Ad4mWayn3

I just imagined the set of countable ordinals, and there's a universe where I'm right

Reading this gave me a headache

So old school of you to play 1.5 instead of 1.6

Freeman's mind is youtube gold. I can't play half-life without imagining gordon being a sociopath asshole.

I mean, just because you implemented something in a low level lang, it doesn't mean you're gonna have the fastest implementation. Even in high level langs, there's usually heavy optimization involved in things that are done all the time (e.g. web servers)

NTA. Your PS4, your rules.

A vibe programmer that built a palm-sized fusion reactor in a cave over the course of 3 months with a single companion? Perfectly respectable to me. And he probably made his own AI too :)

I've always imagined peak programming as building up from low level languages, putting on some layers of abstraction and automatization written by yourself, and end up writing some trivial commands to produce very interesting outputs... Who knows? Maybe throwing around some holograms and voice-commands asking for nonsense. It doesn't get much more vibey than that.

Programming in vim and emacs does look like that lol.

It gets deeper. It's also the same as the 0-k-vector, the 0-k-blade, the 0-multivector, the only number that is its own square besides 1, etc...

0! = 1 isn't an exception.

Factorial is one of the solutions of the recurrence relationship f(x+1) = x * f(x). If one states that f(1) = 1, then it only follows from the recurrence that f(0) = 1 too, and in fact f(x) is undefined for negative integers, as it is with any function that has the property.

It would be more of an exception to say f(0) != 1, since it explicitly denies the rule, and instead would need some special case so that its defined in 0.

Who did ever say that? Not a single article that I've read about Terryology has praised it. I guess the Joe Rogan podcast helped it gather some followers?

Multiplication order in current mathematics standards should happen the other way around when it’s in a non-commutative algebra.

The good thing about multiplication being commutative and associative is that you can think about it either way (e.g. 3x2 can be thought of as "add two three times). The "benefit" of carrying this idea to higher-order operations is that they become left-associative (meaning they can be evaluated from left to right), which is slightly more intuitive. For instance in lambda calculus, a sequence of church numerals n~1~ n~2~ ... n~K~ mean n~K~ ^ n~K-1~ ^ ... ^ n~1~ in traditional notation.

For example, we can’t write 2ω for the next transfinite ordinal because 2ω is just ω again on account of transfinite and backwards multiplication weirdness, and we have to write ω·2 or ω×2 instead like we’re back at primary school.

I'd say the deeper issue with ordinal arithmetic is that Knuth's up-arrow notation with its recursive definition becomes useless to define ordinals bigger than ε~0~, because something like ω^(ω^^ω) = ω^ε0^ = ε~0~. I don't understand the exact notion deeply yet, but I suspect there's some guilt in the fact that hyperoperations are fundamentally right-associative.