Right, the real world doesn’t blow up. So if N-S does then it means in some situations it doesn’t model the real world well. That’s important because if we can understand those situations we can avoid erroneously relying on it.
Limits can be defined within finitism as long as the end result is finite. Essentially it’s just a process which lets us get as close to 2 as we want.
A better example would be a limit that equals sqrt(2) which finitists would probably say cannot represent a real object because it is only defined as the end of an infinite process.
300 songs is not many at all. I have purchased around 20,000 songs in my life. Would it have been cheaper to use Spotify? I suppose so but (a) they don’t have all the music I want and (b) I prefer having the independence to control my media. Also Spotify didn’t exist when I started :)
300 songs might not sound like many, yet that is how many items have been added to my library or to a playlist in 12 years.
So I can't really speak to anything else than that. That's my usage pattern, yours may be different.
I keep yearly playlists (starting 2023) where I add songs I like and each one is only about 30 songs on average, so that somewhat matches the aggregate number over a decade..
I guess I stick to the things I like and find things I like in DJ sets or on the Gym radio- I'm not investigating new music through subscription services.
LLMs seem to be much better at finding counterexamples than other types of proof. It’s unlikely the other millennium problems will be solved with counter examples
Finding counter examples might be easier, but AI's also useful for assisting in creating proofs. For example, Anthropic just published a formalization of Fermat's last theorem a few days ago, something that human researchers have been working on for decades.
Isn’t that how research works? You build on what others have done. I don’t understand the big deal. I’d rather have the result available sooner than later just to assuage some egos
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