LLMs have already discovered new proofs for math problems that were previously unsolved. Granted, this hasn’t been done with a commercially available model as far a I know, but you are technically wrong to say they will never discover anything new.

Taught should be replaced with trough.

No has said it because it’s not true.

My favorite version of this proof:

Let S be the subset of natural numbers that are not interesting. Suppose by way of contradiction that S is inhabited. Then by the well ordering principle of natural numbers, there is a least such element, s in S. In virtue of being the least non interesting number, s is in fact interesting. Hence s is not in S. Since s is in S and not in S, we have derived a contradiction. Therefore our assumption that S is inhabited must be false. Thus S is empty and there are no non interesting numbers.

A group is not an algebra. A group consists of a single associative binary operation with an identity element and inverses for each element.

A ring is an abelian (commutative) group under addition, along with an additional associative binary operation (multiplication) that distributes over addition. The additive identity is called zero.

A field is a ring in which every nonzero element has a multiplicative inverse.

A vector space over a field consists of an abelian group (the vectors) together with scalar multiplication by elements of the field, satisfying distributivity and compatibility conditions.

A non-associative algebra is a vector space equipped with a bilinear multiplication operation that distributes over vector addition and is compatible with scalar multiplication.

An (associative) algebra is a non-associative algebra whose multiplication operation is associative.

You can read more about these definitions online and in textbooks - these are standard definitions. If you are using different definitions, then it would help your case to provide them so we can better understand your claims.

There’s a general negative attitude towards chromium browsers due to some anticompetitive practices pulled by Google in addition to privacy concerns and probably some more issues I’m not aware of. So that includes chrome, but also edge and most other chromium based browsers.

It is. Either we need guns for protection and it is okay to point them at people in certain circumstances, or we don’t need guns for protection and they should be outlawed beyond certified uses like sport shooting, hunting, and collecting. I don’t understand your seeming belief that guns are okay to own, but not okay to use.

The definition I’m aware of for non associative algebras has them distributive by default, so I believe the chain of equations is valid.

Containers aren’t an alternative to serverless computing. That’s like saying “roads are a scam, I’ll just drive my car instead.” The only serverless compute service they mention, Lambda, literally allows you to deploy custom containers.

It’s not the same, and you kinda answered your own question with that quote. Consider what happens when an object defines both dunder bool and dunder len. It’s possible for dunder len to return 0 while dunder bool returns True, in which case the falsy-ness of the instance would not depend at all on the value of len

Interesting. I think it isn’t unital either otherwise Ω=0.

0=Ω+Ω=Ω+ΩΩ=Ω(1+Ω)=ΩΩ=Ω

For some reason, people will sometimes flip the fraction when calculating decreasing percentages, so this roughly means that the old number of crossings is beyond one hundred percent greater than the current number of border crossings. It’s really dumb

Not sure I understood all the metaphors

🟦🟦🟦🟦

🟨🟨🟨🟨

🟩🟩🟩🟩

🟪🟪🟪🟪

Yeah. That makes sense. It is definitely a real problem.

I respectfully disagree. Its thesis is simply that you can have a better life if you stay alive. The “proof” is simply all the changes the artist went through in order to find a better life. The changes aren’t supposed to be a recipe on how to make your life better - I don’t think the artist is telling people to divorce their spouses. There isn’t anything “just be happy” about getting a divorce.

In the US, I think red pepper could get confused with chili peppers, but maybe that’s just me.

I shot my shot with my bartender. Nine years later and we are married with a kid. Someone’s it works. Oftentimes it doesn’t. Be grateful for all the times it doesn’t work because that’s just one more crappy relationship you don’t have to put up with.

That’s not true. There isn’t anything special about jury nullification. If it happens, it happens and that’s the end of the trial. If the jury is hung because some of the jury members wish to nullify and others don’t, then it will lead to a mistrial simply because the jury cannot come to a unanimous decision - not because of jury nullification. Of course, any verdict can be appealed as usual, but there’s no guarantee the appeal will be granted - even in the case of jury nullification.

No. I’m just wrong, lol

I think that means alcohol poisoning

It actually means tuberculosis