Learing the hard way manga

Hi Everyone. I am an undergraduate taking Real Analysis 1 this semester. The course uses Abbott's 'Understanding Analysis', 2nd ed. Although the book's explanations are clear, it has one downside for me: no solution manual. I usually struggle with solving the problems following each section. This is mainly because when I solve a problem, I do not know if my proof is correct/complete, and if I did not solve it, I would not find any hints or solutions. Moreover, my professor is usually unavailable/hard-to-reach.
Therefore, it would be an invaluable learning tool for me to have if anyone could share a Problem List / Test Bank with solutions. Thank you! :).

So I've been looking into replacing the encoder on my Logitech G305 recently as it's starting to fail (occasionally moving up instead of down, not moving at all until I scroll the other way, etc.) and the rest of the mouse is still working fine.
I spent some time looking around and noticed the TTC Gold encoder seems to be popular, but I couldn't really find an exact explanation for why.
I was looking for an encoder that's very durable (all of my mice have ended up with malfunctioning scroll wheels), but I couldn't find any info on which are more and which are less durable.
I'd like the steps to be medium to well defined.
if anyone could point me to some sources for information it would be greatly appreciated!
edit: almost forgot to mention: the encoder on the G305 is 10mm

I naturally want a high paying job and all that your regular MBA-aspirant wants and I want to know the best way to achieve it becuase foreign schools need impressive resumes and work experience and that kind of resume seems hard to get unless you already have an MBA and already work in a good firm so I was wondering if a double MBA with a 4-5 year gap is the best way to go about it.
I don't want to be one of those people that live life getting random degrees from different places without actually getting ahead so I want to make sure if this is the best way to secure what I want.
Also could someone tell me the options of going to the Middle East or Singapore with just an IIM-MBA becuase I'm open to that too

Hello!
I've been considering coming to NA for a long time but I've always had some hangups with it. I finally recently decided to visit an outpatient treatment facility that my insurance covers (I'm taking a week off work and doing the intensive all-day shit starting Monday), and low and behold they do the 12 steps. Of course. So I guess there's no avoiding it. I suppose at least NA can accommodate my work schedule so that's at least feasible long term.
I'm just curious: 1) How exactly do you "work" the steps? 2) Anyone not work the steps and still benefit? 3) I know that "higher power" can mean anything, but even then I still struggle with it. I'm not a spiritual or religious person in any way and I've thought long and hard what my higher power could/would be, and idk I just don't feel like anything I pick could mean as much to me as god means to other people. If that makes sense. 4) NA vs AA? This treatment center is more involved with AA. But I'm an opiate addict (well on my way to being an alcoholic though lol) and I guess I wanna be with my people. 5) If I'm sober from my DOC for 15 months but I keep using other drugs that I want to quit, when is my clean date?? Subjective I know, but curious of opinions. 6) I don't like some of the steps, for example "make a list of people you've harmed" and make amends or whatever. That seems overwhelming and difficult. And a lot of steps seem super Jesusy (and again I know higher power can mean anything, but still, at the end of the day they mean the Christian god) 7) Anything I can read/study to prepare myself?
Idk I just wanted to type my thoughts out loud. You all seem like a lovely bunch. I appreciate any support!

I'm an Elise OTP, and after 13.5 i'm really struggling due to farm changes. I can make Elise work, but many times is way too much effort for too little result and too much risk, so I need to expand my pool a bit. I can play other champs for sure, but not at the same level.
My playstyle is usually quite aggressive invading early on and trying to secure objectives as fast as possible. For that Elise is strugglink right now, so I need someone that can do that but still providing decent ganking potential. I used to play Eve and K6, but i think they're quite bad. I know Eve is considered S tier, but i have no idea why. Her clear is mediocre, she needs to snowball and she is easily invaded early on and shut down by anyone with some brain and a pink ward.
What I can't play are tanks. I want to be able to do stuff without needing people to follow, so a good skirmisher would be nice.

I have seen this advert a while ago and can’t get it out of my head and i need to see it i believe it was a bingo advert but the main bit i remember is a black male buying a lawnmower with his winnings and then states ‘i love my new lawnmower’ in a extremely recognisable way if someone could help find this i would really appreciate.

I’m not sure if I’m overthinking the situation, so would like other opinions. This morning, I stopped at a gas station on my way to work for caffeine. It was seconds of me getting out of my car that the only person working walked out of the store, greeted me, and pulled out his phone. When I reached the door, I glanced back at him and he had his phone pointed at me as if he was taking a picture of me or something. Now, I cannot say with 100% certainty that’s what he was doing, but I find this very odd. I go in, grab my caffeine, and head up to the register to check out. He’s still on his phone at this point and slowly made his way back inside to ring me up. I watched him set down his phone, which had the camera pulled up and looked like he took a photo of his torso, then watched him send a message to someone while he rung me up. I find this very odd and I’m not sure what to make of it, but I’m paranoid. Thoughts?

I just wanted to swap some tips for me 2 after watching legend of total war charge his cav in an (IMO) improper formation.
Also, I fully acknowledge that he is a much, much better player and more experienced than I will ever be, but I feel he might have done it wrong this once.
The charge I am referring to ; https://youtu.be/LGykFg0EwtE at 7:13 (timestamp)
1.) The formation of the bigger cav unit was way too spread out, It could have done with some depth as like 20 percent of the knights charged thin air + it should have gone ham on center and the smaller cav should have charged the right(From viewer's POV).
2.) Always maneuver your cav and adjust it's formation depth and arrangement to fit the intended victims. Too wide, You waste some potential, Too narrow, You reduce the surface of impact and hence the effectiveness.
3.)An overlooked but vital thing is to allow your cav a few seconds to reform before committing to a charge when you cycle-charge. It increases the impact and also ensures your cav penetrates to a similar depth to ensure a quick and low-casualty withdrawal.
Bonus, Non-related tips :
1.) Have cheap infantry spread out in loose formation in front of your main infantry body to absorb charges and missiles. They seriously reduce the effectiveness of frontal charges and allow your main line to mount an counter charge as well as for your archers to retreat, If needed
2.) Use light missile cav to catch enemy light missile cav and then charge the cav with your heavy cav. Usually Works as long as you surprise them, Just allow them to close the distance to skirmish and while they are trying to close the distance, Rush 'em they won't be able to react I time.

Hello, crafters! I am on the hunt for a fastening tool for a poster that has a movable flap. I want the flap to be swung/spun out of the way by its top left corner to reveal information underneath. The poster will be printed on card stock.
I've identified brads as a potential solution, but I worry that the paper won't stay up if the brad is too loosely fitted to both pieces of paper. I've also looked at grommets—would these allow the top flap to move freely, or would it be too tight? Would I need a washer in-between the front and back of the grommet? Is there some other material that I'm missing?
Would super appreciate some suggestions. Thanks!!

Winter Soldier is a classic example of a character who combines two power sets- Cybernetics and Firearms. I decided to give him a few Shield Bearer powers, though none of the ones involving an actual Shield. He could have gotten them from Martial Arts, but I think it's a more fun way to represent Bucky's connection to Steve, and his own Infinity formula.
Google Sheets:https://docs.google.com/spreadsheets/d/11-TleUqKmYmVIpPXXJiWmA9p0CulfTl2RBCd6rKQRkU/edit?usp=sharing
PDF:https://docs.google.com/spreadsheets/d/e/2PACX-1vRABCjnDAafUDS_tF5ewX9A8YyjovFcFkeD4DwEIxdeZ4_ejQ9L6XEiU9ygwYypekDrz_uH6qcTSr-1/pub?gid=1522404290&single=true&output=pdf
As a bonus, here's a sheet for Sam Wilson as Captain America. It's pretty similar to the one for Steve, I mostly just swapped some of the Tactical Mastery powers for Flight.
Google Sheets: https://docs.google.com/spreadsheets/d/1bg8pI0YlvTbJTOkhZnlF193L_UtKbc0gWxDHeIJQOkA/edit?usp=sharing
PDF: https://docs.google.com/spreadsheets/d/e/2PACX-1vQ5ZizbRfUBU8gqk1hpiAMNylIfjdeknzhcgyy-TKYx7xDCZMvF69eMbjQdptyLMkuOvmscWjCgSvpS/pub?output=pdf

Winnipeg Connect is hosting Guys + Gals speed dating for the 30-40 crowd at Little Brown Jug tonight, and we had one guys ticket open up last minute.
If you are up for a fun evening of quick connections, it'd be lovely to fill out the night with 15 gals and 15 guys.
Each round is 7 minutes, and the evening runs from 6:30-9pm with a break half way through.
If you're up for trying something new, we'd love to have you join us tonight.
Find registration info here:
https://winnipegconnect.ticketleap.com/lbj-30-40-march21/

I want to buy a second hand bag online but I can't identify its materials. It doesn't necessarily look like real leather but it also doesn't not look like real leather, meaning it's not something I can completely rule out based on appearance like I could if it was a tote bag or something.
The materials aren't listed and the price is fairly cheap but that doesn't mean much since leather isn't always expensive, and this is a second hand listing.
I'd rather not post images/links of the item, so I'm asking if there is a way I can make sure it isn't real leather through the handful of images provided. All the guides I found are made for in person thrifting. I'm not willing to gamble on wearing animal skin so obviously I won't get it if I'm uncertain, but it is worth asking.

Besides sleeping on the couch? >: I don't know how he can sleep through it and it doesn't seem to be effecting his waking hours. This July it'll be two years since he started this crap. He's been to a doctor multiple times, he's been on multiple drugs, and he's more than once stated that maybe I'm the problem because I can't sleep through it.
The last two nights he's started into jerking, twitching, hip thrusting, IMMEDIATELY after falling asleep. It scares the crap out of me as I'm trying to doze off and at this point I don't know why I bother even going to the bed since as soon as he falls asleep I go to the couch.
I even tried to set up a motion camera to get some of this recorded just to show him what's going on. I wanted to know if he was doing it ALL night or if he just does it when my REM cycle is at its lowest for me waking up. The only thing it recorded was me getting up and going to the couch.
I've got an appointment next Monday to set up a primary care doctor for myself and I'm wondering if there's something I can ask for to knock my ass out (because not only will he not sit still, we have an entire neighborhood of irresponsible dog owners who let their dogs out to bark at 7AM). After something wakes me up I have a VERY hard time getting back to sleep immediately. And the cycle continues all night.
Yes, I've been told he should get a sleep study. No, he hasn't. I have to be the bad guy and CONSTANTLY tell him to go back to the doctor as it is because this isn't working. The doctor upped his MGs two weeks ago, we're working on getting his iron up a bit (he had/has hemochromatosis, so while it's still in safe levels, it's toward the low end). People keep saying to buy two twin beds and shove them together and, not only do I NOT want to buy ANOTHER bed after ours is only three years old, we might as well just sleep apart for all the sheets pulling he does. And, unfortunately, we don't have enough room for a second bedroom/bed. It's couch or floor at this point.

[F4A] Fantasy Foundation, Highly Adaptable Scene where the sky is the limit!~
{Hiya! This is an older scene I used to do, so it's not the best prompt but I can promise you it's highly adaptable! I love taking this scene in as many directions as possible so if you have an idea or a character you'd like to fit in please just add it in your message! I'm extremely open minded, and love talking things out, so please, feel free to message me even if all you have is a theme or concept you'd like to chase after!~}
The sun had finally set on the town stained red with the putrid, stagnant blood of the hours before, an atmosphere that should have lead to an painfully uncomfortable tension and sense of dread hanging over the town. The small town located fae from any major city, located all the way out in the boonies, the people of the town had enjoyed an almost perfect existence away from the bustle and the politics of the kingdoms powerhouse cities, with the closest the town ever getting to weighing in on global events was the ever frequent platoon of troops appearing to scout and draft new recruits for the kings army, yet the town knew that if this was the price to pay for their simple way of life, it'd be one they'd gladly take. This was not to say the town was free of problems, with it's own sub culture and a plethora of races calling the town home, it wasn't a perfect society but it was theirs nonetheless.
However, peace in times like these never trully lasted long, as ambushes on traders and muggings became a part of their everyday life, it was only long before the culprits became dissatisfied with the scraps they could manage to snatch from the various merchants, and set their sights on sieging the town itself. Even though a bandit with a conscience made it into the town square to give the people warning, their was only so much a town with not enough true soldiers and barely enough men to put every weapon they had to use. Even though this thought would be clear to any outsider or even any onlooker with any sense of logic, the town bowed their heads and banded together for the oncoming slaughter. Barricades were set up in the town square and every person who either couldn't hold a weapon or couldn't afford to be lost in battle held up in the middle of the town offering whatever aid they could as the bandits finally descended on the town.
The young women dressed in white and adorned with intricate and almost hypnotic golden lining was to no surprise to anyone, not from the small town. Ophelia herself had been raised by the church, with not a single memory left of anything that came before her time as part of the doctrine, with the church and the faith being all she had ever known since such a young age. The girl had been raised as a part of a programme, belonging to a very specific sect of the church to raise a new generation of exemplary figures to lead and carry out the will of their lord throughout the land, being not only well versed in every religious text and passage their was, but also being trained in a passable level of combat along with the church's own ever elusive branch of holy magic.
Even though she had never had much choice in the matter, Ophelia's fairh was pure and unwavering, never having had it brought into question, and it was this sole fact that allowed her to rise through the church swiftly as an example of what true faith and commitment could lead too. Her faith led her to becoming a strong willed, fiery member of the cloth who's use of holy miracles and incantations could scarcely be rivalled by only the bishops themselves of the church, allowing her to join a sub-section of the church known as the inner-choir, a rank similar to that of a cardinal priest in status yet without the title itself, allowing the general public to acknowledge them as pillars of the order but not all in the church could say the same.
Ophelia had only spent the lesser part of a week with the town, with it being one of the few stops on her journey that she was specifically told to take note of and assess the town on a more personal and real level than any real census could. It was the kindof task that she found herself being given on top of any other work that her brothers and sisters of the clergy were tasked with. Not that she ever complained, having lived a sheltered life being raised by the church in to the shining beacon of light that the world could see her as.
The town had welcomed her with open arms, allowing her to take refuge in their chapel with everyone offering a warm welcome to the young girl. It was never part of her job, but she always made a point to talk and introduce herself to as many of the town's people as she could, hearing their struggles and doing everything in her power to aid them and pass on whatever blessings she had at her disposal. She was the talk of the town, and she loved to hear the stories and fables of the towns culture, becoming absorbed and obsessed with learning and hearing as much about their own little secluded world as she could.
It would be hard to say that the young girl being there on that day, lending her aid in both combat and healing of the wounded, didn't have a drastic effect on the outcome of the day. Her prowess allowed the fatalities to stay low and for the towns rag-tag militia to keep fighting until the ruthless bandits retreated for now, leaving there casualties in the streets to the roars of celebration from the town. Now, even on a day that should be treated solemnly and respectfully, the entire town was in celebration over their survival and the grit they had shown today. People took to the streets, the fields and most importantly the taverns to let the world know that they would not be crushed that easily.
Now Ophelia sat, at a table with her travel companion and bodyguard, a man who was there more for company than anything else as the table top was cluttered with a plethora of drinks and plates of food that had been bought for her, thanks from the town as she hungrily wolves down bowl after bowl to bring her energy back so she can return to tending the wounded before she collapses for the day. She barely got a minute to enjoy herself, between bites groups of people at a time would come up to thank her and offer her tokens and praise, as she gladly accepted their kind words, giving her work that feeling of purpose that she had always strived for.
The only thing that bothered the girl was a new face in the tavern, someone that she couldn't place from her walks of the town, congregation or even the battle that happened prior, which confused the girl greatly as she felt the eyes on her every now and then. The face dissapeared eventually as she shook her head, returning to her food as her bodyguard gets up to speak to a few of the men that he had met earlier, as the girl is now left alone to her devices as she continues with her food, her mind still trying to place the face she had just seen.

I take the PATH train, which uses a SmartLink tap to pay card. This card is not compatible with Apple Wallet. However, when you tap your iPhone near the reader, Apple Wallet pops up but doesn’t go through and take normal card payments. Is there a way to hack the SmartLink card onto Apple Wallet and be able to pay by tapping my iPhone? It feels doable to me but I have no clue if it is. Thank You!

As I've been working I've noticed that things keep circling back to my past negative experiences - A higher level supervisor reminding me of my psychotic step-dad in the way he puts standards on us that no other supervisor does. - coworkers constantly joking around with each other while I'm trying to focus and work, much like high schoolers who would rather make noise and tease me while I struggle to get work done It always seems I can't concentrate on what I'm doing because my mind always brings up the past things that bothered me. Is this a common thing?