenheit might be inferior for most things but it's the far more logical and superior way to measure outside temps.”
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Your presents inferior my presents superior!!!
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Flags of countries with white-red and red-white flags but gerrymandered so that superior white-red flags outnumber the inferior red-white flags
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My mom has a superiority complex and I'm really at my limits...

It's gotten to the point where I literally just can't enjoy my day for 2 hours without her trying to get her little burst of serotonin from talking shit on me.

I spend a lot of time in my room either playing a game or programming/studying. For some reason my mom always decides to go into my room and peek her head in and say I should leave my room more and then proceed to degrade me and compare me to her friends' children (outgoing + extroverted people, the polar opposite of me). She then proceeds to berate me about how "behind" I am. For the record, I'm not behind in any capacity, she just needs something to talk shit about. My mother who is a college dropout (nothing wrong with that, just ironic) loves to belittle me for not studying when she's looking (which is rarely). And when I clearly don't take her shit (cause I'm not a dumbass), she also loves throwing in the "if you don't pass after giving me this attitude, you will see what I will do". She threatens me. A 21 year old who could just as easily leave. She still acts like I need her and I'm so fucking sick of it. She doesn't value my privacy, doesn't respect my hobbies, and wants to determine what happens in my life. She is literally trying to live through me and it's fucking pathetic. I love her for raising me (although very badly, with a lot of trauma), but this shit has to end. I'm so close to just leaving.

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