skysight-inc/HackerNews huggingface dataset:
I remember having a hard time solving this in my first year of college. This is really impressive.

So I have this problem here: given that for positive integers m and n, 0 ≤ x[m + n] ≤ x[m] + x[n], I need to prove that the limit of x[n]/n exists. Hmm, okay, let's see how to approach this.

…

Alternative approach: maybe I can show that a_n is convergent by showing that it's a Cauchy sequence.

But that might be complicated.

Alternatively, perhaps I can use the subadditivity to bound a_n.

Wait, let's consider the following:

Since x is subadditive, x[m + n] ≤ x[m] + x[n].

Let me set m = n, then x[2n] ≤ x[n] + x[n] = 2x[n].

Therefore, x[2n]/(2n) ≤ x[n]/n.

So, a_{2n} ≤ a_n.

That means that a_{2n} ≤ a_n.

Similarly, x[3n] ≤ x[2n] + x[n] ≤ 2x[n] + x[n] = 3x[n].

So, x[3n]/(3n) ≤ x[n]/n.

Similarly, x[4n]/(4n) ≤ x[2n]/(2n) ≤ x[n]/n.

It seems like a_{kn} ≤ a_n for any integer k ≥ 1.

This suggests that as n increases, a_n tends to decrease or stay the same.

But wait, in the example where x[n] = n, a_n = 1 for all n, so it's constant.

In the example where x[n] = sqrt(n), a_n = 1/sqrt(n), which decreases to 0.

So, in some cases, a_n is decreasing, and in some cases, it's constant.

But in general, a_n is bounded below by 0 and is decreasing along powers of 2, for example.

Wait, from x[2n]/(2n) ≤ x[n]/n, and x[4n]/(4n) ≤ x[2n]/(2n), and so on, so along the sequence n, 2n, 4n, 8n, etc., a_n is decreasing.

Maybe I can use this to show that a_n has a limit.

Let me consider n = 2^k, for integer k.

Let b_k = x[2^k]/2^k.

Then, from x[2^{k+1}] ≤ x[2^k] + x[2^k] = 2x[2^k], so b_{k+1} = x[2^{k+1}]/2^{k+1} ≤ (2x[2^k])/2^{k+1} = x[2^k]/2^k = b_k.

So, b_{k+1} ≤ b_k, meaning that b_k is a decreasing sequence.

Since b_k ≥ 0, it must converge to some limit, say L.

Now, I need to show that x[n]/n approaches L as n approaches infinity.

Given that b_k is decreasing and converges to L, and for general n, a_n is bounded below by L, and perhaps approaches L.

Wait, more carefully:

For any n, there exists k such that 2^{k-1} < n ≤ 2^k.

Then, x[n]/n ≤ x[2^k]/2^{k-1} = 2(x[2^k]/2^k) = 2b_k.

Since b_k approaches L, for large k, b_k is close to L.

But I need to show that x[n]/n is close to L.

Wait, perhaps I can bound x[n]/n between b_k and something else.

Given that 2^{k-1} < n ≤ 2^k, then x[n] ≤ x[2^{k-1}] + x[n - 2^{k-1}] ≤ x[2^{k-1}] + x[2^{k-1}] = 2x[2^{k-1}].

Therefore, x[n]/n ≤ (2x[2^{k-1}])/n ≤ (2x[2^{k-1}])/2^{k-1} = 2(x[2^{k-1}]/2^{k-1}) = 2b_{k-1}.

But b_{k-1} approaches L as k increases.

Similarly, since n > 2^{k-1}, x[n]/n > x[2^k]/2^k = b_k.

But b_k ≤ b_{k-1}, and both approach L.

Therefore, x[n]/n is squeezed between b_k and 2b_{k-1}, both of which approach L.

Therefore, x[n]/n approaches L as n approaches infinity.

This suggests that the limit exists and is equal to L.

Therefore, the limit of x[n]/n exists.

Alternatively, if I recall correctly, this is exactly what Fekete's lemma states.

So, in conclusion, the limit of x[n]/n exists.

*Final Answer*

\boxed{\lim_{n \to \infty} \frac{x[n]}{n} \text{ exists}}
> Yet that jurisprudence pertains to all aspects of life.

As does secular law. Is it feasible for everyone to become a lawyer? Because that's the analogue.

> to expect so little in the way of questioning and intellectual exercise from the people who follow its tenets.

But that's just not true. You would only assume that if you were not acquainted with the Islamic intellectual tradition. Rather most people simply do not put in the effort that's necessary to develop the rigor and depth required to join the discussion. That's more of a comment on average human nature.
HN user pg, aka Paul Graham, the (co-)founder of both this site, i.e. HN, and YC itself, the "parent" site, was probably the guy (or one of his early colleagues) who implemented the karma feature here on HN.

I am saying this because the feature has been there from pretty early on.

No need to believe me, go verify it yourself, by any means you choose.

And see:

https://en.m.wikipedia.org/wiki/Karma

https://commons.m.wikimedia.org/wiki/File:EndlessKnot03d.png
Why don't they just compile to C to Go like modern c does for SQLite?
> Well, keep in mind that the full linking step has to be done at the end of an incremental build.

Does it have to be that way? For an incremental build, particularly in the "not much has changed except some function contents" case, is it plausible to reuse the previous linker output and update the incrementally updated part?
I don't think this question is super hard. ChatGPT 4o mini gets this one correct consistently without being asked to reason step by step.
That Chan really made some eye Candy there ;)
I am aware of the additionals, like COOLWSD. But since they run this in their Android apps, it seems this can already be Pi-ready
They're giving two business days' notice for new product and three months for existing product?
Didn’t even have to open the link to know it was Author and Punisher.

Great aesthetics. Reminds me a lot of early Throbbing Gristle in the DIY process of the work. Very inspiring.

Much like nerds who build cyber decks and mod retro computers and console.
It's actually very common to fine manufacturers for negative externalities. We even tax some manufacturers for some negative externalities. For example, we have a federal tax on cigarettes that pay for some health programs.
Exactly, and this isn't adding anything significant from what I can see that isn't already achieved in much more clear and openly presented repositories. Take coqui for example. Cloning as as easy as recording an example of your voice and using

```python
from TTS.api import TTS
tts = TTS("tts_models/multilingual/multi-dataset/xtts_v2", gpu=True)

# generate speech by cloning a voice using default settings
tts.tts_to_file(text="It took me quite a long time to develop a voice, and now that I have it I'm not going to be silent.",
file_path="output.wav",
speaker_wav="/path/to/target/ speaker.wav",
language="en")
```
>Algorithmic and Spotify-owned editorial playlists

Any guesses if this includes New Releases and Discover Weekly playlists?
If we held any of the top ballers in 2024 to a standard even slightly more honest than the color scheme of the political party we’d apply that -100 to basically all of them, wouldn’t we?

By all means hold Musk to account, it’s the right thing to do.

But it’s borderline religious to duck the obvious corollary that this is a war for all the marbles. Blade Runner or TNG.

Pick a side.
And have them run on a regular schedule, within and between cities. Imagine the benefit to the public and the environment. It could even be funded by tax payers.
Oh, man, word by word my experience.

I bought a fancy, customizeable, ergonomic, mechanical keyboard. It feels great! But it's too much hazzle to learn, customize, OS changes etc.

I bought it because I was having wrist pain, and my old keyboard was one I got for free from the college surplus back in 2011. So I thought it was a sensible purchase.

I'm back to cheapo surplus keyboard.
Depends on what you're using the bike for. If it is for work or transport (as it used to be for paperboys and delivery gigs a few decades ago), you'd want it to be as smooth and light as possible.
True, America bulldozed their cities to build parking lots and roads, which made them much worse for anything but driving.
The essay is thoughtful but the analogy itself is incoherent.
Making driving way more expensive takes care of that.
Weirdly the Dutch take the train plenty and also have lots of cars
I have 100k of cloud credits to spend in the next 12 months – what do I build?
Somehow received around 100k worth of credits with a certain cloud provider that I can spend on anything (compute, gpus, etc..) Looking for interesting ideas and side projects to spin up
We both pay $10 a month. This month, I listen to 99 songs from a single artist, and you listen to one song total. $9.90 of my money goes to my artist, and $0.10 goes to your artist. $9.90 of your money goes to my artist, and $0.10 goes to your artist
Santa, a CLI app in Go for generating Secret Santa pairings
The app enables you to define your participants and the email(s) they will be receiving. Preferences include excluded or predestined recipients, and extra recipients with potentially excluded givers.

Santa makes it simple to debug and even print the pairings before randomising the gift-givers and recipients (taking everything into account) and firing off your stealthy emails using your Mailgun account.
I think you can just buy them in japan.

I've had this vision where we create a niche in a building for restroom placement by fork lift. For the low end ones the interior can be 3d printed melted down and recycled. They can be pressure washed with high pressure steam.

For the high end ones you can have the marble finish with gold trimmings then when it tickles your fancy have it replaced with a different color marble, different light and different ornaments.

You can do various lease formulas where you get to enjoy the fancy designs until you [need to] downgrade to the economy version.

That formula could also allow exotic designs that wouldn't sell as permanent installations. You could have a different marvel character theme every week/month while you wait for the steam punk and Victorian units to become available. Star wars, startrek etc. I mean, you wouldn't want a ycombinator themed restroom permanently but for a week or~so it would be hilarious.

https://google.com/search?q=themed+restroom&udm=2
A million processes?
Performance Improvement Plans are hated, and more popular than ever
It doesn't take that much space, and not all languages have option to easily map an initial range onto an iterator that produces tasks. Most are dominated by the size of state machines/virtual threads.

Please note that the link above leads to old code from .NET Framework.

The up-to-date .NET implementation lives here: https://github.com/dotnet/runtime/blob/main/src/libraries/Sy...
On previous thread of this topic, someone on hn claimed to have worked in tire industry and that some small additive that would cost few percent extra would largely address thos issue.
This benchmark is nonsense. Apart from the fact that Go has an average Goroutine overhead of a 4kB stack (meaning an average usage of 3.9GB for 1M tasks), the code written is also in a closure, and scheduling a 2nd Goroutine in the wg.Done(), so unlike some of the others it had at least 2M function calls on the event loop stack in addition to at least 1M closure references. So yeah, it’s a great example of bad code in any language.
Related, it always seemed weird to me that lithium was leading the way (initially, at least) for grid storage. Lithium won the battery race for mobile applications (e.g. cars, laptops, etc.) where energy density is critical. For grid storage, though, battery weight should hardly be a concern at all. It seemed to be like lithium was ahead solely because there was so much industrial knowledge learned from optimizing for energy density first, but that other battery chemistries had to be better for grid storage once we invested the same economies of scale in them, too.
Using Pandoc and Typst to Produce PDFs
The referencesource repository is only relevant if you are using the legacy .NET Framework. Modern .NET has a special case for passing a List<Task> and avoids the allocation:

https://github.com/dotnet/runtime/blob/1f01bee2a41e0df97089f...
I went to the toilet in a very understaffed kfc and it was so dirty that I will never eat there again. The kitchen cant possibly be any better than the restroom.
Thats stress on the road, as in things like the road surface, not tire wear. The physics about what's happening to the tire surface are pretty different from what's happening to the road.
Is there some fun tea here? Ninja themselves describe them as blenders, has the community mythologized them into something else?
I think you have a very skewed view of what people interested in cryptocurrency are like.
If it were malicious, they would have increased prices in Europe as well. They could try and extract money from European customers just as much as American ones.

And the bandwidth pricing is still quite cheap, $0.001/GB. Major cloud providers usually charge nearly 100x that (AWS 90x, GCP at 85x or 120x depending on whether you want standard or premium, Azure at 80x or 87x depending on standard or premium).

You used to get 20TB for free and now you get 1-8TB free. If you had to pay for 19TB, that's another $19. If you had to pay for 19TB from a major cloud provider, that'd be $1,556-2,335. Even if you had DigitalOcean, they'd be charging you $0.01/GB (10x) and you'd be hit with a $190 bill.

I think the issue is that in the US, they don't have their own network. They peer with a single company in Virginia for 200Gbps and then pay for transit on 1Tbps. That's a lot of transit to be paying for - and 5x more transit than peering. In Europe, it looks like they have their own network between Finland, Germany, France, Amsterdam, UK, Austria, and Czech Republic. They also have a much better ratio of peering to transit. So they can use their network to carry the traffic to a lot of Europe and then maybe they have peering arrangements to handle most of their traffic when they need to hand it off.

In Europe, they're more likely to face owner economics while in the US, they're effectively renters - and the more their customers use, the more it's going to cost them.

If this were really a cash grab, it's a pretty terrible cash grab. It will certainly impact some users, but the maximum it will impact any user is $19/mo (if they're on a server with only 1TB of included traffic). But most people don't use many TB of traffic. Consuming all Bluesky posts in zstd compressed JSON is 30GB/mo. These weren't servers that had unlimited traffic on a 1Gbps port. They had a 20TB limit. If you were hitting that and intend to continue hitting that, it's another $12-19/mo.

If I had to guess, I'd say that they probably thought they'd expand more in the US and build out a fiber network here (as OVH has done), but that didn't happen and now they're looking at continuing to pay transit for the foreseeable future. Though I feel like the optics of this are pretty bad given that most people probably use less than 1TB and those users will still feel like something is being taken from them (even if they were never using that much anyway).
> this is why (HN cough) multi-cloud/dedi k3s

As long as you don't factor in the cost of the effort to make that work as seamless as it sounds.
The more the western boomers fight about "clean energy" products, the more China will eat our lunch

At the same time we saw Northvolt going to Ch 11 due to costs and lack of expertise.

A lot of what comes from China might be low quality (especially for internal consumption) but it's cheap and they're specializing

> Sodium-ion cells are however much less energy dense, as illustrated by BYD’s new product only packing 2.3MWh per 20-foot container, much less than the 5MWh and more than is now standard in the lithium-ion BESS space.

Which really doesn't matter if you're on a stationary application, especially if the cost/longevity is competitive.
Hey.

Sorry about your diagnosis.

Thanks for sharing. This is an interesting, though somewhat disappointing, paper.

One thing I didn't get while reading it was the specific blood concentration achieved. I noticed they mentioned 12 rounds with 3 infusion days and 1.5g/kg. I'm assuming they injected that amount daily.

I noticed they injected over a period of 3 hours. To my knowledge the half life of vitamin c in blood is only 2 hours. I wonder if the concentration of vitamin c ever got sufficiently high to induce apoptosis.

At IV clinics near me they offer 75g bags of vitamin c on the website that are administered over an hour. I bet you could go back to back and get a higher concentration. In the same trip I wonder if you could get something fun - an IV clinic near me offers a nootropic, methylene blue, might charge you up for a day of studying cancer treatments.

One final idea I've had, not sure how useful it is to you, is that you can an at home ultrasound for a few thousand dollars. You should be able to use it to see your intestines and the tumors growing inside. You could use this to monitor your own treatment - i.e. take daily pictures and examine before and after vitamin c therapy, to see if it does anything.

Best of luck to you. If you want to bounce ideas for DIY cancer treatments off of anyone let me know and we can exchange emails.
> Pick a side.

Never, even if I disagree with one side 99% of the time, still never.

Picking political sides is surrendering your agency to group think.
> I have no idea what Go is doing to get 2500 bytes per task.

TFA creates a goroutine (green thread) for each task (using a waitgroup to synchronise them). IIRC goroutines default to 2k stacks, so that’s about right.

One could argue it’s not fair and it should be timers which would be much lighter. There’s no “efficient wait” for them but that’s essentially the same as the appendix rust program.
I hope that our tariff situation in the coming years doesn't leave us behind the coming tech curve.

Our entire energy future in the US could be held back severely if we are kept from adopting the best technology by politicians trying to prop up oil. The market must be allowed to choose the most efficient technology on its own. (And even the oil companies know that their future is limited, the only question is how long they can delay that future and how much money they can extract from consumers through higher prices than the alternatives.)
My impression is that Buddhism has a focus on "inner life" rather than the material world. So their pragmatism would naturally be employed on spiritual attainment, rather than science. After all, large factions within Buddhism believe that the reality around us, is mere illusion.
> Decimals are integers

No, most decimal types are decimal floating-point. (So, sure, technically redundant, but a lot of people say "floating point" to mean IEEE 754 specifically, even if that's technically incorrect).
The votes are strong majorities of both houses - great to see a functional democratic government act on such an important issue.

They specifically don’t prescribe any particular age verification methods. This would be a great time to follow up with legislation that updates their national IDs to be able to provide cryptographically secure proofs of age without leaking identity.

Absent that, I’m sure many of the comments to come will worry about the privacy implications. It really would be great to see the government act with expertise to solve the problem in a way compatible with a free and open society.
True... but whether the ability to so is a superpowers strength or a debilitating weakness depends on both your values and point of view!
FLAC also doesn't give you the information these google'd API's did.

My bicycle won't run out of gas but that doesn't mean it's more useful/reliable than my car for a cross country road trip
You're only a tube of glue and a bad decision away
Looking forward to it! I really enjoyed the HN meetups in London and Cologne, but it's been quite a few years since they had the last ones.
I'm a strong supporter of giving more material to Ukraine, but unfortunately a couple squadrons wouldn't make much of a dent. For air supremacy where you can do whatever you want in the air, you need to destroy enemy air defenses; even if you don't have complete air supremacy you need to create localized air supremacy to do missions. SEAD and DEAD (suppression and destruction of enemy air defenses, respectively) is extremely difficult and there's really one one country that has the means and requirement to do so, the US. Currently most aircraft in Ukraine on both sides are engaging in standoff attacks because getting anywhere near the front exposes you to massive amounts of air defenses. If the US could donate several squadrons, including specialized electronic warfare craft, and could train Ukrainian pilots on SEAD/DEAD then there'd be a chance to roll back Russian air defenses, but that's unlikely to happen even in the best case scenario. It's important to keep sending planes to Ukraine to prevent them from losing the air war, but I doubt there's anything that can be done for Ukraine to win the air war
The same thing but twice the work !
OP here - We just wanted to make it easier on folks to send out! We just posted the template on the site now if people want to write their own!
We’re a nanny state, the government is just going to use it to track us
Oh I read the most important thing, the original page.

>TrunkVer is a SemVer-compatible versioning scheme for continuously-delivered, trunk-based applications and systems that don't follow a release scheme.

It's not compatible with SemVer. I've explained why it isn't compatible in any sense multiple times now in various comments, probably most of them in reply to you.

>Repeat after me: the use case that fits this involves a need to integrate with a deployment system or tooling that expects semver versions.

Just because it fits doesn't mean it's "compatible". If you apply this TrunkVer scheme to a library, continuously deployed or not, the result is a disaster.

>I really don’t get what your obsession is with compatibility and package managers.

>the use case that fits this involves a need to integrate with a deployment system or tooling that expects semver versions.

A "deployment system" that you need to integrate with is most commonly a package manager.

>Repeat after me: the use case that fits this involves the need a versioning scheme that’s better than a meaningless incrementing integer

This may be more informative than an incrementing integer, but it is still not compatible with SemVer as the original page claims, and it is neglects many important considerations like variance between the build date, code version, and authorship date.

If you're going to reply to me again about this I suggest that you follow your own advice, because I've given fairly definitive objections to this scheme already:

>Stop and actually read what people are telling you before replying.
And what if the runtime does poorly on even such a simple loop? Go is surprisingly slower here than Java and Kotlin.

I agree with the author of the blog here - microbenchmarks are just experiments and they can be very useful if you do proper analysis of the results. You can definitely learn something about the runtimes even from such a simple for loop benchmark.
Consumers are not part of the problem. There is literally no action a consumer can take to ameliorate this situation because there are no tires produced that don't have this problem, and many consumers need to have a car to live.
even if that were true, do you want to be the person to trigger that for them? i don't.

in general i think the issue is simpler tho. comedy is just subjective, not everyone enjoys the same stuff