Yes it's "likely" to be transcendental, maybe there are some evidences that support this, but this is not a proof (keep in mind that it isn't even proven to be irrational yet). Similarly, most mathematicians/computer scientist bet that P ≠ NP, but it doesn't make it proven and no one should claim that P ≠ NP in some article just because "it's most likely to be true" (even though some empirical real life evidence supports this hypothesis). In mathematics, some things may turn out to be contrary to our intuition and experience.
It comes with the explicit comment "Not proven to be transcendental, but generally believed to be by mathematicians."
That's really all you can do, given that 3 and 4 are really famous. At this point it is therefore just not possible to write a list of the "Fifteen Most Famous Transcendental Numbers", because this is quite possibly a different list than "Fifteen Most Famous Numbers that are known to be transcendental".
So "Fifteen Most Famous Transcendental Numbers" isn't the same as "Fifteen Most Famous Numbers that are known to be transcendental"?
I might be OK with title "Fifteen Most Famous Numbers that are believed to be transcendental" (however, some of them have been proven to be transcendental) but "Fifteen Most Famous Transcendental Numbers" is implying that all the listed numbers are transcendental. Math assumes that a claim is proven. Math is much stricter compared to most natural (especially empirical) sciences where everything is based on evidence and some small level of uncertainty might be OK (evidence is always probabilistic).
Yes, in math mistakes happen too (can happen in complex proofs, human minds are not perfect), but in this case the transcendence is obviously not proven. If you say "A list of 15 transcendental numbers" a mathematician will assume all 15 are proven to be transcendental. Will you be OK with claim "P ≠ NP" just because most professors think it's likely to be true without proof? There are tons of mathematical conjectures (such as Goldbach's) that intuitively seem to be true, yet it doesn't make them proven.
Sorry for being picky here, I just have never seen such low standards in real math.
You are not picky, you just don't understand my point.
"Fifteen Most Famous Transcendental Numbers" is indeed not the same as "Fifteen Most Famous Numbers that are known to be transcendental". It is also not the same as "Fifteen Most Famous Numbers that have been proven to be transcendental". Instead, it is the same as "Fifteen Most Famous Numbers that are transcendental".
Again, it seems we are arguing because of our subjective differences in the title correctness and rigor. Personally, I would not expect such title even from a pop-math type article. At least it should be more obvious from the title.
"Transcendental" or even "irrational" isn't a vibesy category like "mysterious" or "beautiful", it's a hard mathematical property. So a headline that flatly labels a number "transcendental" while simultaneously admitting "not even proven" inside the article, looks more like a clickbait.
Not sure why you would think that anyone thinks that transcendental is a "vibesy" category, or why you would think that you are more invested in the "hardness" of mathematical properties than anyone else here.
You clearly still don't understand. And to call the title "clickbait" is pretty silly.
Unfortunately IDEs are not yet directly connected to our minds, so there's still that silly little step of encoding your ideas in a way that can be compiled into binary. Playing the broken telephone game with an LLM is not always the most efficient way of explaining things to a computer.
> “Tact is the art of making a point without making an enemy." - (supposedly) Isaac Newton
Never heard of this quote, but I could certainly use a large dose of tact as defined above! The quote seems to be due to an advertising executive though, Howard W. Newton, not Isaac Newton [1].
I can relate, thanks for sharing. Indeed, that doesn't sound like something that Isaac Newton[^1] would say :-)
[^1]: My idea of Isaac Newton comes from Stephenson's novel. But I trust that Mr Stephenson's research because it aligns with Newton's other quotes (i.e. "standing in the shoulder of giants" is nice but he's calling another man a moron, eloquently) and the his relationship with Leibniz wasn't the one I would expect.
Yes, I am wondering if opaque types would be difficult to implement somehow in TypeScript? It should really be part of TypeScript if at all reasonably possible.
I'm not that familiar with the TS internals. They'd have to add a keyword to the language which could break stuff. The smart move would be to reserve the `opaque` word a few versions in advance of introducing the feature that gives it a meaning
Dude. You take money from Google. Really? All the people ranting about AI, but taking pay checks from Facebook, Amazon, Google, Microsoft, ... Hypocrisy much?
I for once enjoy that so much money is pumped into the automation of interactive theorem proving. Didn't think that anyone would build whole data centers for this! ;-)
When Go was launched, it was said it was built specifically for building network services. More often than not that means using protobuf, and as such protobuf generated code ends up being a significant part of your application. You'd have that problem in any language, theoretically, due to the design of protobuf's ecosystem.
Difference is that other languages are built for things other than network services, so protobuf is much less likely to be a necessary dependency for their codebases.
What I've found over the years is that protobuf is actually not that widespread, and, given that, if you ignore gogoprotobuf package, it would generate terrible (for Go's GC) structs with pointers for every field, it's not been terribly popular in Go community either, despite both originating at Google
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