:panting:

A simple process for finding the radius of convergence:

1.) Observe the point where the series is != 0 and set the sequence of the series to some "a_n" .

2.) Apply the ratio/root test

3.) Simplify as much as possible. The goal here being to simplify the sequence so you have some clear idea of how it behaves at the end points. I'm not really sure how to word this differently, but like if during the process of evaluating, lets say, a ratio test: lim n-> infinity |3(x-2)^(n+1)/3(x-2)n| you can see that the 3's cancel, and (x-2)^n+1 / (x-2)^n simplifies to just |x-2| (since division of exponential is the same as subtracting their powers, you can review this in algebra)

4.) Using our previous little example |x-2| < 1 converges and diverges when |x-2| > 1 (these are just the property of the ratio test) so the radius of convergence is R = 1.

To answer the part about how do you know if it's a bounded and monotonic sequence:

A bounded sequence is a sequence which has a definite lower bound and definite upper bound. And a monotonic sequence is one which is either non-decreasing or non-increasing so {1/n} is bounded and monotonic because {1/n} is bounded above by a_1 (a_1 = 1) and bounded below by 0 since the sequence never gets to 0 and thus never goes lower than 0. There is not a single element in the sequence which is greater than the previous one, the sequence is {1, 1/2, 1/3 ...} , so it is non-increasing and that makes it monotonic.

Once you apply the root test/ratio test you treat the resulting limit as a limit of a sequence to determine convergence/divergence. So yeah, just evaluate the limit at the endpoint. It's even better if you have a bounded & monotonic sequence as the result of the ratio/root test, so you want to try your best to evaluate a limit that has those two things, if you can discover it with some nifty algebra.

Oh, okay. I must have misunderstood you since I thought contradiction meant a lack of consistency, not being plain wrong. But I understand now. Yeah, Richard Wolff is wrong on lots of the finer details of his points for sure.

If you could enumerate where you see contradictions, I think that would be helpful because I watched the interview and didn't really find any contradictions since he seems to frame his answers out of definitions that he is keeping consistent throughout the interview.

Congrats! :cat-vibing:

I think there’s a lot to this, because I study math, which similarly has this quality of being “exceptionally specific and hard to read”, but because it gives my brain happy juice I’ve found myself consuming all of it as quickly as possible. Now that isn’t so easy, because of how math requires a lot of practice, but I haven’t stepped away from it yet. But I do find that less applied things are not as fun, whereas things like Chaos Theory

I think I’ll try to trigger this “letting theory sink its claws into me” thing and hopefully I’ll still have time for at least some things (like math!)

Yea! This has been pretty much my go to for the time being. I’m hoping one day, maybe once I get on medication, I’ll be able to sit down and engage with theory. Idk if that’s how it works, because I have no clue what being medicated is like though, so.

Ah, okay, my bad. No, looking back on it, your advice is helpful especially with you mentioning about this being a learned part of your perspective.

Other than that, I apologize for assuming you didn’t know what I was going through because if I hadn’t assumed that, then your initial post would have made sense. Idk why I assumed that too, probably because I’m working in “real life, no one understands this” mentality, but you’re right.

Your insight here was incredibly helpful, and I think I’ll go forward being able to be better about things since I’ll probably be like “just remember what septbear said, don’t assume your immediate emotional reaction is how people view you.” It’s been a life long struggle of mine, and I only recently (like maybe 2 weeks ago) was diagnosed with adhd and RSD, and so it’s been like “I have all of the validation that I have ADHD + RSD but none of the work has been done by myself to now reframe my life experiences and build reinforcing strategies.

I want to stress that I apologize for the portion of my response where I essentially said “you don’t know what I’m going through!”, because if I had exercised a bit of good faith, I wouldn’t have immediately assumed you weren’t working from an informed perspective.

:Care-Comrade:

Thanks but genuinely that’s not my immediate assumption, and then even more so, my question was to the people in this comm, because I am affected by a comorbidty of adhd called rsd, something people here understand very well, and for you what could have been taken in good faith, couldn’t for me, not because I’m not being charitable, but because I couldn’t help but feel ashamed about something I had no control over.

And I’m not even trying to call you out, but telling me “maybe you should just act in good faith” when I came to a comm to ask people who have similar experience a question, doesn’t really come across in whatever way you’re trying to have it come across, unless you’re just being mean about it.

Thanks comrade. I couldn’t have explained what motivated me to ask people in this comm this question if I tried. :Care-Comrade:

Thanks for the resources, and while reading is indeed a problem, and audio books/TTS are great, the issue is a lot more nuanced than “just read something but in a different way.”

Namely, I can’t even go through my day to day getting (like I mentioned) the basic tasks of human existence done. I can’t eat consistently, or make food when I want to eat, and that’s just one aspect.

The other aspect is in that, even if I start a book, I just cannot will myself to read it. I mean it took me close to a year to read wage, labor and capital, because I’d read a paragraph and not pick it up for 6 weeks or something.

So if I’m answering your potentially rhetorical question pointedly: the medium isn’t the problem (for me at least) the problem is in my general life and with being able to be consistent on any given task that doesn’t come with some mechanism of giving my brain dopamine at video game levels.

Yeah, but look at what comm you’re in and the question I asked. I was asking the people who usually are here.

I wasn’t stirring shit or trying to slander you, you did dm me and were good, but I made this post asking other nd comrades for validation, because, maybe (key word) something you don’t know, is ADHD comes with other comorbidites of which I have 1 of them: RSD or rejection sensitivity disorder.

Almost no posts here blow up, so it’s not like I was expecting to wake up to a whole thing. If we’re acting in good faith, please try and understand that almost nothing here ends up going onto everyone’s active feed lol.

The king of sauces: Buffalo sauce

Well I appreciate your honesty about it, but it’s just a little annoying when people levy these criticisms of people who don’t read, and generalize that to be “anyone who doesn’t read theory is an enemy” regardless of the fact that maybe some people just can’t engage with even audiobooks because I can’t even will my brain to consistent on anything.

Like I get it, neurodiverse comrades are usually everyone’s afterthought, I just wish people would consider that constantly being told you’re not good enough by society in general (“oh you’re just lazy.” And “well just do y if you don’t like x”) doesn’t feel good, and then doubly so on here with people I respect.

Have you ever considered your neurodiverse comrades that can’t make time in their day to even do the basic tasks of being alive, let alone read? Does that also make me traitorous and counterrevolutionary?

Look, to be honest, I'm don't want to dox information about myself. But I just got diagnosed with ADHD at time that almost seems too late in life, and I dunno, it's so bittersweet. Like yes, finally diagnosed and it's great that I'm going to be able to get the help I need to get, but I also have been put through a lot of shit because of being un-diagnosed (like chronic unemployment, a big reason I wanted to get diagnosed is because I would just sporadically quit my job for no reason with no prior planning). It just really fucking sucks how the world is not made for people who are ND. But a small win, and some closure on chapters of my life that never really made sense.

Well certainly it won't be happening under any kind of neoliberal world order. My estimation is that it would need to be an industry which is suppressed by a proletarian state.

individual stances don't matter, this is just reactionary none-sense. Our beliefs are driven by our material conditions, and the reason you have so many people saying "I agree with vegan being morally superior" isn't because they want to transcend to some moral high road and just can't because of weakness, it's because our planet is fucking cooking and it has to do with the overproduction of animal products for human consumption, and everyone that has any sense knows it.

this is unironically just as reactionary, to think that you (in the general sense, not calling you out specifically) have some ideological superiority over the masses of working class people around the world, and the same liberal elitism that we all cringe at on a daily basis.

there actually is a middle road that can exist on this issue, where you don't have to force ethics onto people who wont accept them anyways, but also significantly reduce the sum total suffering animals face, because we ought to cut animal husbandry way down, ya know, to keep all the humans and animals alive. And that's going to force people to eat a diet that replaces meat with vegetable options, and likely will convert more people to being vegan anyways.

and yeah, i may not be a vegan, but i am a vegetarian, so its not like i want to stick up for eating meat products. so even though i dont get to "win the moral high ground" or whatever elitist nonsense vegans often try to win, i do get to win in the "not being an elitist liberal" and the "proposing something the working class across the world would be willing to accept", since ya know, the material conditions inform our beliefs. and anyone thats not an idealist will agree with me on this.