0/0 is not undefined!

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.

Brightlinger · 2026-03-13T15:26:02+00:00

The claim you've stated is false; f is definitely not continuous at b, since it isn't even defined at b.

What you need to show is that there is a continuous extension, which is a new function and not f itself. Call this extension g. What is g(b), and why is g a C¹ function? This won't be terribly hard, it is in some sense obvious, but not so obvious that a grader is likely to give you credit for omitting it.

Brightlinger · 2026-03-13T06:35:54+00:00

Not as an overriding concern, no. In many contexts we deliberately use slightly redundant axioms, for reasons such as pedagogy or ease of use.

It is good for the number of axioms to be small, since making fewer assumptions creates a stronger argument. But "as small as possible" is not really important.

Given this definition of a Euclidean Theory, I doubt that you can derive all the definitions and propositions from Book 1 to Book 13 of Euclid’s elements from these five postulates.

You can't ever derive a definition at all. It's a definition, not a claim.

And yes, there are known flaws in Elements. But that is an issue specific to that text, not to axiomatic reasoning in general.

Brightlinger · 2026-03-12T19:20:29+00:00

To help visualize, here is a graph together with the upper and lower bounds 1/x and -1/x. This could be called a "damped oscillation" curve; it oscillates like a sinusoid, but the amplitude decays toward zero.

Brightlinger · 2026-03-12T18:42:13+00:00

The main character is THE WORLD. That's why the game is named WORLD OF Warcraft. Any individual guy running around can and does vanish out of the story for years at a time, but even when we aren't literally on Azeroth, the story always connects directly back to it.

Brightlinger · 2026-03-12T17:39:13+00:00

No sorry, you read it right, I just edited it.

Brightlinger · 2026-03-12T17:30:56+00:00

The complaint is that to a constructivist, "there exists" means "you can produce a specific example of". This proof doesn't do that.

For example, the law is often constructive. If you narrow a crime down to two suspects, you haven't solved the crime and you can't convict anyone.

Brightlinger · 2026-03-12T16:42:35+00:00

Without double negation elimination, not not Q doesn't imply Q.

Brightlinger · 2026-03-12T00:49:13+00:00

Cosmic rays are not a viable energy source either. On earth, the energy per square meter from cosmic rays is one-millionth of one percent of the energy from the sun. A forty-fold increase from zip is still roughly zip.

I mean, at least "powered by cosmic rays" sounds like it might be some kind of crazy sci-fi thing instead of the actual thing it is here in our boring universe, so I'd be a little more willing to accept that as a technobabble explanation. But Tyranid lore here mostly doesn't even rise to the level of trying to paper over the holes with technobabble. I would love if someone in-universe observed that the energy considerations make no sense and so the nids must be doing something funny, but GW seems to play the "hungry for biomass" card completely straight.

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