We used Z a lot when dealing with modular arithmetic and complex roots of unity, mostly just to quantify our variables. I can't recall ever using N or Q in high school, though.
Also, you don't need to mention Dedekind cuts at all when dealing with R - it can be defined by the fact that it's the smallest extension of Q that's closed under limit-taking (and I think most high school math students do understand that).
I don't think so - I can't imagine Apple caring much about Hackintoshes, which are already a pain to install, when the main draws of Apple laptops are their trackpads and cases, and the tight integration between hardware and software.
I agree with your first point, but strongly disagree with your remaining ones.
For me at least, the process of putting together a hackintosh isn't very hard at all.
First I research hardware that is compatible that I can source at a good price. This is the key step since non-compatible hardware is a world of misery. I'd say in the order of 50% of motherboards and 75% of graphic cards have this attribute. This is the hardest step and the community could make life easier for everyone if it maintained a database of such parts but sadly it's mostly geared toward people getting the hardware they already have to work.
Second I get a flash drive of some variety, format it and run the Clover installer on it, then I drag the EFI folder from the standard archive from olarila.com onto the EFI partition of this boot drive. The Hackintosh is now bootable as a vanilla Mac. The boot drive remains attached at all times to enable this.
Finally I install macOS as it was a real Mac, from an installer flash drive, booting through the Clover boot loader on the boot drive of course.
The reason I use macOS (and always have, previously on Apple hardware) is because it delivers a superior user experience. The OS software is far and away more usable than Windows and Linux machines. There is no sign either of them are catching up.
Next steps I did on my last hackintosh were install Clover Configurator to mount the hackintosh EFI, back it up, and update it with the functioning one from your boot flash drive. I still keep it just in case an update breaks the bootloader.
Yeah I have numerous copies. They're useful if the first one fails of course but also to try out updates of bootloader software or settings tweaks.
But I really don't understand why people make their OS drive their boot drive. Besides the potential for catastrophe it also means you can't move the OS drive between machines or do OS drive backups freely.
As someone who built a hackintosh (on 10.12) with what were widely considered to be 'compatible parts' (I did a lot of research), I think you're downplaying how easy it is and how often issues can arise. I didn't have much trouble doing the initial install after following steps/guides online, but there were a lot of small niggling issues and problems that can arise that make me hesitant to recommend it (like for example, getting imessage/facetime activated was a huge hassle). There may be better tooling now, but it's still not for the feint of heart.
That said, I've switched to an eGPU setup with a Radeon Rx580 and my 15" mbp, and it largely gets me to where I wanted to be with my hackintosh. Using an eGPU with macos is surprisingly easy.
All you really have to do is check that someone has already used a particular set of hardware with the level of support you desire, and you're golden.
The software has improved a lot recently. Plugins like WhateverGreen and VirtualSMC means there is broader hardware support out of the box without fiddling with settings.
But yeah if you are happy with Mac hardware then Hackintoshes are entirely pointless. Laptop Hackintoshes are also more challenging without really competing with comparable Mac hardware.
Re representative democracies, why are opinions on disparate issues like the economy, abortion, climate change, etc. all packaged into one party? At least 99% of people won't find a party that agrees with them on every single issue, so it feels like there should be a better system.
Because the US has first past the post. Sure you could vote for someone who matches every single one of your ideologies, but the chance that they win is zero.
I'm not sure you are attacking representative democracy, but instead are attacking the US two party system. I'm def not going to argue against you on that. Just wanted to say that in a representative democracy, one does have a say in policy. I do very much agree that the US tries to give us all as little of a say as possible, as the "adults" (read: billionaires) decide things for us
Yeah, it's a shame the GitHub is starting to actually take advantage of their hosting monopoly, to the detriment of solutions like OpenCollective and Liberapay.
On the other hand, Git is distributed. Can't you just use GitHub as a mirror, and direct users elsewhere for actual development through the README?
Maybe the quality would improve? There's a condition I call "open-source-itis" that a lot of projects suffer from, where tons of new features (usually of dubious merit) get added but nobody ever bothers to fix bugs or make sure the foundation is actually solid. It makes sense, because that's unsexy work that people generally don't want to do and they're all working for free, but it makes a lot of open source software really crap.
However, if people were getting paid for fixing bugs and cleaning up old code, maybe that'd improve.
In my line of work there are perverse incentives for hyping up new stuff and then not dealing with bugs and problems. It's not been me doing that but I've suffered by comparison against others who embraced that dark pattern.
Complaints are publicity. They bump internet discussions, create buzz, and often go along with protestations of 'I really love (FooBazBar), I promise it's the best thing ever, now if you would only fix this bug…' and then angry flames over the bugs and defenders coming to protect the honor of FooBazBar.
Fix bugs and people are happy and stop talking. They return to happily using the product. Again, we're talking perverse incentives for just the sort of obnoxious behavior you describe, or worse.
What does "functional" mean to you? If "OO" has a hundred different meanings, then "functional" must have at least a thousand. To me, JavaScript is definitely not functional - it lacks a notion of purity, and its meaning is the evaluation of statements, not the construction of expressions.
Yes, it certainly does. I wouldn’t view it as a huge positive, though; it certainly confused me for a while, especially since synthetic nodes actually exist in the DOM.
Also, you don't need to mention Dedekind cuts at all when dealing with R - it can be defined by the fact that it's the smallest extension of Q that's closed under limit-taking (and I think most high school math students do understand that).