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a+b = b+a
Commutative addition
ab = ba
Commutative multiplication
a+(b+c) = (a+b)+c
Associative addition
a×(b×c) = (a×b)×c
Associative multiplication
x(a+b) = ax+bx
Distributive
a+0 = a
Identity addition
a(1) = a
Identity multiplication
a+b is real
Inverse addition
a×1/a = 1
Inverse multiplication