u/Quintic

I grew up playing on PvP servers, mostly because that was the servers where my friends played. Nowadays, I like my casual PVE strolls through stranglethorn vale.

(1) In part (iii) he needed an upper bound on |b_n| (convergent sequences are bounded) to handle b_n in a product. Here b_n is in the denominator, so it flips: to get an upper bound on 1/(|b||b_n|), he needs a lower bound on |b_n|. Replacing |b_n| with something smaller but still positive makes the fraction larger, which gives the upper bound.

(2) |b_n| >= delta > 0 just says |b_n| stays at least some fixed positive distance from 0. Once you have that,

1/(|b||b_n|) <= 1/(|b| delta)

which is a fixed number that doesn't depend on n. Any delta with 0 < delta < |b| works. He picks delta = |b|/2 because it gives tidy algebra. He chooses N_1 so that n >= N_1 implies |b_n - b| < |b|/2, which gives |b_n| > |b|/2.

(3) "Closer to b than to 0" is just a geometric way of saying |b_n| > |b|/2:

|b_n - b| < |b_n| implies |b| <= |b_n| + |b_n - b| < 2|b_n|

It isn't necessary, though. You could use delta = |b|/1000000 instead of |b|/2, which allows b_n much closer to 0 than to b, and the proof still works.

(4) |b|^2/2 is the denominator of the upper bound from (2):

1/(|b||b_n|) < 1/(|b|^2/2)

He picks N_2 so that |b_n - b| < epsilon |b|^2/2 because he knows he'll divide by |b|^2/2 later and wants the result to be exactly epsilon. With a different delta, he would choose N_2 so that |b_n - b| < epsilon |b| delta.

At that price point your options are probably a small or used dobsonion. My first telescope was Heritage 130p which is about $270 right now, you might be able to find it used. You can find 8" dobsonions for $250 used if you look hard enough.

With the default eyepieces you should be able to make out details of Saturn and Jupiter, but may want to budget and extra $50-$100 if you want more magnification for planetary targets, for clusters I would stick with lower magnification.

A lot of people have played this game for 20 years, and paid for a beta key. No one is entitled to beta access.

You should do whatever is the most fun for you in the time you have to play the game.

For some people, rushing to 60 and min/maxxing every aspect of the game is the fun for them.

For others it's maxing professions and leveling one of every character. Some people don't even touch a raid.

This is ok. Play the game you want to play.

I have an R100 for a camera, Heritage 130p and Orion xt10g dobsonians.

I have been unable to get either to give me focus with the camera. I think they need a significant mod to work.

I've had terrible time trying to get my phone to work with telescopes. I might just be too dumb to use the cell phone contraptions available. 

I use an SV Bony 305c camera to get good images with both of them. Usually for planetary since it's hard to get good deep sky with alt/az mounts. 

This is what I use to connect my R100 to the telescope eyepiece.

https://a.co/d/0g4DbPz4 1.25 inch T-Adapter https://a.co/d/01xLS0p1 RF T-Adapter 

I've tried to use a barlow lens, but haven't had luck there either.

Who is us?

Because I answered the question you asked already, and you're having trouble comprehending it. Low comprehension tends to carry over to other things.

It's becoming clear why your contributions are not accepted.

The entire context of your post is that you are trying to contribute to Kubernetes, which is an open source project, and wondering why the project is not accepting your contributions.

My response answers why you shouldn't expect open source projects, including Kubernetes, to necessarily accept contributions from unknown third parties, e.g., you.

I am not trying to answer whether or not Kubernetes is open source. It's clearly open source. 

Open source does not necessarily mean anyone can contribute. I am sure occasional external contributions are accepted, but reviewing code from unknown contributors is a huge burden on a team.

The best way to take part in open source is by building your own extensions or forks. This is how open source is supposed to work. An open source license is not a license to contribute upstream, but a license to use, modify, and redistribute.

If your extension or fork becomes popular enough, the upstream project may decide to integrate your feature, since it now has a proven track record. Reviewing a change that has already been battle-tested is far less of a burden. But getting merged is a nice to have, not the goal. The goal is to contribute, and a healthy ecosystem of extensions and forks is a win even if nothing ever gets merged.

You're fine. If someone pushes you on it, just laugh it off and say it was a joke. If someone with authority says it is a problem, apologize, and thank them for their feedback (as earnestly as you can). Do good work, so people will remember you for that and not your jokes or insufferableness.

Ok? My comment and the OP's post are talking about what's it's called (I.e. named) which as you mentioned is WoW Forever.

I'm am sure it is referred to in many ways, but it is called WoW Forever.

And what? The game is called WoW Forever, not Classic+ which is what the OP claimed. 

The game is called Forever.

There is a version of WoW that does this already, it's included with your subscription.

What are you trying to say here?

If you say it's going to rain every day, you'll be right every time it rains. Maybe it'll rain soon, it'll definetly rain eventually.

Associative is what makes the lack of parenthesis unambiguous, commutative is what allows you to rearrange the terms.

I mostly play Alliance, Horde feels the same way. I've leveled Horde characters, but at the end of a day of grinding, I prefer to hang my hat in Stormwind.

I think you're putting a bit too much weight into forever. It's just another WoW expansion. 

When an item drops, players bid gold on it. That gold goes into a pool that gets split among everyone at the end of the raid, usually with the raid leaders taking an extra cut. It's basically bid DKP, except you can take your DKP with you if you switch raid groups.

Blizzard equates it with RMT and gold buying because it incentivizes gold buying, since having more places to spend gold increases its value. However, that's true of all in-game economic activity, like the auction house. So even with GDKP banned in Anniversary, RMT remained a major problem. RMT isn't caused by GDKP. It's caused by a player base culture that's more accepting of buying gold, at least in private.

I think 2 is most likely, but 4 is better.

Yeah Java does that, but does also have runtime exceptions that don't need to be documented. I think there are other languages that end up requiring exceptions to be documented in various ways too. 

However, if you restrict yourself to only throwing runtime exceptions for truly exceptional behavior, meaning bugs, then this solves a lot of the problem.

Languages like Go and Rust try do solve this by removing exceptions, and do it to varying degrees of success.

Go ends up having panic which can be caught with a recover statement, which some people end up using similarly, but they have a error return similar to Google's Status for typical errors, however they don't have nice macros so you end up with verbose if statement handling. So some people try abuse the recover system to make the language write nicer.

Rust has a Result type very similar to the Status type that is used for return, and fixes the verbose if statements with something called the ? operator. Rust also has panics and catch unwind, but I see it abused far less often, but I assume it's used too. Rust also has a bunch of other guarantees such as it being nearly impossible to accidentally throw null pointer exceptions. 

The argument starts with "Assume there are finitely many primes, p_1, ..., p_n."

Our goal at this point is to show that this assumption makes the mathematical universe we are in absurd, i.e., that it leads to a contradiction.

Before we can do that, we need to have established that every number greater than 1 has at least one prime factor (proof at end if you don't know it yet). The number N is constructed so that, if there are finitely many primes, none of them is a prime factor of N, which contradicts a fact we've already established.

That is our absurdity, so our assumption must be false. If it is false that there are finitely many primes, then there must be infinitely many.

(Appendix)

Theorem: Every number N greater than 1 has at least one prime factor.

Proof: If N is prime, we are done, because N | N. If N is composite, let d be the smallest number greater than 1 that divides N (it exists by well-ordering). If d is prime, we are done, because d | N. Otherwise d is composite, so there is some number e with 1 < e < d and e | d. But then e | N, contradicting d being the smallest number greater than 1 that divides N.

Under the hood it's an if statement and a return statement. A very simple macro saves 2-3 or so. 

A raised exception can move you multiple layers up the stack, and where you end up isn't defined by the place the error is raised.

Raising an exception also is not documented by the function interface, so a caller needs to somehow learn the exception is something they may need to handle. With the Status return types the error is made explicit by the type system. 

These two things together is what Google is arguing makes exception control flow more complicated and more prone to bugs. 

However, with good exception higiene people can and do make it more manageable, so it's really just a preference at the end of the day.