I don’t think this is a topic where joking around is appreciated. Thousands of people have died on both sides of the war.

If you’re wondering how you get the proof for finding Sn, that’s something that I think is very difficult to cover in a small internet comment. You really need some good pencil and paper to illustrate how it works.

But in a nutshell, you can list down all the terms:

Sn = a, ar, ar^2, … , ar^(n-2), ar^(n-1)

Then, you write down rSn (common ratio multiplied by Sn), so you get:

rSn = ar, ar^2, a^3, … , ar^(n-1), ar^n

Then you subtract rSn from Sn, and you can see that a lot of it cancels out [ ar, ar^2, … , ar^(n-1) ]

It’s a little hard to show in text form, but it makes more sense once you write it down. This leaves you with this:

Sn - rSn = a - ar^n

Sn(1 - r) = a(1 - r^n)

Then you divide by (1 - r) to get a simplified expression for Sn!

Sn = a(1 - r^n) / (1 - r)

And for the other equation (where absolute value of r > 1), you instead subtract Sn from rSn, then divide by (r - 1) instead of (1 - r). It’s the same logic though.

This, however, does not work if the absolute value of r is greater than or equal to one. The sum of all terms for such a geometric sequence would not be finite. (think 2 + 4 + 8 + …, the total sum is infinite as r = 2)

And for an infinite series where | r | < 1 (absolute value of r is less than one), you can get a finite value. But how can this be? Let’s look back at this equation.

Sn = a(1 - r^n) / (1 - r)

When n tends towards infinity, it becomes very big. And since r is very small, r^n tends towards zero. You can try it out for yourself, typing a positive number less than 1 to the power of a really big number nets you a very very small number. As n becomes closer to infinity, r^n becomes closer to 0. So we can substitute r^n with zero like this:

Sn = a(1 - 0) / (1 - r)

= a / (1 - r)

And since this both a, the first term, and r, the common ratio, is finite, Sn must also be finite! And to go back to Zeno’s paradox. Let’s say a = 1 and r = 1/2. This means:

Sn = 1 / (1 - r)

= 1 / (1 - 0.5)

= 1 / 0.5

= 2

You find that Sn is the finite value 2. Maths is cool!

Trying to do a math proof in a comment is hard, but I’ll try my best:

A term in a geometric series is defined as: u =ar^n-1

where a is the first term and r is the common ratio (the multiplier you use to get the next term)

so the sequence is a, ar, ar^2, … , ar^(n-1) where n is the number of terms in the sequence.

The sum of all the terms in a sequence, the geometric series, can be found using this for (absolute) values of r that are below 1:

Sn = a(1 - r^n) / (1 - r)

for (absolute) values of r above 1, it looks like this:

Sn = a(r^n - 1) / (r - 1)

But both equations will work with any value of r, they are just rearranged to make the maths easier. Where n is the number of terms in the series. For example, the series 2, 4, 8, 16 has four terms, the common ratio of 2 and a first term of 2. This means:

Sn = 2(2^4 - 1) / (2 - 1)

= 2(16 - 1) / 1

= 2 * 15

= 30

And if you check 2 + 4 + 8 + 16, you will find that it correctly equals 30, meaning the maths is right! In this case, it would be easier to add them up individually, but using the formula is useful when you have a large series with many different terms or when you have limited information (i.e. you are not given every individual term)

Well, this Zeno guy was an ancient philosopher who existed long long ago.

A “series” is the summation of all the terms in a sequence. In the modern day, we now know that an infinite geometric series, where there is a common ratio r, can be finite if the absolute value of r is less than 1! There’s a neat bit of maths behind that proof too.*

So in the case of Zeno’s paradox, it’s an infinite geometric series with r = 1/2. So if you had a distance of 1 metre, the next ones are 0.5m, 0.25m, etc. Each term is half of the previous. And since the absolute value of r is less than zero, the sum of the infinite series is finite, in this case it’s simply 2.

Infinity is a little weird.

*See replies below if you want to see my attempt at conveying it within the confines of an internet comment

And it is not always cosmetic either

Which is why I specified cosmetic surgery.

The word plastic in this case does not mean that actual plastic was inserted or injected.

And that is new to me! That makes more sense, plastic surgery being named after plasticity since it’s changing the shape of something and having it stay like that. Plasticity is the converse of elasticity (the latter describing a material that goes back to its original shape when deformed). I have added an edit to the post now.

Ok that’s pretty cool :0

Ah okay that makes much more sense. Interesting, I did not know that!

Oh, so they’re way down below the muscle mass? Did not know that. And yikes, salt water leaking out into your inner bits sounds bad. (but presumably if you were to have such a large injury you would probably also be bleeding and such)

edit: Oh wait, the salt water is low concentration. It’s not like seawater, ok, that makes much more sense.

And Central America is part of North America! The North and South Americas is split by the Panama canal (which is located in Panama. Central America is usually defined as the bits below Mexico and above Colombia (but it occasionally includes parts or all of Mexico too, depending on who you ask). Belize is right next to Guatemala and below Mexico, so it’s considered part of Central America!

Even more confusing, “Latin America” is pretty much any country in the Americas that speak either Spanish, Portuguese or another Romance language, excluding of course the English speaking nations of the US, Canada, Guyana, and Belize (as well as a few Carribean islands), as well as the Dutch speaking Suriname. It does include French Guiana (since French is a Romance language). Hispanic America is all the Spanish speaking nations in the American continent(s)

Not just any shark. A very cute shark!

Another thing to add, FelixCress is a moderator of the community “OPisafuckingidiot”, along with a user called “MeatEater” (hmm I wonder what their shared belief is)

And it seems like they are the main user of that community, with a majority of posts posted by them. The community is intended to mock certain Lemmy comments, mainly replies to their own posts that they disagree with. Mocking people is generally seen as not very nice :(

Looking a bit into this Pablo Stanley guy, he seems to be a vibecoder, and is a dev at “efecto” (an “AI-native tool” that is designed to that lets you “tell an agent what to design”, and without the buzzwords, basically LLM website design). Stanley is also a huge “AI creator” in a platform called Lummi, which advertises itself as a site for these “AI creators” to share AI-gen stock images. He has over 15 thousand images with 3.6 million views, which seems to be a lot (unsure if this is normal though, given that these are all AI generated. I don’t explore these kinds of platforms so I have no idea. They are big numbers though)

Plenty of his comics, articles, and posts are all about “agents”, “context engineering”, those sort. The comics seem to be human drawn though (there’s no explicit mention of image generation for making the comics, but I can’t find anything that makes it clear it’s not though), and in one article, he mentions how the use of AI is like a “slot machine” (addicting but harmful). This is then followed by him stating that, even still, he “loves to create with AI”.

Take it for what you will. Some sources I looked at:

https://medium.com/@pablostanley

https://www.linkedin.com/in/pablostanley1

https://www.lummi.ai/creator/pablostanley

I found the relevant xkcd: https://xkcd.com/1361/

The DNS server is, in a nutshell, the middleman between your computer and the web server you want to access. It lets you use URLs (easy to remember words) to access web servers, which have IP addesses (usually difficult to remember). The browser sends the URL (which includes the protocol, usually HTTPS, as well as the domain name and other bits) and the DNS server checks it against a list of IP addresses.

If they find a match, the request is sent to the correct web server and a connection between the browser and the server is established. When no match is found, other DNS servers are contacted to see if they have the entry. If there is still no results, you get an error telling you the URL does not exist.

As others have mentioned, it’s a bit like a phone book where you look for somebody’s name (the URL) to find the phone number that you can use to communicate with them (the phone number). But I think it more resembles calling a friend (the DNS server) for the phone number of the person you want to contact (the web server), and the friend can either tell you what it is, if they know this person, or call other friends to see if they know their phone number.

The most common DNS service is Google’s, so if you’re not using Cloudflare, NextDNS, or similar, Google is the middleman yet again! You might have seen that xkcd on the “8.8.8.8” DNS service, where all other products are hypothetically killed to focus on their Google DNS.

According to their website, KDE Neon ships with a beta version. It also looks like it will be part of the Plasma 6.7 release next month ish

Most computers should be able to run Nextcloud, but to double-check, look at the minimum requirements for Nextcloud. I run my instance using an old laptop I had lying around, and I think it has an 11th gen Intel processor of some kind and 8GB of RAM. It runs fine with plenty of headroom for many other services

plus, the apps you create can be installed normally without a stupid waiting period on custom ROMs like LineageOS, GrapheneOS, iodeOS, and e/OS!

I think it’s still fine, especially given that non Play Store apps will still be runnable, albeit with a very stupid 24 hour waiting period if no action is taken by relevant regulatory bodies.

But if you are looking to eventually ditch Android for Linux phones, you could always try your hand at making Linux-native mobile apps!