And like he also said, ‘Pause’.

What do you mean the emperor is ‘naked’?

Now, ask yourself this question, ‘is 0.999…, or any real number for that matter, a series?’. The answer to that question is ‘no’.

You seem to be extremely confused, and think that the terms ‘series’ and ‘the sum of a series’ mean the same thing. They do not. 0.999… is the sum of the series 9/10+9/100+9/1000+…, and not a series itself.

EDIT: Also, the author does abuse the notations somewhat when she says ‘1+1/2+1/4 = 2’ is a geometric series, as the geometric series 1+1/2+1/4+… does not equal 2, because a series is either just a formal sum, a sequence of its terms, or, in German math traditions, a sequence of its partial sums. It is the sum of the series 1+1/2+1/4+… that is equal to 2. The confusion is made worse by the fact that sums of series and the series themselves are often denoted in the same way. However, again, those are different things.
Would you mind providing a snippet with the definition of the term ‘series’ that she provides?

EDIT 2: Notably, that document has no theorem that is called ‘convergence theorem’ or ‘the convergence theorem’. The only theorem that is present there is the one on convergence and divergence of geometric series.

Ok. In mathematical notation/context, it is more specific, as I outlined.

It is not. You will routinely find it used in cases where your explanation does not apply, such as to denote the contents of a matrix.

Furthermore, we can define real numbers without defining series. In such contexts, your explanation also doesn’t work until we do defines series of rational numbers.

Ok. Never said 0.999… is not a real number

In which case it cannot converge to anything on account of it not being a function or any other things that can be said to converge.

because solving the equation it truly represents, a geometric series, results in 1

A series is not an equation.

This solution is obtained using what is called the convergence theorem

What theorem? I have never heard of ‘the convergence theorem’.

0.424242… solved via the convergence theorem simply results in itself

What do you mean by ‘solving’ a real number?

0.999… does not again result in 0.999…, but results to 1

In what way does it not ‘result in 0.999…’ when 0.999… = 1?

You seem to not understand what decimals are, because while decimals (which are representations of real numbers) ‘0.999…’ and ‘1’ are different, they both refer to the same real number. We can use expressions ‘0.999…’ and ‘1’ interchangeably in the context of base 10. In other bases, we can easily also find similar pairs of digital representations that refer to the same numbers.

I meant what I said: “know patterns of repeating numbers after the decimal point.”

What we have after the decimal point are digits. OTOH, sure, we can treat them as numbers, but still, this is not a common terminology. Furthermore, ‘repeating number’ is not a term in any sort of commonly-used terminology in this context.

The actual term that you were looking for is ‘repeating decimal’.

Perhaps I should have also clarified known finite patterns to further emphasize the difference between rational and irrational numbers

No irrational number can be represented by a repeating decimal.

The explanation I’ve seen is that … is notation for something that can be otherwise represented as sums of infinite series

The ellipsis notation generally refers to repetition of a pattern. Either ad infinitum, or up to some terminus. In this case we have a non-terminating decimal.

In the case of 0.999…, it can be shown to converge toward 1

0.999… is a real number, and not any object that can be said to converge. It is exactly 1.

So there you go, nothing gained from that other than seeing that 0.999… is distinct from other known patterns of repeating numbers after the decimal point

In what way is it distinct?
And what is a ‘repeating number’? Did you mean ‘repeating decimal’?

The decimals ‘0.999…’ and ‘1’ refer to the real numbers that are equivalence classes of Cauchy sequences of rational numbers (0.9, 0.99, 0.999,…) and (1, 1, 1,…) with respect to the relation R: (aRb) <=> (lim(a_n-b_n) as n->inf, where a_n and b_n are the nth elements of sequences a and b, respectively).

For a = (1, 1, 1,…) and b = (0.9, 0.99, 0.999,…) we have lim(a_n-b_n) as n->inf = lim(1-sum(9/10^k) for k from 1 to n) as n->inf = lim(1/10^n) as n->inf = 0. That means that (1, 1, 1,…)R(0.9, 0.99, 0.999,…), i.e. that these sequences belong to the same equivalence class of Cauchy sequences of rational numbers with respect to R. In other words, the decimals ‘0.999…’ and ‘1’ refer to the same real number. QED.

Comrades, I urge you all to read at least a bit every day. Treat it as a work-out in a library. Go to bed every day a better version of yourselves than you did yesterday.

Good bot.

I ran $ curl -s "https://archlinux.org/mirrorlist/?country=FR&country=GB&protocol=https&use_mirror_status=on" | sed -e 's/^#Server/Server/' -e '/^#/d' | rankmirrors -n 5 -. Where should I see an option to update to KDE 6.1?

No? I just said that China’s trans policy is awful and backwards and my solidarity goes to those who suffer from it in China and that the US is better in that respect.

And I can just as easily point out that the US was much worse and more backwards not at all long ago. And the US has seemingly been experiencing much more of a backwards push than the PRC.

US imperialism is awful and the past half-century of exploitation and subjugation by the US is also terrible. One does not exclude the other

One of these things, however, is unambiguously much, much worse than the other.

On that front, I am indeed more aligned with the US than China, but it doesn’t mean I don’t also hate the US

Okay, can you explicitly come out and say that your positions overall are more aligned with those of the PRC than with those of the US?

Because I support trans rights?

The US kills trans people and other LGBT people in the third world. You seem to be more fine with that than with the PRC giving trans people a somewhat subpar package of rights.

I’m fundamentally, as an anarchist - not fine with the US or China. It’s in the name.

So, are you more fine with the rest of the world fighting for liberation from you, even if it is done using states (I’m going to note that anarchists have not had much success fighting for anybody’s liberation anywhere, to my knowledge - this is the best that people around the world have managed so far; I’m also going to note that anarchist organisation fundamentally sacrifices military capabilities, which are necessary in the world’s liberation from NATO), or are you going to engage in equivocation between NATO and its victims?

If it’s the former, then I take most of what I said back. If it’s the latter, my points stand, as equivocation between the perpetrators of colonialism, genocides, etc. and their victims is, in effect, support for the former.

See? I’m not some imperialist stooge or a jingoistic patriot and I’m happy to praise China where it’s due.

Alright, so can you come out and explicitly say that your positions are overall more aligned with the Global South than with NATO?

No. I’m by no means an expert, but there’s tons of resources online and offline that aren’t memes or the U.S. State Department. Even just reading the sources on Wikipedia isn’t usually a bad start

You mean the sources like Radio Free Asia? Lol.

No. If anything Anarchists are the leftists who actually do stuff like organize mutual aid networks or at the very least squat vacant properties of the rich

More than 100 years of activity, and all that western anarchists have managed to achieve is get supported by the FBI to disrupt socialist movements as part of COINTELPRO and to become a machine for regurgitation of USian anti-communist propaganda.

No. Where did I simp for any country here?

Here:

So the US is better off in that regard, I’d much rather live there and their government positions align more with my own and I’m anti-China and “anti-authoritarian” in that sense, but still a socialist.

You claim that the positions of the US government are more aligned with yours than the positions of a government that has not started any wars in more than 40 years, and which has been a victim of colonialism of NATO states (including Japan, which is de facto a NATO state), and which has been (one of, if not) the most successful state in the world in terms of improving the living standards of working-class people.

By your own admission, your positions are more similar to those of a state that has been the most prolific aggressor in the world for a century or so, which has been carrying out genocide after genocide, and which has also been engaging in colonialism, than to those of a state that has not started a war in more than 40 years, that has been at the forefront of production of green energy units, that has been the most successful at improving the living standards of working-class people in the world.

Either explain yourself, admit to having been wrong, or admit to being a supporter of genocides and colonialism.

No, again, where did I do that?

Have you changed your position on the PRC, then? Or do you want to both claim that you find the positions of your genocidal empire align more with your positions than those of the PRC, and that the PRC is not the absolute evil that your empire claims it to be?

Also, on this note, I’d like to ask if you support the states (and state-like polities) that have been victims of your empire’s colonialism in their struggle against your empire’s colonialism? This includes such boogeymen as the DPRK, Hamas, and, to a much lesser extent, Russia (where, again, NATO killed millions via shock therapy legislature which it took part in designing).

No. I decry authoritarian overreach wherever I see it, be it the US or China

Sure, you say that, but then you go ‘therefore, I support the US’, which you have already admitted to. Again, what you said is already saved, there is no use denying or hiding that.

Instead of liberation of the vast majority of the world from your yoke, you claim that third world countries are evil, authoritarian, and barbarous, and that, therefore, the victims of NATO colonialism should remain victims of NATO colonialism.

It’s extremely likely that out of the sides of the Korean war, you support the US and its colonial government set up in the parts of Korea occupied by it. You support the killing of millions of Koreans and flattening of their homes during that war. Because the exceedingly popular movement that arose from trade unions was ‘authoritarian’. You likely complain about the DPRK today as well, because the victims of your colonialism are ‘authoritarian’, while ignoring the conditions in which they have to exist (in particular, the threat of your empire which killed millions of them when it invaded last time and destroyed most of the country).
You likely also support the European colonial government of South Vietnam, and have an issue with the victims of your colonialism, again, being ‘authoritarian’, while ignoring the conditions in which they have to exist. You likely also support the blockade and the attempted invasion Cuba by your empire, because of Cuba being ‘authoritarian’, while ignoring both the fact that they have probably the most pro-LGBT legislature in the world right now, and while ignoring the conditions in which they have to exist. You likely also support NATO’s collaboration with Guomindang and the RoC, despite them enacting white terror in Taiwan, killing dissenters, and establishing a very authoritarian dictatorship in Taiwan. After all, you did say that you are more aligned with your empire under which that happened than with the state that the Guomindang fought against. You probably also support NATO’s invasions and the killing of millions in Iraq, as well as the invasion and two decades of active warfare in Afghanistan, because the states of those countries are ‘authoritarian’. After all, you are more aligned with the empire that did that than with the state that hasn’t started any wars in more than 40 years. You likely also support NATO transforming Libya from a country with the highest HDI in Africa into a haven for open-air slave markets. Because not allowing slavers a free reign is so ‘authoritarian’.

I’d be happy to be proven wrong about you supporting all of that, but then I’d like to ask you, in what way are you more aligned with your empire than with the PRC?

in context of LGBT issues, things are worse in China than the US, but the last century of US’ imperialist foreign policy where it imposed it’s will on the globe are all horrifically awful things too

You are saying this as if the issues with LGBT rights in the PRC are anywhere close to being as bad as what the US has done throughout its history (starting with the whole settler-colonialism stuff in the Americas as an organ of the British polities).

Again, either the positions of the US government are NOT aligned more with yours than those of the PRC, or you think that the US having a bit better situation with regards to LGBT rights for USians (for now, at least, considering that there is more of a push against LGBT rights in the US than in the PRC, as far as I can see) outweighs the fact that the US has been the most prolific killer and torturer of people around the globe, which includes LGBT people. And yes, this means that if the latter is the case, your positions are that killing LGBT people in the third world is fine so long as your empire gives you a bribe.

It’s like some folks just cannot comprehend that you don’t have to simp for any empires at all, and you can critique them all at once

Cool. But you go further. You equivocate victims of your empire’s colonialism with the perpetrators of said colonialism. Worse yet, there is at least one case where you have come out and said that your positions are more aligned with those of the perpetrators of colonialism rather than with those of the victims.

If you think that I don’t have criticism of states like the USSR or the PRC, then you are incorrect. I, however, do not think that my own well-being is something that is more valuable than the well-being of other people, and I also don’t make claims like ‘I support the most prolific genocidal force in the world more than a state that hasn’t started a war in more than 40 years and which has not perpetrated any genocides’.

No. In fact it is the exact opposite

So, either what you are saying now is true, or what you said before - about the positions of the US government being closer to yours - is true. Which is it?

I know trans folks, I understand our struggles here in the west and I do not think of trans folks in China as being some ‘other’ who must enjoy being under the boot of oppressive, backwards laws, I have nothing but solidarity and support for them in achieving liberation just as we aim for here

If you wanted solidarity with them, you wouldn’t be supporting the US government, which has been trying to induce economic crises in the PRC and which has been trying to spark a war with the PRC.

Furthermore, the US is the most prolific killer of LGBT people by virtue of just how many people it has been killing around the world. Do you think that the LGBT people of the world should enjoy being under the boot and bomb of the US?

I do not want to be presumptive, but frankly if anything this view that you have seems to be of someone who hasn’t traveled much, which is totally fine, neither have I really, it is a purposeful injustice that few people have the means to do so, but from my experiences traveling, people are people, and they are mostly the same everywhere, most working people want the same things and there is nothing wrong with being critical of the forces of capital or religion or governments that transcend borders and require international solidarity from us

I never had enough resources to travel much, but I did not need that to come to the very simple conclusion that people are people everywhere, especially considering that where I’m from is not an ethnically - or, for that matter, religiously - homogenous place.
If you actually want international solidarity, then you shouldn’t support what is literally the most prolific genocidal force in the world.

One doesn’t exclude the other

Also, you seem to not understand why you were told to focus on your country/state.

Supposedly, you know more about where you live than about countries where you never set foot in and which you are only informed about by memes and other forms of osmosis. This makes you more qualified to deal with the former than with the latter.

Supposedly, also, you have a greater ability to influence the situation in the country where you live than elsewhere (unless you join your military to invade other countries, in which case you are welcome to be rightfully punished for that).

Westerners who consider themselves to be ‘anarchists’ sure do tend to ignore all that and simp for their genocidal states while regurgitating said states’ propaganda about how evil and barbarous all of those countries that are outside of the imperial core are.
Your beliefs are neither anti-authoritarian, nor are they rooted in international camaraderie and recognition of people from other countries as fellow human beings.

I think just because I critique an empire you like from an anarchist perspective doesn’t make me an imperialist, but we can agree to disagree I suppose.

Lol. You literally think that not starting any wars in general for more than 40 years is just as bad as constantly invading the rest of the world and killing and torturing non-white people - including LGBT people.

Hell, you have come out and said that you are more aligned with the latter than with the former, so yes, it’s safe to say that you are an imperialism supporter. Your ‘anarchist perspective’ is just ‘it’s good that my state kills millions abroad for my benefit’.

One doesn’t exclude the other. I’m not sitting about foaming at the mouth about China all day

You have already said that you are more fine with a regime that can’t exist for one second without invading somewhere and committing genocides than with a state that has provably made massive improvements in the lives of working-class people, has been at the forefront of switching the world’s energy to green, which hasn’t committed any genocides, and which hasn’t started any wars in more than 40 years.

On the grounds I get to benefit?

You quite literally are saying that because you would personally benefit from the empire that has been committing genocide after genocide throughout its history and which has been the most prolific aggressor in the world for a while, you choose to be more aligned with it instead of with the rest of the world. You choose for your position to be an oppressor-nationalist one and anti-internationalist.

Going to quote the relevant line lest you decide to hide it later:

So the US is better off in that regard, I’d much rather live there and their government positions align more with my own and I’m anti-China and “anti-authoritarian” in that sense, but still a socialist

So are you implying that the relative freedom for queer folk in the US is a direct product of imperialist foreign policy

No, it’s a consequence of LGBT community fighting for its rights, and not a consequence of your empire voluntarily giving LGBT people their rights.

Also, it wasn’t too long ago when your empire was more hostile to LGBT people than the PRC is today, or other non-Imperial core states of the past. You seem to assume that it is impossible for relevant things to change.

In any case, you are a chauvinist. You will find another reason to support your empire’s genocides. If it’s not LGBT rights, it would somehow be women’s rights. If not that, it would be some vague ‘human rights’. If not those, it would be no less vague ‘freedom’ in general and ‘freedom of speech’ in specific. Those are all just excuses.

You literally support genocides of non-white people and killing and torture of LGBT people across the world on the basis that you, personally, get to benefit from your empire.

So, let me get this straight, you think that not participating in warfare for more than 40 years is just as bad as constantly invading the rest of the world, committing genocides, torture, etc. in the name of colonialism on the grounds that you get to benefit from the latter regime? And you want to be taken seriously?

Yeah, seems like you are just simping for the empire that kills and tortures non-white people en masse because you are, personally, a beneficiary of said killings and torture.

Yeah, I was trying to do stuff like sudo install. I was not aware that it is used in combination with other commands like that.

I was wondering what I was doing wrong with sudo.

Try Settings > Window Management > Desktop Effects > “Windows Management” section > Overview and configure it

The problem is that there is no such option there, which is why I’m asking.

It seems that I need to install kdeplasma-addons. I will need to look into how people usually use pacman, as it keeps asking me to login as root.