cruegge

5 ms·

1.
by cruegge 6mo ago
Correct me if I'm wrong, but I don't think humans are reptiles, phylogenetically. The Synapsida (containing mammals) and Sauropsida (containing reptiles) are sibling groups inside the Amniota.
2.
by cruegge 7mo ago
Probably Majutsu, https://github.com/0WD0/majutsu
3.
by cruegge 11mo ago
They're not infailable, though. For example, TeX's primitive for fractions is actually {a \over b}, LaTeX's \frac is a macro on top of that. The consequence is that while typesetting a formula, the engine does not know the cu
4.
by cruegge 2y ago
I think a = sqrt(2), b = log(9)/log(2) with a^b = 3 is easier. To show that b is irrational, assume b = n/m for integer n, m. Then 9^m = 2^n, which can't be the case since the lhs is odd and the rhs is even.
5.
by cruegge 3y ago
> Yes, I thought this was clear from my statement. Yeah, sorry, wasn't really necessary to repeat that point. I was too focused on the "limiting the height of the tree to 32" formulation. I have to admit that I don't
6.
by cruegge 3y ago
It's not limited to 32, but afterwards search will be linear along child[0]. Using rotation would not make a difference, since you're in the collision case already, so you would effectively always branch to the same child for leve
7.
by cruegge 4y ago
A more advanced example of mutual recursion: it's possible to perform an exhaustive search over the "Cantor space" of all infinite sequences of bits that either finds a sequence satisfying a (total, computable) predicate or d
8.
by cruegge 4y ago
Ok, the more I try to understand this, the more confused I get. Probably just scrap everything I said, I'll need to do some more reading.
9.
by cruegge 4y ago
I see. Checking the formulation of the incompleteness theorem again, I noticed that I probably misunderstood something here: it indeed essentially requires proofs to be verifyable, which second order theories do not provide. So second order
10.
by cruegge 4y ago
What I meant to say is that multiple models are not the only reason for something to be true but unprovable, the incompleteness theorem also holds in more general conditions. Concerning multiple models of ZFC: I'm always confused by su
11.
by cruegge 4y ago
That's a good intuition for first order PA, where the completeness theorem holds, but not the full story either. PA in second order logic only has a single model, but is still incomplete: there are statements that are true in the only
12.
by cruegge 4y ago
If found “TeX by Topic” a great introduction, it's less overwhelming than the TeX book. Also really helpful in wrapping your head around macro expansion is the `texdef` cli tool, which allows you to quickly evaluate a line of macro cod
13.
by cruegge 6y ago
It does double the residue, but modulo 19. 2 * 18 = 36 = 17 (mod 19) and 2 * 10 = 20 = 1 (mod 19). The reason is that the method consists essentially of two steps. (1) Subtract a suitable multiple of 19 to make the number a multiple of 10.
14.
by cruegge 8y ago
They have an FAQ item concerning that: https://jmap.io/#why-is-it-not-rest-based ?