https://www2.kenyon.edu/Depts/Math/Paquin/GeomSeriesCalcB.pdf

Here’s a standard introduction to the concept of the Convergence/Divergence Theorem of Geometric Series, starts on page 2.

Its quite common for this to be referred to as the convergence test or rule or theorem by teachers and TA’s.

In my personal experience, basically no insurance in America is worth anything.

Nothing you would actually need insurance to cover ends up being covered, or, it covers a huge portion of an absurd cost which is only so absurd because of basically a corrupt cost inflation feedback loop between insurers and providers that you end up personally paying prices that are absurd to all but the very well off.

It ends up just being further cost requirements to basically exist, which means if you are poor fuck you, die.

Oh you want to challenge your insurance and force them to actually cover something?

Hire a lawyer! Those are cheap!

The ellipsis notation generally refers to repetition of a pattern.

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

This technicality is often brushed over or over simplified by math teachers and courses until or unless you take some more advanced courses.

Context matters, here’s an example:

Generally, pdf denotes the file format specific to adobe reader, while in the context of many modern online videos/discussions, it has become a colloquialism to be able to discuss (accused or confirmed) pedophiles and be able to avoid censorship or demonetization.

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

Ok. Never said 0.999… is not a real number. Yep, it is exactly 1 because solving the equation it truly represents, a geometric series, results in 1. This solution is obtained using what is called the convergence theorem or rule, as I outlined.

In what way is it distinct?

0.424242… solved via the convergence theorem simply results in itself, as represented in mathematical nomenclature.

0.999… does not again result in 0.999…, but results to 1, a notably different representation that causes the entire discussion in this thread.

And what is a ‘repeating number’? Did you mean ‘repeating decimal’?

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

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

Climate change fueled wildfires cause home and rental insurance rates to surge; State Farm solvency in question.

There! Fixed the headline. Journalism is so hard!

Pack 100 of compsognathus (compsognathii?) says hello.

Not sure how out of date the research is, but in the original Jurassic Park book, there are roaming packs of these things that overwhelm and kill people.

Though the on screen scene of them killing people happens in the second movie, it actually takes place in the first book IIRC… anyway, they’re basically depicted as land piranhas.

(Again, IIRC, Jurassic Park the book basically gets set in motion with a family of tourists being eviscerated by a pack of compys… but the first movie dropped this from the story, then when the second movie comes out they basically use this scene as the intro for that, but its on a different island and used to set off an entirely new story?)

There are a lot of concepts in mathematics which do not have good real world analogues.

i, the _imaginary number_for figuring out roots, as one example.

I am fairly certain you cannot actually do the mathematics to predict or approximate the size of an atom or subatomic particle without using complex algebra involving i.

It’s been a while since I watched the entire series Leonard Susskind has up on youtube explaining the basics of the actual math for quantum mechanics, but yeah I am fairly sure it involves complex numbers.

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

In the case of 0.999…, it can be shown to converge toward 1 with the convergence rule for geometric series.

If |r| < 1, then:

ar + ar² + ar³ + … = ar / (1 - r)

Thus:

0.999… = 9(1/10) + 9(1/10)² + 9(1/10)³ + …

= 9(1/10) / (1 - 1/10)

= (9/10) / (9/10)

= 1

Just for fun, let’s try 0.424242…

0.424242… = 42(1/100) + 42(1/100)² + 42(1/100)³

= 42(1/100) / (1 - 1/100)

= (42/100) / (99/100)

= 42/99

= 0.424242…

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.

I used to have a Prius C, got it used.

95% of shops wouldn’t touch it for anything non cosmetic. Hybrid, confusing, scary!

Learned how to work on it myself, before it got stolen.

Guess I just got the beta version of not being able to have your car serviced, due to good old fashioned blue collar laziness and incompetence.

The individual desires judgement. Without that desire, the cohesion of groups is impossible, and so is civilization.

Yeah, its infuriating that punk has become a suffix.

There is nothing punk about steampunk, dieselpunk, atompunk. They are just fantasy technological scenarios / art styles.

Cyberpunk has an both a recognizable aesthetic and a whole lot of political, social and philosophical views baked into it. You get the punks in cyberpunk as either a direct ideological opposition to the power of corporations, or as an indirect result of said corpos creating a hell world for 99% of people.

There is nothing inherently rebellious about worlds or characters within worlds with more prevalent / advanced steam or diesel or nuclear power.

Solarpunk arguably has some actual punk to it if you actually try to follow the idea of personally minimizing your fossil fuel usage, but mostly its a utopian or post-dystopian setting / art style.

Its now like -gate being affixed to any kind of publicized controversy.

Most people do not understand what Watergate even was and why it was so significant.

Yep, thats my impression as well so far.

Trump is confidently blazing through (what should be) obvious lies, while Biden is mumbling and forgetting what he is trying to say half way through saying it.

I’m from the wet side of the PNW and we have all of those as well, excepting possibly northern widows, I’ve not heard of those.

I’ve spent weeks in cabins and lived in houses and apartments all over WA.

Every single time I have ever seen a spider in a house or apartment, its been something that is totally harmless to humans.

Out in the boonies? Sure, thats where you’ll actually run into some dangerous things.

That being said, I’ve never lived in MN, perhaps dangerous spiders are a more serious threat in urban/suburban areas, and yeah, climate change fucks up everything.

Something absolutely absurd started happening a few years ago, right in the middle of Seattle, like 2 blocks from a main road:

Coyotes.

I’ve seen coyotes out in the foothills occasionally, on trails far from cities, in the brush on the east side of the state.

But… basically that heat wave a few years back, and wildfires and droughts managed to drive a population of coyotes into residential areas of Seattle, likely hunting the rabbits.

That was pretty stunning to me.

RIP sandy buddy.

Unless I am mistaken, aren’t basically every kind of Tarantula you can keep as a pet non venomous?

I’m the kind of person that’ll take basically any kind of spider save a black widow and just put it outside while my gf is screaming at 115db to murder it and will then be angry with me for 3 days that I didn’t.

Poor tarantula.

Oh right, this ‘politician’ is an amazing argument for lowering housing costs such that people can afford studios instead of living with crazy ‘main character’ people like this.

Nah, it was my handwriting, used the same lingo and joke I remember using at the time, took up most of the board… which is why I was so shocked it hadn’t been erased.

Most of the time people wrote on it, they were gracious with the space.

Due to typing far more often than writing, and many years later me figuring out oh haha I’m actually naturally left handed, my writing is a fairly uncommon kind of small cap block print, otherwise I am basically the only one capable of reading my non block print scribbles.

I recently returned to a hole in the wall restaurant that I used to frequent in my college days. One of the few actual restaurants in the city that never closed.

A decade later, a semi nonsensical scrawl about being kind and good to people I’d written on a dry erase board while quite drunk… was still there.

It only needed minor updating to be more gender inclusive, which someone else had done without removing any of my writing.

When I was frequenting this restaurant, the whole board was wiped every week or so.

For some reason, what I wrote persisted for a decade.

I couldn’t believe it.

I thought Paulogia’s minimum witnesses argument is basically that Paul could have hallucinated, and that those who witnessed an empty tomb basically did see an empty tomb, but circumstantial confusion led them to misinterpret what they saw?

I’ll have to rewatch some of his vids.

Also, hey, Goju Ryu! I trained in Shito Ryu =D

All things are possible through Christ lol

Well dang, I have never heard of that!

I’ll have to see if anywhere around me carries it

Its generally more up to date with newer standards and such than Debian, but it is by no means bleeding edge.

Bleeding edge is generally bad unless you really need some specific thing for a specific reason.

If your whole set up is bleeding edge then congrats, you are a basically alpha testing an OS.