Algebra 2: Basic Properties of Real Numbers and Operations

Closure

If a and b are real numbers, then a+b∈R and ab∈R.

Commutative (+)

a+b=b+a

Commutative (x)

ab=ba

Associative (+)

a+(b+c)=(a+b)+c

Identity (+)

a+0=a or 0+a=a

Inverse (+)

a+(−a)=0

Inverse (x)

a⋅1/a=1

Distributive

a(b+c)=ab+ac

Reflexive

a=a

Transitive

If a=b and b=c, then a=c.

Def. of Subtraction

a−b=a+(−b)

Symmetric

If a=b, then b=a.

Def. of Division

a÷b=a⋅b⁻¹

Add. POE (Addition Property of Equality)

If a=b, then a+c=b+c.

Mult. POE (Multiplication Property of Equality)

If a=b, then ac=bc.

Mult. Prop. of 0 (Multiplication Property of Zero)

a⋅0=0

Associative (x)

a(bc)=(ab)c

Identity (x)

a⋅1=a