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22 Cards in this Set
- Front
- Back
Closure Axiom of Addition
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CLAA
If a+b=c, then c is a real number |
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Closure Axiom of Multiplication
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ClAM
If ab=c, then c is a real number |
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Commutative Axiom of Addition
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CAA
a+b=b+a |
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Commutative Axiom of Multiplication
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CAM
ab=ba |
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Associative Axiom of Addition
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AAA
(a+b)+c=a+(b+c) |
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Associative Axiom of Multiplication
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AAM
(ab)c=a(bc) |
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Axiom of Zero for Addition
(Identity for Addition) |
A0A
(Id+) a+0=0+a=a |
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Axiom of One for Multiplication
(Identity for Multiplication) |
A1M
(Idx) ax1=1a=a |
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Axiom of Additive Inverses
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AAI
a+(-a)=-a+a=0 |
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Axiom of Multiplicative Inverses
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AMI
*A cannot equal 0* a x 1/a = 1/a x a =1 |
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Distributive Axiom of Multiplication over Addition
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DAMA
a(b+c)=ab+ac |
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Reflexive Axiom
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a=a
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Symmetric Axiom
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If a=b, then b=a
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Transitive Axiom
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If a=b and b=c, then a=c
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Definition of Subtraction
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a-b=a+(-b)
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Definition of Division
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a(division symbol)b or a/b = a x 1/b
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Binary Operation
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A rule for combining two real numbers (or things) to get a unique (one and only one!) real number (or thing)
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upside down A
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means "for all, for each, for every, for any..."
universal quantifier |
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backwards E
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means "there exists for at least one, for some..."
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backwards E with !
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means "there is exactly one x, or a unique x"
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straight vertical line
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means "such that"
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Ring
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system in math with these axioms is called a ring
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