hhhhhhh homework in the summer ?
Although I know in Japan they give them such horrors

It sounds like you’re just beginning you journey in higher maths

I’m actually old and lurked in university stuff for a long time and dropped out of engineering in university and started with math all anew, yet at the same time I’m still a beginner.

Hmm. Where did the question in OP come from?

I don’t exactly remember How I started thinking about the “distance between plane and a point formula”, I think I stumbled upon it while organizing my old bookmarks. Tried to make a proof, and in the process that question came, and when I couldn’t solve it on the fly I though like “it’s so over for me”. Then ChatGPT also got it wrong and was like “It’s so over for mankind”. And I ended up making this post to share my despair. Actually many answers were eye opening.

How first reading felt:

How the second reading felt at the beginning:

How it ended up:

What is {y∈V | O(y) = 0} ? If the plane doesn’t pass through $0_V$ then how would that 0 be the image of some point ? Most likely you’re using something from linear algebra that I didn’t learn in my course (I didn’t learn projection I think, only examples when learning matrices).

DUH! If this was math.stackexchange I’d choose this as answer

I tried again, I don’t find mistakes in your statements, I just don’t see how they make up for “instant in-mind proofs” for the problem I think I see it now, nevermind. Your got a very good visualization for 3D CanadPlus. It seems so intuitive that “the set of points that map to H with orthogonal projection is a straight line”, but do you happen to have a pocket proof for that ?

I couldn’t make sense of the first paragraph, are you sure it is right ?

https://www.youtube.com/watch?v=7rkiwtQjlVI

when I say forums, that includes math.stackexchange, please don’t call it shitpost, people there are really something to say the least.

hhhh abstract algebra and proof writing courses.

ChatGPT is trained based on forum discussions and pretty likely pirated books. If it found the idea in a previously established text it would have answered correctly. That’s why I DO think it is representative of what the average good student was taught (not how smart, or good at problem solving they be). What’s funny is that after reasoning it found the right answer, which is counter intuitive, since ChatGPT is supposed to be good at retrieving information, not at reasoning!

I think it is a shame that I’m a math student in university and needed to verify about such a thing. And if we’re talking about people doing physics it might be even worst if they suck like me at 3d geometry.

hmm, I’m not really that interested about the jailbreak part since I don’t ask about politics that much, I use other resources for that.
I’m mainly asking about the GPT-4o access part, if that’s real then, it’s actually big thing.

the Github page also claims that it achieves this, but I can’t understand Javascript to verify myself.