#flo #disorganized #inclass
1 chapter :clap: review clap
field: group with + and * eg. complex #, real # F: field -- usually real and/or complex
don't need to worry about distributivity!
we are gonna use a lotta fields and not a lot of groups
figure it out in low d then just aplly to high d
addition -> commutative in f1, extrapolate to fn
inhereted comutitivity!
3d vis on 2d means losing info, thus point has a line of points that all fall there
additive and multiplicative identity need to be separate!
any group with zero will not be groups under *! Q*=(Q\{0}, *) pluck out zero
1.0.1 associativity check, with integers!
let \(a,b,c \in Z\)
goal: \(a+(b+c)=(a+b)+c\)
\(a + (b+c) = ( 1+1+1+1+...+1) = ( 1+1+1+1+...+1) + ( 1+1+1+1+...+1) + ( 1+1+1+1+...+1)\)
and then scoot over?
#review
1.0.2 * 3x1 matrices
- equal indicies
no * everything by 1 cus ai !+ ia :(
dot and cross product