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ChatGPT uses auxiliary models to perform certain tasks like basic math and programming. Your explanation about plausibility is simply wrong.
ChatGPT uses auxiliary models to perform certain tasks like basic math and programming. Your explanation about plausibility is simply wrong.
If you fine tune a LLM on math equations, odds are it won’t actually learn how to reliably solve novel problems. Just the same as it won’t become a subject matter expert on any topic, but it’s a lot harder to write simple math that “looks, but is not, correct” than it is to waffle vaguely about a topic. The idea of a LLM creating a robust model of the semantics of the text it’s trained on is, at face value, plausible; it just doesn’t seem to actually happen in practice.
I’m not a physicist, I don’t know one way or another. But it’s possible that there’s a leading explanation for the formation of the universe based on a mathematical model that predicts exactly one big bang.
Based on the comment you’re replying to, I assume they would say “no, nothing materialized from nothing because there wasn’t a ‘before’ in which nothing could have existed”
It wouldn’t have been published, and he’s only relatively famous if you’re a topologist, but it was Charlie Frohman. Not that it must carry the same weight for you, but I value his insight highly, even if it’s just a quip.
Yes, but it proves that termwise comparison with the harmonic series isn’t sufficient to tell if a series diverges.
The assumption is that the size decreases geometrically, which is reasonable for this kind of self similarity. You can’t just say “less than harmonic” though, I mean 1/(2n) is “slower”.
Quoting a relatively famous mathematician, linear algebra is one of the few branches of math we’ve really truly understood. It’s very, very well behaved
Yes, with Iosevka font
Google it? Axiomatic definition, dedekind cuts, cauchy sequences are the 3 typical ones and are provably equivalent.
I’m fully aware of the definitions. I didn’t say the definition of irrationals was wrong. I said the definition of the reals is wrong. The statement about quantum mechanics is so vague as to be meaningless.
That is not a definition of the real numbers, quantum physics says no such thing, and even if it did the conclusion is wrong
Only if you’re trying to get a numerical point evaluation. For example, one can use Fourier series to represent complex signals in terms of sine waves, and then reproduce the sine waves with hardware to reproduce the original signal. This is how a simple synthesizer produces different kinds of tones.
Hom functors exist for locally small categories, which is just to say that the hom classes are sets. The distinction can be ignored often because local smallness is a trivial consequence of how the category is defined, but it’s not generally true
Typst is pretty functional
It’s common to just use “log” in pure math, since nobody uses the base 10 log.
But not all mathematicians are logicians.
That’s not what I meant.
??? You just don’t understand the difference between a LLM and a chat application using many different tools.