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Number sets - Basic identities

Real numbers : a, b, c
 

  1. Additive Identity 
    a+0=a
  2. Additive Inverse 
    a+(-a)=0
  3. Commutative of addition 
    a+b = b+a
  4. Associative of addition 
    (a+b)+c=a+(b+c)
  5. Definitation of subtraction 
    a-b=a+(-b)
  6. Multiplicative Identity 
    a.1=a
  7. Multiplicative Inverse 
    \(a.{1 \over a}=1, a \ne 0\)
  8. Multiplication Times 0
    a.0=0
  9. Commutative of Multiplication 
    a.b=b.a
  10. Associative of Multiplication 
    (a.b).c=a.(b.c)
  11. Distributive Law
    a(b+c)= ab+aac 
  12. Definition of Division 
    \({a\over b}= a . {1 \over b }\)