notes

In here are the list of things I did for a particular hour or day. Also included here are the screenshots of games I played, or videos I watched or listened to, or just random things I stumbled upon. I'll occasionally write down what I'm thinking, or things I'm planning to do.

[ 2024-02-20 ]

🕑 14:42

🕛 12:16

🕛 12:15

🕚 11:04

🕚 11:02

🕚 11:01

🕚 11:00

10:51 [link] [context] #math

 (x + y)~ = x~y~(x~ + y~)~ 
 x + y    = xy(x~ + y~)
 x00~

 (x^2)~  = x~2
 x~^2    = x~2

 x^(y~)
 sqrt(x) = x^0.5 = x^2~
 cbrt(x) = x^0.333.. = x^3~

 (x^a)x~ = (x^a)(x^-1) =  x^(a-1)

 (x^a)^b    = x^(ab)
 (x^a)(x^b) = x^(a+b)

 x^(n^-1)
 x^(n^m) =? (x^n)^m
 x^(2^3) =? (x^2)^3
 x^8 =? (xx)^3
 x^8 =? xx xx xx

Hmm, the operator ^ is also non-commutative, and non-associative, that's just as crippled as division.

Oh well, for today's morning, I've thought about why 0~ is undefined. Wikipedia gives me a lot of answers, but for some reason it still doesn't sit right with me. I should continue on with the calculus book, anyway, until I find another equation that seems difficult to solve with exponential notation.

I'll probably want to explore logarithms as well later.

🕓 04:55

🕓 04:15

🕒 03:39