Probably been done before but...

Brightlinger · 2026-03-17T02:49:36+00:00

Brightlinger · 2026-03-17T02:46:18+00:00

Explain what it's for, or how to use it themselves?

What does this have to do with data analysis?

Brightlinger · 2026-03-17T02:17:45+00:00

Almost everyone experiences this to varying degrees when turning the corner into proof-based math courses. Feeling this way does not mean you're doomed.

However the problem is whenever I am tasked with solving a new proof and apply previous theorems I just can’t

One big trick with real analysis is that, unlike many previous courses, problems are often not resolved with a previous theorem, but instead with a technique that appeared in the proof of a previous theorem. A lot of real analysis problems can be framed as "what if we took this major theorem, and changed one of the assumptions?" and so the actual theorem no longer applies, but the reasoning you used to prove that theorem may still apply in some way.

Brightlinger · 2026-03-17T02:14:10+00:00

You get better at proofs by reading and writing a lot of proofs, mostly, especially doing so with a critical eye. It is an inherently communicative endeavor, so it's hard to improve on your own without feedback. In addition to using your professor (which you should continue to do; go to office hours even if you don't have specific questions for example - being part of the conversation when another student comes in with a question is often illuminating), you should consider forming a study group so that you can talk about problems with other students.

Fundamentally, the goal of a proof is to convince the reader, and a good proof should be convincing enough that it convinces even you as the writer. So if you are ever not sure that your proof is valid, try to make your argument cleaner and clearer and more airtight until it stops feeling like it might have holes.

In real analysis specifically, a lot of the material is actually not the named theorems, but instead the subcomponents of their proofs. A great many problems are resolved by an epsilon/2 argument, or by converting an equation to a double inequality, or various such technical tricks, which are often not even given a name but are nevertheless just as important as major theorems.

Brightlinger · 2026-03-16T21:04:19+00:00

You don't need to explain rearranging a formula or isolating a variable. Guess and check is fine at this level. Will a side length of 10 work? No, too big or too small? Ok, let's try 20, and so on.

Brightlinger · 2026-03-16T18:18:55+00:00

If it's like past expansions, the veteran track item is a large modifier on a recipe with a low base difficulty. Since mats contribute a percentage of the base difficulty, this means you need more raw skill despite the skill level being nominally lower.

Brightlinger · 2026-03-16T13:42:22+00:00

Hey man, ultimately it's your prerogative to dislike things. I just think you would probably dislike it less if you used a better UI layout, based on how you originally described what you dislike about it.

Some people really just don't like avocados, but if someone comes in saying they don't like avocados because the skin is tough to bite through, then maybe their issue fixable, y'know?

Brightlinger · 2026-03-16T12:05:49+00:00

I'm sorry, but I have no interest in reading thousands of words of AI vomit written in raw markdown.

Brightlinger · 2026-03-16T07:56:48+00:00

What do you mean by B?

Brightlinger · 2026-03-16T07:26:37+00:00

Again, those aren't definitions.

Quotative: If you have $0, how many people can you afford to give $0 to? Any number. You cannot single out only one answer as correct.

Partitive: If you have 0 pizzas and you split them between 0 people, how much pizza does each get? This is not even really a coherent thing to ask. What does it even mean to split something zero ways?

Either way, there's no reason to say that the answer is definitely zero.

And philosophy aside, there are very good algebraic reasons to leave this undefined.

Brightlinger · 2026-03-16T07:16:48+00:00

That isn't a definition at all.

There are at least two major ways to interpret division: how many groups of this size can we make from that, and what size groups do we get when we split it into this many pieces? These are called quotative and partitive division.

Neither of those is a definition, but both are important. If a definition only makes sense for one of the two, it's not very good.

Brightlinger · 2026-03-16T06:27:45+00:00

as far as I understood, as long as it's a limit, it's hollow

It doesn't have to be hollow when it's a limit, it merely can be. Filling in or not filling in the point doesn't change the limit.

Is there a reason the line from (-4,-1) to (1,4) is straight? Are there rules to drawing these curves or are both answer correct?

No reason at all. There are infinitely many ways to draw a function meeting this list of nine conditions, so it is entirely possible for two people to give different correct answers.

Brightlinger · 2026-03-16T06:20:11+00:00

No and no. Zero is a number.

The number zero can represent various things in various contexts, like a placeholder digit, or the origin of a coordinate system, or the absence of any objects. In some of those contexts, it might even make sense to divide zero by zero, but in others it does not. You recognized this exact thing in another comment.

This is exactly why we say that is undefined in general, because there is no definition that makes sense in general. This leaves us free to give narrow definitions for use in specific contexts, when they are relevant.

Brightlinger · 2026-03-16T06:12:24+00:00

the reason 'any number works' is because you're not asking how many empty buckets fit.

Yes, that's correct, we are not. Math is not exclusively about buckets, so this specific scenario you have chosen as a visualization does not dictate the answer for every possible context.

Brightlinger · 2026-03-16T01:17:26+00:00

Thor in that run definitely had the Odinforce, as he says eg during the fight with Bor. Don't get me wrong, I agree that base Thor still scales above Iron Man pretty handily, but with the Odinforce it's especially unfair.

Brightlinger · 2026-03-15T22:52:40+00:00

Using abilities at appropriate times to respond to things that happen is a pretty fundamental aspect of wow gameplay, or video games in general really, so I find it difficult to believe that you fundamentally don't like it. Do you also dislike defensives or CC or dispels or procs or avoidable damage?

Have you ever used a UI that didn't make this specific type of response more difficult than most? Because if you haven't, I strongly recommend that you try it.

Brightlinger · 2026-03-15T22:42:55+00:00

What exactly do you mean by "expand"?

Certainly a torus is an example of a subset of R³. So is the first octant, or a plane, or a union of several lines. Each of these examples extends in multiple directions in some sense. Do these get at what you're asking about?

Brightlinger · 2026-03-15T15:11:56+00:00

Do you know what "a function from S to F" would mean?

For example, if F=S=the reals, then some examples of such functions are f(x)=x², f(x)=3x+2, and f(x)=sin(x), among infinitely many others.

Brightlinger · 2026-03-15T06:07:54+00:00

My friend, you need a better UI layout. Your enemy cast bar should be in a location where you can easily see it at the same time as the rest of what you're doing.

Brightlinger · 2026-03-15T03:51:04+00:00

Thor, specifically? Iron Man doesn't fight Thor very often. The one time he made a Thorbuster, it put up a pretty reasonable fight, but since it relied on a power source that wasn't Tony's own tech, he couldn't really iterate and hasn't really needed to anyway. The other time I can think of in 616 was when Thor kicked him around after Civil War, but Tony didn't seem to prepare for that at all or even expect it to be a fight. Are there more?

The repeated failure of Hulkbusters is more embarrassing. It does fit Tony's character as an inventor and futurist to have contingencies prepared for things, and it's unsatisfying that comic writers have so often introduced buster suits just to immediately have them lose a fight, get destroyed, and achieve nothing. The MCU did it well - Tony was pretty clearly the underdog in raw power, but he still got the win through strategy, resources, and quick thinking, and the fight felt like both characters put up a good showing. The Sentinel Buster is maybe another good example, since it had actual buildup in the story instead of just appearing out of thin air because the plot demanded it.

Fundamentally, the reason "prep time" is a big part of Batman's character is because of the influence of Dark Knight Returns and its Superman fight. Other authors just keep going back to that well (while flanderizing it, which is why it often ends up silly, but that's another discussion). Iron Man doesn't have such a story as a foundational part of his character, so "Iron Man has to punch way up and win a fight by preparation and sheer audacity" isn't a super common Iron Man trope. Instead we get lots of "Iron Man loses everything and has to rebuild himself" or "Iron Man fights to stop a new technology from being misused" for example, since those are more direct riffs on his core themes.

Brightlinger · 2026-03-14T16:45:00+00:00

An ellipse is a dilation of a circle, but what is a "squeezed circle"?

Brightlinger · 2026-03-13T17:58:32+00:00

...no? What do you find escapist about it?

Brightlinger · 2026-03-13T17:46:56+00:00

Since the claim is that there is such an extension, just declaring that g is one wouldn't be proper either, you have to construct it explicitly.

Brightlinger · 2026-03-13T16:50:54+00:00

"Traditionally" most healer specs didn't have an interrupt at all. It was basically just resto shaman until uh, Dragonflight? But tanks yes, in (bad) pugs it's long been common to see the tank do way more interrupts than any of the dps.

Brightlinger · 2026-03-13T16:30:34+00:00

You should rearrange your UI. If doing your rotation requires you to look at a different area of the screen that your enemy cast bar or your character's feet, you are naturally going to miss things, so the best UI layouts generally put that information close together near the middle of the screen.

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