Integer Axioms

# Integer Axioms - Term Definition Closure a b are Z or N a b...

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Term: Closure Definition: a, b are Z or N: a+b and a*b are also integers Term: Definition of < Definition: If a, b are Z, a<b if a+n=b for some N, n. Term: Trichotomy Definition: If a is Z, then one of the following is true: a<0 (negative), a=0, a>0 (positive) Term: Positive Integer Definition: If a is a positive Z: then a>=1 Term: Reflexive Property of Equality Definition: a is Z: a=a

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Term: Symmetric Property of Equality Definition: a, b are Z: if a=b then b=a Term: Transitive Property of Equality Definition: a, b, c are Z: if a=b and b=c then a=c Term: Additive Property of Equality Definition: a, b, c are Z: if a=b then a+c=b+c Term: Multiplicative Property of Equality Definition: a, b, c are Z: if a=b then a*c=b*c Term: Transitive Property of Inequality Definition: a, b, c are Z: if a<b and b<c then a<c.
Term: Additive Property of Inequality Definition: a, b, c are N: if a<b then a+c<b+c (not true in Z) Term: Multiplicative Property of Inequality Definition: a, b, c are N: if a<b then a*c<b*c Term: Substitution Principle Definition:

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