# Math 368

 A1 Addition is associative:(x+y)+z = x+(y+z) for all x,y,z elements of Z A2 Addition is commutative:x+y = y+x for all x,y elements of Z A3 Z has an identity with respect to addition(0) A4 Every integer x in Z has an inverse with respect to addition...(-x) A5 Multiplication is associative(x*y)*z = x*(y*z) for all x,y,z elements of Z A6 Multiplication is commutativex*y = y*x for all x,y elements of Z A7 Z has a identity with respect to multiplication(1) A8 For all integers x,y,z, x*(y+z) = x*y + x*z(distributive laws) P1 If a+b = a+c,then b=c P2 a0 = 0a = 0 P3 (-a)b = a(-b) = -(ab) P4 -(-a) = a P5 (-a)(-b) = ab P6 a(b-c) = ab - ac P7 (-1)a = -a P8 (-1)(-1) = 1 A9 Closure PropertyZ+ is closed in Z wrt + and *If x,y elements of Z+, then x+y is an element of Z+ and xy is an element of Z+ A10 Trichotomy LawFor every integer x, exactly one of the following statements is true:x is an element of Z+-x is an element of Z+or x = 0 Q1 Exactly one of the following holds:a0, then -a<0 and if a<0, then -a>0 Q3 If a>0 and b>0,then a+b>0 and ab>0 Q4 If a>0 and b<0, then ab<0 Q5 If a<0 and b<0, then ab>0 Q6 If a0, then acbc A11 The Well-Ordering PrincipleEvery nonempty subset of Z+ has a smalest element; that is, if S is a nonempty subset of Z+, then there exists "a" element of S such that a < x for all x elements of S Authorsainy ID15210 Card SetMath 368 Descriptionaxioms and properties of integers Updated2010-04-19T21:03:22Z Show Answers