The difference between cooking something in a pot and coverings it completely with clay is that the clay can be completely closed, meaning it is a sort of a pressure cooker, while a normal pot will always have some air escaping underneath it's lid

This is interesting, but it doesn't answer any of OP's questions

No offence, but this doesn't actually explain anything. You use a lot of words to say "stars don't fuse iron because they can't".

You even have to throw away your analogy at the end, because it doesn't make sense.

I don't understand why people think ELI5 means they should anthropomorphise stuff. Sometimes that's useful, but sometimes (like now), it just serves to cover the fact that you didn't explain anything. "I don't actually know, little Timmy, but here's a nice story to occupy your mind, so you don't have time to ask any more questions."

Because they are useful for describing certain things. For example, they are heavily used in electrical engineering and signal processing, because you want to work in two dimensions, and imaginary numbers are a convenient way to do that.

But the question is itself nonsensical. Nothing man-made needs to do exist. Negative numbers don't need to exist, you could just say there's no solution. Fractions don't need to exist, you could just say there's no solution. Natural numbers don't need to exist, you could just not count things. Language doesn't need to exist, we could just not speak, plenty of animals get on with their lives just fine without a language.

People really get hung up on the word "imaginary", and it drives them crazy, but it's just a name. Real numbers aren't any more or less real than imaginary numbers. Natural numbers aren't more or less natural than integers. Rational numbers don't have a mental capacity, and irrational numbers don't run around making dumb decisions. A turing machine isn't actually a machine with cogwheels inside. They are all made up, and they are all just names we gave them.

Not to be mean, but this is a terrible question for this subreddit. You could have just looked it up on wiki dictionary (or any dictionary).

In very simple terms, overfitting is when a model appears to work very well on one datatset, but it completely breaks down on another one. Usually this means that it performs well on the training and validation sets used during development, but it doesn't actually work when it's given data that it's actually supposed to process in practice. That's why it's bad: it ends up being useless.

What overfitting actually is depends on the model, but in general it means that the model has learned to exploit some peculiarity of the training dataset that is not present "in the wild". For example, if you were training a model to look at pictures of people and tell you wether they have blue eyes or not, and every single blue eyed person in your training datatset had blonde hair, the model could learn to actually recognize blond hair. Then if you gave it a picture of a brown haired, blue eyed person, it would tell you that they don't have blue eyes.

Ok buddy, what happens if it isn't a right triangle? Never heard of a rhombus?

Also, you keep using the words "formal algebra". I don't think they mean what you think they mean.

The question is if you make a Thales triangle, is it a right triangle? You start by assuming that if you have a right triangle, then you flip it over the hypothenuse, and you get a rectangle. Well, of course you do, it was right triangle to begin with! If it wasn't a right triangle, and you did your construction, you wouldn't get a rectangle.

The proof is the "reason and logic" behind it. I understand what you're asking, but that's just not how math works. You want some pretty, intuitive reason for why it is true, but not every proof in math is elegant like that. Plenty of things just work becuase you show they do, and it's not always pretty, clear, or obvious. Sometimes you make a bunch of reductions and inferences, most of them seemingly completely unrelated, until you go from what you know to be true, to what you want to prove to be true. And it's not pretty, and it's hard to follow, and it challenges some people's notion of math being this elygant, aesthetically pleasing set of rules that are somehow hidden in the universe, and we have to discover them.

That's not how math works. It wasn't hidden in the world by God. Humans made it up, and sometimes, even if we start from something simple and pretty, and we end at something simple and pretty, the journey may be complicated and ugly. And we just have to deal with it.

So yeah, you can look up the proofs online, no need for someone to transcribe them here, but there's no guarantee you will like them. They are not meant to be elegant, they are just meant to be correct.

This assumes the triangle was already a right triangle. Circluar (pun intended) reasoning. Also it only explains those two specific triangles.

Your question is a little unclear. What does "what happens with an education system" mean?

I've genuinely never seen this happen, maybe you should ask the people that you've seen doing this. But here's my best guesses:

1. In English, you capitalize letters of "words that carry meaning" (I don't know the correct term, but I mean nouns, verbs, adjectives and such, but not prepositions and such) in a title. For example you would write "The Lord of the Rings". The first "the" is capitalized, because it's the first word of the sentence, and "lord" and "ring" are capitalized because they are nouns.

2. In german, all nouns are capitalized, not just the first word in a sentence, so if you saw germans do it, it might be a that.

Yes, that is called eugenics, and it is generally frowned upon.

Also, how do you propose we would do that? I feel like from the past few years we should all know that this is not only not a trivial matter, but also basically impossible. We couldn't even get people to take a disease that was killing thousand s of people every day in front of them and majorly disrupted their lives seriously. How do you think people would treat a disease that doesn't affect them in basically any way? What's more, we couldn't even get people to take very simple measures to pyevent it, how do you think everyone would react to what you're proposing?