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22 Cards in this Set
 Front
 Back
Closure Axiom of Addition

CLAA
If a+b=c, then c is a real number 

Closure Axiom of Multiplication

ClAM
If ab=c, then c is a real number 

Commutative Axiom of Addition

CAA
a+b=b+a 

Commutative Axiom of Multiplication

CAM
ab=ba 

Associative Axiom of Addition

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

Associative Axiom of Multiplication

AAM
(ab)c=a(bc) 

Axiom of Zero for Addition
(Identity for Addition) 
A0A
(Id+) a+0=0+a=a 

Axiom of One for Multiplication
(Identity for Multiplication) 
A1M
(Idx) ax1=1a=a 

Axiom of Additive Inverses

AAI
a+(a)=a+a=0 

Axiom of Multiplicative Inverses

AMI
*A cannot equal 0* a x 1/a = 1/a x a =1 

Distributive Axiom of Multiplication over Addition

DAMA
a(b+c)=ab+ac 

Reflexive Axiom

a=a


Symmetric Axiom

If a=b, then b=a


Transitive Axiom

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


Definition of Subtraction

ab=a+(b)


Definition of Division

a(division symbol)b or a/b = a x 1/b


Binary Operation

A rule for combining two real numbers (or things) to get a unique (one and only one!) real number (or thing)


upside down A

means "for all, for each, for every, for any..."
universal quantifier 

backwards E

means "there exists for at least one, for some..."


backwards E with !

means "there is exactly one x, or a unique x"


straight vertical line

means "such that"


Ring

system in math with these axioms is called a ring
