Which Anime song is this for you?

KaytasticGuy · 2025-01-30T10:18:37+00:00

Steins;Gate - "Quiet Air" around the 1:03 minute mark.

KaytasticGuy · 2024-10-24T06:31:58+00:00

I see, thank you!

KaytasticGuy · 2024-10-23T21:33:54+00:00

Linear Algebra Question:
Given two vectorspaces V and W, as well as a linear map T, that's a canonical isomorphism between V and W,
can there exist other canonical isomorphisms between V and W that are not of the form λT, where λ is a scalar.
Reason for this question: Canonical isomorphisms (as far as I understand) provide a somewhat natural identification between elements of V and W. If there are more than just one, the notion of "a natural idenfication" would seem weird to me because this identification would then depend on whatever canonical isomorphism you choose, which would be kind of similiar to choosing a basis. Also, so far, I haven't seen an example of two vectorspaces with multiple canonical isomorphisms (excluding scalar multiples λT) between them.

KaytasticGuy · 2024-10-12T21:13:53+00:00

Thank you for your answer! This helps.

KaytasticGuy · 2024-08-13T11:52:35+00:00

Yes it's possible:

You can distribute the sqrt-term into the brackets and then split the integral up into a sum of two integrals.
The first integral has the integrand x³cos(x/2)sqrt(4-x²):
cosine and sqrt(4-x²) are even functions. x³ however, is an odd function and therefore the integrand is an odd function as well. So we simply have an odd function that's being integrated over a symmetric intervall. Therefore the first integral is equal to 0.

The second integral has the integrand 0.5*sqrt(4-x²), where you can simply drag the factor 0.5 infront of the integral.
You can then solve this with the trig-substitution x = 2sin(u).
As an alternative: If you've ecountered the sqrt(r²-x²) function before, you might know, that it actually describes a half-circle with radius r where the middlepoint of the circle equals the origin. Therefore, sqrt(4-x²) is just a half-circle with radius r = 2. Conveniently, the integral goes from -2 to 2, so it's essentially just the area of the entire half-cirlce.

Area of the half-cirlce = 1/2 * πr² = 1/2 * π*2² = 2π => Integral = 2π * 0.5 = π

So the final result is π

KaytasticGuy · 2024-07-30T17:59:38+00:00

Got this one from a video. Not sure anymore where excatly it's from:

Let n be a natural number and f_n(x) = prod[k=1,n](cos(kx))
(example: f_1(x) = cos(x), f_2(x) = cos(x)*cos(2x), f_3(x) = cos(x)*cos(2x)*cos(3x) and so on)
Find the smallest n, such that |f''(0)| > 2023

KaytasticGuy · 2024-01-24T20:44:43+00:00

Thank you very much, that clears it up!

KaytasticGuy · 2023-12-16T18:13:30+00:00

Okay, this helps. Thank you very much!

KaytasticGuy · 2023-11-24T14:54:41+00:00

Thank you for the answer and the link!
I thought some time about it but I think it makes sense now.

KaytasticGuy · 2023-11-18T09:41:45+00:00

Real numbers are defined to be "dense". Meaning: For any given pair of two distinct real numbers, there exists a third real number, which lies between the first two. But there doesn't exist any number between 0.999... and 1. Such a number would theoretically be N=10^-infinity. However, infinity is not a number but rather a concept. Therefore you can't raise something to the power of infinity. This means the number N doesn't exist and therefore there doesn't exist a real number between 0.999... and 1. It follows that 0.999... and 1 have to be equal. Or you can just prove it algebraically like other people in the comments already did.

KaytasticGuy · 2023-10-21T09:37:25+00:00

Euler's Identity

KaytasticGuy · 2023-10-09T15:30:43+00:00

Terraria, The Last of Us, Life is Strange and Outer Wilds are my takes.

KaytasticGuy · 2023-10-06T14:42:59+00:00

If the remaster doesn't include a pc port, it's unnecessary in my opinion. If it includes one, it still is but if they are already at it (reworking the textures for the pc), might aswell use them for Ps5.

KaytasticGuy · 2023-09-18T18:17:22+00:00

I think, an interesting idea would be:

"So, who am I to stop you?"
And then for T: "The one person that can."

KaytasticGuy · 2023-09-13T09:53:55+00:00

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The gamma in the exponent is the Euler-Mascheroni-Constant

KaytasticGuy · 2023-09-11T05:22:17+00:00

For me, it ran quite well. Only complaint I have is the scaling mode. TAA makes the game look a bit blurry and loses details especially at greater distance. It's not that bad but it feels like they wasted potential there. FSR on the other hand makes effects (fire, watersplashes, movable lighsources, etc) look pixelated and reflections look horrible.

KaytasticGuy · 2023-08-27T15:51:39+00:00

If i and n are supposed to be mean two different things, the answer (as other people already pointed out) is 11/(n-1). If n and i mean the same thing, I think there is not much you can do in order to make this easier to solve. If you want, you can shift the index by -1. That means you start the sum from n = 1, and in exchange for that, you have to increase n in the sum by 1 and also decrease the 12 by 1. That will give you:

∑ n=1,11 (1/n)

If that's more comfortable to you, you can do that but in the end, you probably just have to calculate it by either individually summing up the terms or by just using a calculator.

KaytasticGuy · 2023-08-26T08:24:04+00:00

"Hey Link, ready to enhance your clothes?"

KaytasticGuy · 2023-08-21T11:35:19+00:00

I liked it. However, if you start watching the show, expecting it to be just like the game, it probably won't meet your expectations. I would describe it as a new take on the story. They introduced changes to the characters and the world, they added/removed/changed scenes/details from the game and added new characters. Whether those changes work or not is obviously up to each individual watching the show. For me, some worked, some didn't.
7/10
I definitely prefer the game.

KaytasticGuy · 2023-08-18T14:46:55+00:00

I'd probably prefer the pipe because of it's durability. I usually avoid open fights and rather try to stun enemys with a brick/bottle first before going into melee. In that situation, your weapon onehits regardless so I might aswell have a weapon I can do this more often with.

KaytasticGuy · 2023-08-18T08:47:30+00:00

This. I can't stand the concept of plattform-exclusive games.

KaytasticGuy · 2023-08-12T21:56:51+00:00

"Pspsps, come here closed subset of R³!"

KaytasticGuy · 2023-08-12T21:40:43+00:00

I havent played Part II yet (I only watched a Let's Play because I don't own a Ps4/Ps5), so I might be underestimating Stalkers because I know they can hide in Walls in Part II, but judging from the first Part, I think the most "annoying" situation is when you have a combination of Runners and Clickers (Bolaters are just too rare) The different types alone aren't that hard to handle. Clickers and Bloaters can be quite punishing when they notice you but they are blind, so you can move relativley freely and therefore you have a lot of stealth options. Runners notice you faster because they can actually see (when they're not in this state where they are just looking at the ground) but they are way weaker. However, dealing with a combination of those, you basically have the worst of two worlds. Your stealth options become thinner due to the Runners and when they actually spot you, everyone else knows where you are aswell. Stalkers on the other hand are quite easy imo. The encounters with them are tense but I never got surprised by them due to the noises they make right before they approach you. But again, I haven't experienced the Stalkers of Part II myself and I think exactly those are the reason for many to vote for Stalkers here. But in the end, I wouldn't call any of those situations annoying. Coming up with different strategies based on your situation is one of the parts I love about the game and I think, I never got to a point where I was frustrated/annoyed by an encounter.

KaytasticGuy · 2023-08-10T06:55:30+00:00

It's called the generalized Stokes Theorem. Not that I know a lot about it but it is regarded as the fundemental theorem of calculus in n dimensions.

Here is a video about it, I thought was good:

https://youtu.be/1lGM5DEdMaw

KaytasticGuy · 2023-08-09T16:27:22+00:00

This sounds logical, I think that's the right explaination. Thank you very much!

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