Properties of Real Numbers

Let a,b, and c be real numbers



Closure a+b is a unique real number ab is a unique real number

Commutative a+b=b+a ab=ba

Associative (a+b)+c=a+(b+c) (ab)c=a(bc)

Identity There exists a unique real There exists a unique real
number 0 such that number 1 such that
a+0=0+a=a a*1==1*a=a

Inverse For each real number a, For each nonzero real
there is a unique real number a, there is a number -a such that unique real number 1/a
a+(-a)=(-a)+a=0 such that
a*1/a=1/a*a=1

Distributive a(b+c)=ab=ac