I believe this is correct: x/x = 1 everywhere except 0, where it has a removable singularity. So you can extend x/x holomorphically to full C.
This is completely different from the phenomenon described in the article: arccosh discontinuity can’t be dealt the same way. In fact complex analysis prefers to deal with it my making functions path-dependent (multi-valued).
PLEASE explain "So you can extend x/x holomorphically to full C" to someone with only a BSc in math/cs; something about this thread is giving me an existential crisis right now.
- function extension is defining a function where it is not defined
- <Adj> function extension is an extension that keeps (or gives) Adj property
- extended function is usually treated as originals if extension is good enough. Real analysis starts with defining real numbers and extending familiar functions onto them
- in this particular case we do not need C - even continuous extension on R works and agrees with x/x = 1 at 0
- holomorphic (analytic) extension makes function infinitely differentiable at every point of C
- because of the nature of discontinuity you can’t extend the simple arccosh in any reasonable way on C without introducing multivalued or path-dependent functions
- this continuity makes x/x=1 a reasonable simplification for CAS imo but not for complex functions as in the OP
- many things with point singularities in R have more structure in C, but x/x is not one of them. Even 1/x is of a different nature.
“You do not divide by zero” that forces you to carry x != 0 is more of a high-school construct than a real thing. Physicists ignore even more important stuff, and in the end their formulas work “just fine”.
Thank you, but, now I have 10 further “explain it to me” questions. (I never did analysis so this stuff is entirely over my head. I had one semester of algebraic structures. It was the hardest class I ever had in my life.)
Well LaTeX formulas are not part of standard Markdown, which is a few different Header levels, simple lists, bold, italics, blockquote and... that's about it?
If you haven't heard of the modern roguelike genre you've probably been living under a rock, it seems like every other game these days at least calls itself such. Usually the resemblance to Rogue is so remote that it strains the meaning of the term, but procedural generation of levels is almost universal in this loosely defined genre.
Elite is a bit more obscure, but really anybody who aims to be familiar with the history of games should recognize the name at least. Metroidvania isn't a game, but is a combination of the names of Metroid and Castlevania and you absolutely should know about both of those.
Powermonger is new to me.
And while the comment in question didn't mention it, others have: Minecraft. If you're not familiar with Minecraft you must be Rip Van Winkle. This should be the foremost game that comes to mind when anybody talks about procedural generation.
The person you’re replying to has only posted two short comments in this thread.
The reason a few different people are arguing this point is because it is in fact wrong, or at least poorly expressed, to refer to someone’s unfamiliarity with some aspect of a field like the gaming market as “wildly uneducated.”
Ironically, the person using that phrase is demonstrating a lack of understanding of its common meaning, suggesting that they may be a better fit for the word “uneducated”. See e.g: https://www.merriam-webster.com/dictionary/uneducated
> What is going on right now?
As Wittgenstein put it, we’re playing language games.
I can see how you allowed your own stalking tendencies to confuse yourself, but I wasn't referring to that.
Your comment made it sound as though they were being unreasonable in this thread. I don't see that in the two short comments you responded to. Perhaps you were having a bad day.
The difference is that IRL establishments don't sell off that data to anyone else, nor do they have the ability to collate that data with data from other establishments to make a profile of you.
If you think the nightclub that scans your driver's license magstripe isn't selling your data off, when they could be making money off of it? Between PatronScan,Intellicheck, Scantek, and TokenWorks, yeah a dingy bar where it's a dude visually checking isn't it, but a nightclub and quick swipe totally is.
Depends on how you look at it. While the hardware might keep functioning and current software might keep running, some devs also deprecate their software. I have an old 6S+ that I keep software that I don't want to install on my actual device. Slack informed me that it will no longer function after a date set later this year. Other apps have already stopped working on it because the devs do not want to deal with it.
TL;DR sometimes it's not Apple, it's the app devs that deprecate them.
I have a google nexus 7 tablet from 2013. Thanks to Google unlocking all their bootloaders by default, I can install u-boot and a modern linux kernel on it (thanks PostmarketOS).
Since linux runs on it, I can run the latest versions of great pieces of software like ed, slack in a web browser, etc.
It is 100% apple's fault that they do not open up the bootloader for devices they'll no longer offer updates for and allow the community to build a custom darwin or linux fork. Even though we paid for the hardware, we are not allowed to use it any longer than apple says.
> TL;DR sometimes it's not Apple, it's the app devs that deprecate them.
Are the app devs deprecating just because their support matrix is too big, or because current SDKs will no longer build apps compatible with those devices?
I think the later case is less common on the Android side of the fence, but Apple is not great about keeping old versions of the dev tools functional, and you end up needing to keep elderly Macs around to target older versions of the OS.
The primary hard part is testing the old versions. Xcode has decent backdeploy support (Xcode 26 supports targeting iOS 15, the final version to run on the 6S), but there's no way to actually verify that it works other than on an older device that's never been upgraded. It's a pretty substantial increase in testing burden and greatly increases the size of the pile of phones that you need to janitor for your CI setup.
Submitting apps to the app store requires using the latest version of Xcode (with a ~half year lag after a new one comes out), so it's now impossible to submit an update to the app store that supports iOS <15.
It’s because every supported version multiplies support burden and sometimes can prevent use of new APIs that substantially improve quality of life unless the dev is willing to turn their code into a patchwork quilt of version checks (which brings its own problems).
On Android it’s less of an issue because the SDK ships separately from the system, but there are often still substantial behavioral differences between system versions under the same SDK that can be a real pain in the rear, especially when it comes to permissions-related issues. This why it’s common for Android apps to have odd bugs or behave strangely on ancient versions of Android — while it’s easy for the dev to produce a build technically runs on a wide range of versions, properly testing against all those permutations of versions and manufacturer skins is practically speaking impossible unless you’re a sizable company that keeps a lab full of devices with CI rigged up to test against them all.
As ex-iOS dev, usually it's because devs want the new shinny APIs. And after some point stakeholders are OK to stop supporting a tiny percentage of users stuck on old iOS versions. In my experience it was never because of Apple.
I cannot buy a device without resorting to Ebay to test my app on iOS 17. There are still bugs that manifest themselves on real devices and not on the simulator. And some APIs are just broken on the older releases.
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