Section 1-2: The Field Axioms - Aishani
(a)(b) = (1*a)(1*b)
Identity multiplication
(ac) * 1/ac = 1
Inverse multiplication
x(y*1/a) * 1/b = x(1/a * y) * 1/b
commutative multiplication
1+2 = 3
definition of addition
cd + 1 + 1 - a = cd + 2 -a
definition of addition
cw (1/b) = cw/b
definition of division
x/y = x * 1/y
definition of division
2(3) = 6
definition of multiplication
a + (-b) = a-b
definition of subtraction
x-y = x + (-y)
definition of subtraction
2x(ac+de) = 2xac + 2xde
distributive for multiplication over addition
2b + 2c = 2(b+c)
distributive multiplication over addition
9(12+9) = 9(12) + 9(9)
distributive multiplication over addition
1 (11 + 4) = (11+4)1
commutative multiplication
c(b+2) = (b+2)c
commutative multiplication
(xy)(1/a * 1/b) = x(y * 1/a) * 1/b
associative multiplication
2 * (5*2) = (2*5) *2
associative multiplication
a*(b * 1/x) * 1/y = (a*b) (1/x * 1/y)
associative multiplication
x(1/a * y)*1/b = (x*1/a)(y*1/b)
associative multiplication
c(b+2) = c(2+b)
commutative addition
6w + 0 = 6w
identity addition
a(bc + 0) -2 = a(bc) -2
identity addition
a/x + 0 = a/x where x is not equal to 0
identity addition
(b+c) * 1 = (b+c)
identity multiplication
b + c * 1 = b + c
identity multiplication
0 = a + (-a)
inverse addition
4(1/4) = 1
inverse multiplication
