Axioms 1a Flashcards
1
Q
Closure (Addition)
A
x + y
is a unique, real number
2
Q
Closure (Multiplication)
A
xy is a unique, real number
3
Q
Commutativity (Addition)
A
x+y = y+x
4
Q
Commutativity (Mult.)
A
xy = yx
5
Q
Associativity (Add.)
A
(x+y) + z = x+(y+z)
6
Q
Associativity (Mult.)
A
xy(z)=x(yz)
7
Q
Distributivity (Mult. over Add.)
A
x(y+z) = xy+xz
8
Q
Identity (add.)
A
x + 0=x
9
Q
Identity (mult.)
A
x • 1 = x
10
Q
Inverse (add.)
A
x + (-x) =0
11
Q
Inverse (mult.)
A
x • 1/x =1, (x ≠ 0)
