If Apple doesn't offer a Linux product, they cannot be used seriously in headless computing task. They are adamant in controlling the whole stack, so unless they remake some server version of macOS (and wait years for the community to accustom themselves with it), they will keep being a consumer/professional oriented company
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.
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