there are plenty of them where I go “idk how to do this at all” and explode
yeah idk how to do that one at all
how would you transfer and keep safe a button that if you press somebody you don’t know dies
there’s at least one story where this is why the scp foundation was created (i think it’s a joke scp?)
my thought process was basically like
v in S means there’s a, b in S so that a x b = v, but then b x a = -v, so -v is in S. so v in S implies -v in S.
v in S means -v in S means v x -v = 0 in S (yeah I could’ve just used v twice but uhhhhhhh oops)
v in S implies the magnitude of v is one, because if the magnitude of v is greater than 1, then a x b = v implies |a||b|sin(theta_a_b) = |v| which means at least one of a, b have a magnitude greater than one, and then I can snowball infinite vectors out of that with ever increasing magnitudes
same with if v’s magnitude is less than one (here is where I forget about the sin(theta_a_b) possibly breaking this. but uhhhhhh nya)
then that means v, w in S → v, w are orthogonal, because if they weren’t orthogonal their cross product would have a magnitude less than one
then you can be like “ok so WLOG let i be in the set. then -i’s in it, and then j, k, -j, and -k are in it, and so is 0, and nothing else fits, so 7 is the max”
im not sure the government would take a button off the hands of a loser who says it’ll kill somebody if pushed
(I did not realize this at the time but this is false. but uhhhhhhh it doesn’t matter because the other option is having vectors that are rotated versions)
i’m not quaternionpilled enough for this shit
I haven’t done quaternions
this is just what we called them in calc 3 (at least sometimes)
but the n = 1 case with just the 0 vector still works right
yeah it does
right we did also call them that
i’m rusty as fuck
not 7 is the max
7 is mandatory*
(assuming n isn’t 1 (which I forgot at that moment
))
it feels like the problems with less to work with are nicer tbhtbhtbhtbhtbhbthb
like
it means there’s not a bunch of false directions to go in
Someone tell me to sleep who isn’t zug
Reason zug can’t is they are here rn
