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Field axioms

Field axioms and Three equality axioms

QuestionAnswer
Closure under addition axiom x + y is a unique real number
Closure under multiplication axiom xy is a unique real number
Additive inverse axiom x + (-x) =0
Multiplicative Inverse axiom x • 1/x =1 (so long as x does not equal zero
Additive Identity Axiom x + 0 = x
Multiplicative identity axiom x • 1= x
Multiplicative Associative axiom (xy)z = x(yz)
Addition Associative Axiom (x + y) +z = x+ (y + z)
Addition Commutative Axiom x + y = y+x
Multiplicative Commutative Axiom xy=yx
Distributive Axiom x(y + z) = xy + xz
Transitive Axiom of Equality If x=y and y=z then x=z
Symmetric Axiom of Equality If x=y then y=z
Reflexive Axiom of Equality x = x
Created by: egtx
 

 



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