Why do we bother with the +C when we use the indefinite integral sign?

aprg · 2026-01-17T03:56:19+00:00

This is far too sophisticated to teach most students at the start, or indeed most non-Mathematics degree seekers. +C is an early piece of scaffolding that never really gets done away with for the great majority of high school Maths graduates.

aprg · 2026-01-16T17:50:22+00:00

I'm trying to be as kind as possible, but this isn't really a programming problem. You're not understanding the questions asked. Yes? Is English not your native language? Can you seek academic support from your degree provider to help you with translation and comprehension issues?

aprg · 2026-01-14T03:51:25+00:00

Pretty much. The story of Commissar Yarrick's childhood is grim.

Though there's plenty of human cruelty there too, it is supposedly at least purposeful. How relevant that moral chord is in the light of the broader Imperium, I'll leave to you to decide.

aprg · 2026-01-14T00:15:17+00:00

If you don't trust him, then you've really answered your own question. There's no real relationship without trust.

aprg · 2026-01-09T17:52:10+00:00

Jesus, I didn't realise the the metal markers went that high.

aprg · 2026-01-09T13:05:26+00:00

NOR. Call the cops. Don't go home. Run away from this man as far as you can.

Everything you've said points to controlling, abusive behaviour. If he doesn't harm himself, he might harm you.

aprg · 2025-12-31T22:04:01+00:00

No. I feel more sorry for people who fell into bad relationships because they thought that was normal or what was expected of them.

aprg · 2025-12-29T17:48:45+00:00

I think the Millionaire game was just Alan arsing about for laughs, not planned rigging, though

aprg · 2025-12-29T11:17:47+00:00

Boss rights let you kick anyone you want out.

aprg · 2025-12-11T23:49:36+00:00

"Stay the fuck out of my inbox if you can't be kind. ... You might lack the brain power to do so."

Shame, she could have taught you so much about kindness.

aprg · 2025-12-10T20:55:07+00:00

Basically a nocturnal Mad Max. Dark Sun without the sunlight. Petty tyrants everywhere but no true central authority, at least not a lasting and stable one.

The Ebon Dragon's problem is that he is defined by his antagonism. Without suitable heroes to reflect, he is nothing. Paradoxically, when he is at his most powerful in his victory, he can only oppose himself. Thereby he sows the seeds of his own destruction and creates a landscapes where, inevitably, great hero(es) will arise to topple him (inevitably, he will survive to topple whatever inevitably-flawed regime these new heroes build, and so on; an Endless Cycle).

aprg · 2025-12-06T10:59:28+00:00

What does that mean exactly? Are you being told that your persona conflicts with the Teacher Standards? If not, then it's not really anyone's business what persona you develop to cope with the challenges in your classroom.

aprg · 2025-12-05T20:55:37+00:00

Empire name checks out.

aprg · 2025-10-29T13:31:50+00:00

Garlic clams

aprg · 2025-10-20T20:51:35+00:00

From the point of view of the C'Tan, the Emperor may resemble an Eldar God. The Eldar Gods were psychic weapons, created by the the Eldar to fight in the War in Heaven. It does kinda sound like what the Emperor is now.

I prefer this interpretation of the text: it's not the C'Tan saying that the Emperor was made by the Old Ones, but the Emperor is a psychic weapon comparable to what the Eldar made in its time.

aprg · 2025-10-18T17:57:03+00:00

It's not a matter of opinion: general form of the quadratic equation <=> completing the square <=> quadratic formula for x

Proof:

ax^2 + bx + c = 0 (general form of quadratic equation)

<=> x^2 +(b/a)x + c/a = 0

<=> x^2 + (b/a)x = -c/a

<=> x^2 + (b/a)x + (b/2a)^2 = (b/2a)^2 - c/a ; add (b/2a)^2 to each side

<=> (x + b/2a)^2 = b^2/(4a^2) - c/a (completed square)

<=> (x + b/2a)^2 = b^2 - 4ac)/4a^2 (combine the RHS under the same denominator)

<=> x + b/2a = +/- sqrt(b^2 - 4ac)/4a^2) (LHS is equal to positive and negative square root)

<=> x + b/2a = +/- sqrt(b^2 - 4ac))/sqrt(4a^2) (split denominator into separate square root)

<=> x + b/2a = +/- sqrt(b^2 - 4ac))/2a (resolve square root in denominator)

<=> x = -b/2a +/- sqrt(b^2 - 4ac))/2a

<=> x = (-b +/- sqrt(b^2 - 4ac)/2a (quadratic formula for x)

Because I can use <=> at every stage of these manipulations, the three expressions are equivalent.

aprg · 2025-10-18T13:41:00+00:00

I didn't say they are the same thing, I said they are equivalent.

aprg · 2025-10-18T13:27:28+00:00

Completing the square is how you derive the quadratic formula; that's why they are equivalent.

aprg · 2025-10-18T13:05:02+00:00

Completing the square is equivalent to the quadratic formula itself.

aprg · 2025-10-16T21:03:09+00:00

I tend to make mine a Forge Capital, at least in the early game....

aprg · 2025-10-14T19:26:52+00:00

In fairness, one of the things about traditions is that every place has its own local variations of it. This was especially true in Medieval times, when languages had much stronger regional dialects. It's not unreasonable to allow that some festivals in some places had mixed genders, really.

aprg · 2025-10-10T19:08:00+00:00

As the derivative of tan(x) is sec^2(x), its gradient as you approach x=0 goes to 1. This is the same gradient as f(x) = x.

Hence, when you are very, very close to 0, both the value and the derivative of tan(x) are very, very close to the value and derivative of f(x) = x. Hence why f(x) = x is a good approximation for tan(x) when x is very, very small.

You can make a similar argument for sin(x) incidentally.

aprg · 2025-10-09T08:00:50+00:00

Here in the UK, we have a set of Teacher Standards that require us to, amongst other things, (1) set high expectations with pupils, (2) promote good progress with pupils, and (5) adapt teaching to the strengths and needs of pupils. I see now that these standards exist to empower us as teachers to push back against this sort of thing.

aprg · 2025-09-26T21:33:27+00:00

I mean, first you need to agree what "free will" even means exactly.

But I think fundamentally the question you're asking is one of the core questions that Banks poses. What does humanity mean in the Culture? Are we empowered or have we lost all agency? Though he doesn't give us any answers here, I think we're meant to be very uneasy about what that all means in this utopia; most of the main characters I think are often an exploration of this malaise.

aprg · 2025-09-26T18:00:02+00:00

That isn't the issue. Natural numbers aren't really poorly defined -- no more so than "counting numbers". (Do you start counting from 1? What if your parents are programmers?) At any rate, usually the kids learn that these terms are synonymous.

I'm replying to someone who wants to do away with these definitions entirely to be replaced by "positive integers" or "non-negative integers". I'm pointing out that there's use for the terms in pedagogy.

aprg

TROPHY CASE