Tomorrow_Farewell [any, they/them]

I think we have different definitions of what passing knowledge, and familiarity.

The examples of math knowledge that I provided are taught in the first semester/first couple of semesters of university, and are covered in introductions to calculus. It is ‘passing knowledge’.

I think what OP is saying is that folks should leave college knowing how to think and reason mathmatically, philosophically, and scientifically.

Sure, but how would being able to think and reason ‘philosophically’ (whatever that means) would help, for example, a mathematician, a software developer, or an electronics engineer?
And, again, how would the sort of knowledge that I mentioned be helpful to an average historian?

Also, how much of a STEM curriculum would you be willing to replace with humanities and art courses?

Everyone knows you don’t actually learn anything in undergrad

Huh? What? No.
I learned quite a bit at that time in university. This claim is honestly baffling.

OP is just saying that maybe that problem solving should cast a wider net, I think.

What professional problems would humanities courses help STEM specialists solve?

Even a pure mathematician needs to know how to communicate their ideas within their field.

How, and which humanities disciplines would help with that better than practice with communication in the context of engaging in that field which already does train those skills?
It has also been my experience that humanities and art specialists do not communicate better than STEM specialists. Quite the opposite, actually.

EDIT: Also, do you think that the current state of communication in STEM fields in general, and in mathematics environments in particular, is somehow lacking?

I feel like you are mistaking the forest for the trees.

I am not sure what you mean by this.

My point isn’t that by introducing humanities as mandatory, we will somehow magically transform our society into a utopia.

Sure. But you seem to be assuming at least one of the following:

• Forcing STEM students to take humanities exams will make them better at evaluating social utility of their professional decisions.
• Forcing STEM students to take humanities exams will make them evaluate social utility of their professional decisions.
• Forcing STEM students to take humanities exams will make them use the aforementioned evaluation in a way that would improve social utility, compared to how things are now.
• Forcing STEM students to take humanities exams will increase the frequency with which they can make the aforementioned evaluations, even as junior professionals.
• STEM students are not forced to take humanities exams enough.

That is quite a few assumptions, and, considering that humanities (and art) specialists do not seem to be significantly less ghoulish than STEM specialists, I do not think that any of them have a good basis.

Also, how much of STEM curricula do you want to replace with humanities courses? Just one semester of a bunch of disparate disciplines is not going to give them any useful skills, so the courses have to be more thorough, and the students will come out knowing less about STEM fields that they come to study.

My hope is basically just that it might change things for the better a little. Just because people are generally terrible doesn’t mean we cannot work for making them better even if it is just a little bit.

Sure, but how would that improve things? What are the expected mechanisms that would cause things to change for the better? Humanities (and art) do not seem to make people significantly less supportive of things like genocides, colonialism, and capitalism.
What seems to be a better alternative is not forcing humanities and art courses on STEM students, but attempting to instill them with relevant worldviews - ones which oppose the likes of the aforementioned atrocities.

I believe that by educating them we might hope that at least a few might make better choices or not.

Humanities education doesn’t make humanities specialists not be awful. Why assume that teaching less of it to STEM students - at the expense of the knowledge about their fields of specialty - would make them either do more of social utility evaluation, or do that evaluation better, or use that evaluation more frequently and for the common good?

There are many approaches for a business to be both good and also make profit

That’s literally not possible. Making profit means that a business is robbing the rest of society, including its workers.
The presence of the profit motive in an economy has a bunch of other consequences, including things, like the lack of guaranteed housing, which is also ghoulish.

Just as an example, in the periods of comfort, they can focus only on profit. However, in the times of crisis, businesses can instead focus on doing social good

That’s literally not possible. The owners of a business are systemically only interested in a business so long as it provides them with net wealth over their investments, which requires a business to be profitable.
There is no systemic interest for these owners to literally do something antithetical to maintaining their businesses and sacrifice profits for the common good. The only reason for them to do that would be if they were forced to. However, that would require another sufficiently powerful party to be interested in doing so.

but thing is many small businesses around the world

Small businesses also have additional issues that prevent them from actually being net good for society, like the fact that they are less efficient and less technologically innovative.

I am really sorry if you don’t enjoy exams, because I also hate exams.

I do not hate exams. Exams are necessary.
The question is, what humanities and/or art disciplines would you force somebody who chose a STEM specialisation to take exams in to be allowed to graduate, and why?

first I just want to focus on the question what is the purpose of education.

The purpose of education from the standpoint of a state or another sort of group is to reliably produce people capable of some specialised labour (and - usually - to instill them with a worldview that would make them more loyal to said group). Considering that it is states that organise serious education, that’s the only ‘purpose’ that matters.
I hope we are not going to conflate ‘purpose of smth’ with ‘reasons to appreciate smth’. I appreciate education quite a bit, and study almost every day.

I strongly believe that the education helps us to be a better human being

I apologise, but this is rather wishy-washy.
What does ‘a better human being’ even mean? Why would that be in any way important for the people that you decide to force this opportunity to fail to graduate? Why would that be important for a given group that organises a given education effort? Why would that be important to the rest of a relevant society?

Despite the ‘STEMlord’ stereotype of engineers, software developers, and people who do the ‘hard’ science-related stuff being horrible people, I do not think that humanities and art specialists are better. There is a lot of extremely heinous stuff that they say and that gets promoted a lot, including in education. So, I would not really say that humanities would help make a person ‘better’ in any sense that I would recognise as such.

beyond just being a better doctor or a better software developer or a better engineer.

Well, what I wanted from education is to be a better software developer and mathematician. So, if we are to consider my case, I neither wanted nor needed to be better at recognising that most people have no understanding of what idealism is, for example, and to have my degree hinge on taking a philosophy exam where the teacher couldn’t even give any workable definitions. That stuff is completely useless for me in both my personal life, and my professional activities, and has also contributed to me being less able to fit in - including on these very forums, - I would argue.

So, as it happens, the oppressors might establish a monopoly over the fresh water that reaches the village due to aforementioned project. So, despite the project providing some benefit, to the oppressors, it provides almost no benefit to the oppressed class. No engineer would consider these kinds of societal issues while designing the project, despite knowing about the casteism and understanding it’s consequences because they are not educated to combine their engineering skills and know-how with the casteism.

I don’t see how a humanities education would help here, especially in the case of low-level junior engineers (as opposed to senior and leading engineers). What actionable insight could be provided, by what humanities discipline(s), and how much of an engineering curriculum should be sacrificed for teaching those skills? Most importantly, why would engineers opt to use this insight for common good even if they reach it?
From what I can see, if the humanities courses are short, the engineers will not get much in terms of reliable knowledge that isn’t already covered through cultural osmosis. If the courses are long, it means that they get taught significantly less about engineering.

These projects should not just have economic utility, but also social utility or at least should not have negative social utility.

Okay, but that’s not for a low-level engineer or developer to make any relevant decisions about, and a humanities education doesn’t mean that a person would be any more inclined to implement the solutions that have more social utility.

Consider the impact of plastics, fossil fuel and their pollution on the society and individuals. However, for decades, we gladly kept building new roads to accommodate more vehicles purchased by rich people, despite knowing about them.

Okay, but how would a more humanities-focused education of engineers/scientists/etc. improve things in this case? Do you have any evidence for relevant claims?

My hope is that with a humanities education, it will make more engineers to evaluate the social utility of their projects and not just the economic utility.

What would force or make them more inclined to evaluate the social utility in these cases? And what about the engineers/developers/etc. who do not get to make any relevant decisions? And how would humanities disciplines help in making these evaluations?
Also, it doesn’t actually require one to be educated in things like ‘is this ethics system an emotivist one?’ and ‘which of these legal documents has a higher priority?’ in order to want to improve people’s lives, nor does being educated in them make a person not a ghoul.

Considering that humanities specialists - just like STEM specialists - are usually either horrible judges of social utility, or are just outright ghoulish, I don’t really see why one would think that humanities disciplines would change anything relevant.

One interesting theory that I came across was in a book called “Development As Freedom” by Amartya Sen, a Noble Prize winning economist. In the book, he puts forward the idea that “Economic Development must increase the freedoms of individuals and society”. In essence, contrary to popular measures of economic development like GDP, Per Capita Income, he straight-up wants to quantify (or at least qualitatively) the impact of economic and market activity through their social utility.

Is it an actual theory, or just some platitudes about wanting to study those things? Because if it’s the latter, then I fail to see the novelty, as many people have studied relevant things before him.

In essence, all human activity has the goal to serve the humans (both individual and society), this world and the nature we live in.

That is quite obviously not true. People very obviously do, in fact, do things with selfish goals. For example, business owners implementing solutions to profit at the expense of the rest of society, or NATO leaders maintaining a brutal colonial hold over the world.
No amount of humanities education is going to change what a person’s social and economical interests will be, which are the primary factors in people’s behaviour on a systemic level, I would argue.

It irks me to no end when STEM majors can’t write, communicate,

I do have to say that humanities majors do not seem to be any better. Ask most of them to provide definitions that they use, or to communicate how they arrive at their conclusions, and quite often they will be unable to do either.

but an expert engineer should have a passing familiarity with philosophy and ethics

Why? In particular, why should an engineer have an understanding of how to study systems of ethics, and what first- and second-order ethics frameworks there are?

just as a historian should have a passing familiarity with scientific laws and mathematics.

As a mathematician by education, I would also like to ask, why? What would an average historian gain from knowing that a continuous image of a compact is a compact, or that, if a diffeomorphism’s rank is less than the maximum possible one, we can construct a diffeomorphism of the same degree of continuity that works with fewer coordinates in either the domain, the codomain, or both?

Businesses would not be terrible if business education is actually tempered with some humanities.

That’s obviously not true. For businesses to not be terrible, they would have to not operate on the profit motive, which is impossible.

In fact, I am strongly of the opinion that every field of study should have some humanities component to them.

Why? And what disciplines do you want to force people to pass exams in, even if they have no bearing on a person’s skills in the area that they actually chose?

we have to have at least, some appreciation of other fields

Also, why?

Anecdotally, my engagement with philosophy resources, philosophers, and philosophy enthusiasts hasn’t been supportive of this claim.

In particular, I have found them both incurious about math/logic (outside of specifically the parts labelled ‘logic’ as far as they relate to rhetoric) and their verbal skills to be lacking (more specifically, their inability/unwillingness to define their terms).

Going to again note that so long as you do not produce an explanation for what Russia should have done, your claims have no basis.
Considering that you have been unable to do so, we can conclude that you do not have any actual problems with relevant actions taken by Russia.
This is further supported by the fact that you have been caught either lying or being confidently wrong basically every time you tried to assert anything.

How long has Putin been in power now?

For about as long as Merkel was in power in Germany which you are completely fine with.

Going to note that this question isn’t relevant here, especially considering that you obviously do not judge Russia by the same standards that you apply to Ukraine and the rest of NATO.

Not Cowbee, but I want to push back on some more of your what you are trying to imply.

Why do you believe that is an excuse for war

The rest of the world has every right to defend itself against NATO, including when NATO tries to put troops and weapons near highly populated non-NATO-controlled areas, especially when NATO conducts terror attacks.

but Russian interference in the Ukrainian state (to the point that their president was a Russian puppet), was acceptable?

Firstly, what is your evidence for this Russian interference to the point that the president was a Russian puppet?
Secondly, this is at the very least less bad than NATO’s interference and subjugation of Ukraine at least on the basis of NATO being by far the most evil polity in the world, complete with conduction of at least one current genocide. (EDIT: And you are yet to present an alternative course of action for Russia, despite being repeatedly prompted to, and despite the fact that your claims have no basis if there wasn’t any other serious option for Russia.)

Going to note that you didn’t dispute anything of what I brought up (and you did not even acknowledge the fact that you have been supporting Ukraine invading Iraq), but just decided to make a personal attack against me. This is despite you being shown to not have a good understanding of history and of current events that you speak confidently about.

Tankies gonna tank.

People who literally support their tanks crushing independence of countries in Africa, Asia, and the Americas sure do love to say that to people who oppose colonialism and nazis, as if that is somehow bad. All while not being able to refute any of the ‘tankies’ claims. The word ‘tankie’ just means ‘a person who is correct’.

Going to briefly elaborate on the USSR, though: off the top of my head, the USSR not only successfully resisted the Lebensraum and put an end to the Holocaust, it also aided the liberation movements in Korea, Vietnam, Cuba, Mozambique, Angola, Afghanistan, etc., and the USSR improved lives domestically with things like guaranteed housing, guaranteed access to education and elimination of illiteracy, guaranteed access to healthcare, world’s first achievements in the sort of women’s rights that we take for granted today, 60% increase to life expectancy (relative to the pre-WW1 statistics) in the first 30 years of its existence, elimination of famines that were common in the Russian Empire, and so on.

You don’t really have an argument for why the USSR was supposedly bad, and it’s time to admit that to yourself.

Going to note right away that you are yet to explain what Russia should have done according to you.

Also, going to again note the fact that you are weirdly concerned for the success of a literal nazi government that has banned opposition and does not hold elections (while talking about how democratic the relevant astroturfed movement was) and which wants to plunder the rest of the world together with the rest of NATO, than you are for the right of the rest of the world to defend itself against said plundering. You have even implied that Syria should not have defended itself against you, to boot.

There needs to be evidence of NATO aggression against Russia for me to actually try to defend it

NATO did a coup in Ukraine (not sure how you are going to deny this, as there is already evidence of the US picking and choosing who will get what position in the post-coup government, as well as bragging about spending billions on subjugating Ukraine), then the puppet regime in Ukraine attempted to bring NATO troops and weapons near the border with Russia’s most populated areas.
When the most prolific invader in the world does that, that is an obvious act of aggression, especially when they also engage in terror attacks.

There is also the fact that NATO is, as I keep mentioning, the most prolific invader in the world that is engaging in at least one high-profile genocide and must be fought against (unless you also think that Germany and the rest of the Axis should have been allowed to complete the Holocaust and the Lebensraum and to not answer for their other acts of colonialism).

So you believe western volunteers are mercenaries?

You can call the SS auxiliary troops whatever you want.

What would you call Russian prison battalions, kidnapped indian students and north Korean regulars?

Not sure how the former are relevant, not sure why the latter are an issue, considering that they are not mercenaries and that they are/were on the right side of this conflict.
Source your claim about the ‘kidnapped Indian students’ somehow being involved.

Do you know how tiny 100km² is in comparison to the entire of Ukraine?

Hahaha.
So, let’s get this straight - you think that states engage in warfare until they lose all territory?
This argument is especially silly, considering that Kursk oblast is much smaller than 100 km^2, and is a much, much smaller part of Russia than 100 km^2 area is a part of Ukraine. And yet, you brought up Kursk as some sort of an argument for Russia losing.

The reality of the war is a sparsely guarded Frontline across hundred of kms of empty land that frequently changes hands.

Sure, if by ‘frequently changes hands’ you mean ‘Ukraine is losing this territory and fails to retake it’.

Ukraine also still holds land in Kursk according to current osint.

5 m^2 of land? Haha.

When do you think Ukraine invaded Iraq?

In the 2000s. The Ukrainian troops were officially congratulated by the US.

You mean the Soviet union controlled my Moscow?

Haha.
At least study a little bit about this topic.
You probably also think that the most successful anti-colonial force that massively improved people’s lives not only domestically but also abroad by aiding liberation movements (in their fight against you) was somehow bad.

I think NATO sucks, but I also think Russia does. The only thing I care about in this situation is Ukrainian autonomy.

Notably, you seem fine with Ukraine invading Iraq and Syria.
Also notably, you do not seem to care about Russia’s autonomy, Syria’s autonomy, Iraq’s autonomy, etc.

If you believe Ukraine has a right to self defense and self determination then we’re in agreement.

Do Iraq, Iran, Russia, Syria (before your invasion), Palestine, Libya (before your invasion), Afghanistan, non-occupied Korea, etc. have a right to self-defense and self-determination?

Right away going to note that you are yet to explain what Russia should have done about NATO’s aggression.

Russia has completely failed it’s “special military operation” in Ukraine

Not sure how this would be relevant even if it wasn’t fiction.

NATO countries are supplying a trickle of arms to Ukraine, but without a single NATO boot on the ground

Again, you should stop making claims without bothering to double-check them. You are woefully underequipped to make assumptions here.
Non-Ukrainian NATO troops have been involved, both in the form of mercenaries and de jure NATO military personnel, with some of the weapons that Ukraine has been using requiring the participation of NATO troops.

Russia has been stopped in its tracks

Not sure why you think that this is in any way relevant, but Russia has literally been winning more and more ground, with a very recent takeover of estimated more than 100 km^2 within 24 hours.

having even lost actual Russian territory to Ukrainian counter offensives

Your sources are outdated. Kursk has been liberated.
Either way, this shows that Russia’s concerns about NATO are not unfounded, so you are now just contradicting your earlier implied claims that Russia should have just ignored NATO’s activities.

Clearly Russia would not stand a chance if NATO decided to invade them

This is basically an original German nazi talking point about Slavs being subhuman and standing no chance against Germany for some reason.

Either way, you are now claiming that Russia is right to be concerned about NATO’s aggression, and that every polity that tries to join NATO should be fought against like the enemies of humanity that they are.

So that begs the question, if you believe NATO wants to invade Russia, and it’s clear Russia couldn’t stop them, why haven’t they?

Again, you are quite literally working off of wrong assumptions that nobody who has been following the conflict holds.

Right. I agree that NATO tacitly supports US imperialism

Not ‘tacitly’, and not just the US’ imperialism.
You are blatantly trying to absolve the glorified USian provinces of imperialism and colonialism by downplaying their complicity and willingness in subjecting the world to these horrors.

but you’re also conflating the actions of the US with NATO as a whole.

You are, again, trying to downplay the actions of the US’ glorified provinces that is the rest of NATO, and distance them from their own actions.

Turkey did not invade Afghanistan for example.

Turkey did invade Afghanistan. And other places, together with the rest of NATO.

Also the idea that NATO caused the Bosnian Genocide is laughable.

Given that you keep being demonstrated to be wrong about everything, you should stop laughing about things that people who are consistently correct tell you.

NATO did not attack Russia.

The most prolific invader in the world that is engaging in at least one obvious and high-profile genocide doing a coup in a country that neighbours another country’s most populated areas and then attempting to bring weapons and personnel to the relevant border is, in fact, an act of aggression, and the rest of the world has every right to defend itself against NATO.

Russia invaded Ukraine.

As a response to NATO’s aggression.

Notably, you are yet to explain what Russia should have done, despite you being prompted to.

Do Ukrainians have a right to defend themselves from Russian imperial aggression?

Did Germans have a right to defend themselves from the Allies’ ‘imperial aggression’ in 1930-1940s?
Also, going to note that you are completely fine with terror attacks conducted by your empire, including against the Russian population which you deny any right to defend itself against you.
The rest of the world has a right to defend itself against NATO. The population of the most prolific invader in the world that is currently engaging in at least one high-profile genocide is not the priority in this situation (unless, again, you think that the rest of the world should roll over for you).

EDIT: People should stop claiming that the gang of states that are currently engaging in at least one genocide, keep invading everywhere, doing coups is a ‘defensive alliance’.

You mean when the largest european democratic movement in decades ousted a Russian puppet

This is silly.
That’s quite a fantasy you have concocted there.

Firstly, just describing any pro-NATO movement, i.e. a movement that supports literal colonialism, as ‘democratic’ is extremely silly. Especially when such movements are known to be created by NATO and include literal politicians and open nazis. Going to also note that you are fine with the perpetual dictator Zelenskiy.
Secondly, everybody is familiar with things like the leaked correspondence between USian representatives in Ukraine picking who gets to be in what position in the new government weeks before the completion of the coup, as well as them bragging about how much money they spent on subjugating Ukraine.
Thirdly, you can’t even name what was supposedly so bad about Yanukovich. It’s pretty obvious that his sin - in your eyes - was that he did not sell Ukraine off to NATO.

who refused to pass a bill ratified by the Ukrainian Parliament?

Oh no. An elected president vetoed a bill that was being protested against by the same people that you love being in power.
Mind sharing why an elected president vetoing a bill justifies NATO completing yet another coup? Sounds like your standards are very much not applied uniformly.

This never happened.

This is, again, silly.
Do you want to tell us that Ukraine was not trying to join NATO in the years 2014-2022, and that no relevant claims were made by NATO?

NATO is a defensive alliance.

This is also very very silly.
Nobody can seriously claim that invasions of Iraq, Iran, Afghanistan, Syria, Palestine (complete with a very obvious genocide), Libya, Vietnam, Laos, Korea, etc. - all done by NATO - were ‘defensive’.
The only ‘defensive’ thing about NATO is how it protects its members from facing justice for centuries of ongoing colonialism, including for settler-colonial and other genocides.

The closest it’s ever gotten to starting a war was Afghanistan and not every member participated.

Between Iraq and Afghanistan, there is not a single de jure member of NATO that did not participate. And those were very obviously wars started by NATO, with NATO invading those countries.
There is also the fact that not every glorified USian province sending troops neither makes those non-NATO actions, nor negates other forms of complicity in the activities.

And before you wind up the next “gotcha”, there are lots of dog shit imperialist countries in NATO, but we’re discussing the organization itself here.

If every member of this organisation is a ‘dog-shit imperialist state’ - and they all are, - then we can conclude that there is no defense that can be levied for the organisation itself that is the most prolific invader in the world and that is currently engaging in at least one high-profile genocide.

Georgia, Chechnya, Syria, Afghanistan?

This is also silly.
Russia did not invade Afghanistan and Syria. Russia literally helped Syria against your invasion forces and DAESH (which has since become yet another de facto part of NATO, if it ever wasn’t).
Russia fought against the separatist in Chechnya with NATO’s support. The part of the Russian government that supported the separation of Chechnya were shelled with tanks by pro-NATO forces.
Georgia was literally the one that attacked the Ossetian separatists. This is doubly silly, considering that you support Chechen separatists.

And also this is your moral foundation? It doesn’t matter what crimes Russia is committing so long as they never commit more crimes than the US?

Again, the rest of the world has every right to defend itself from NATO. Look at what you did to Iraq, Syria, Libya, Afghanistan, Palestine. On what grounds should the rest of the world just roll over for you?

Russia is literally conducting an imperialist invasion of Ukraine right now…

The most prolific invader in the world - NATO - did a coup in Ukraine, tried to bring weapons and personnel to Russia’s most important border near Russia’s most populated parts, and has been conducting terror attacks against the Russian population.
The rest of the world has every right to defend against NATO, so you either have a good explanation for what else Russia could have done in this regard, or your criticism of Russia is not serious.

Just because Russia “opposes” the west doesn’t make it any better than them.

The fact that Russia hasn’t done anything nearly as bad as things like the invasion of Iraq - let alone the genocide of Palestine - does make Russia better.

Pretty sure that not all NSFW subreddits are focused on images and/or videos,in which case this suggestion does not seem to work.

I would definitely start by sending every NATO leader, every NATO military person, and every unrepentant former NATO military person into the Sun.

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.