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Number System

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tanzina_diu:
Fundamental Properties of  Real Numbers (R):

The Closure, Identity, Commutative, Associative and Distributive properties of the real numbers are important because they are the fundamental justification for many of the steps taken in algebraic procedures.

Property   Addition   Multiplication
Closure


Identity


Commutative


Associative


Distributive   If a and b are real then a+b is real

There exists a real number 0 such that a+0=0+a

If a and b are real then a+b=b+a

If a,b and c are real then (a+b)+c= a(b+c)

If a,b and c are real then a(b+c)=ab+ac
   If a and b are real then a.b is real

There exists a real number 1 such that a.1=a

If a and b are real then a.b=b.a

If a,b and c are real then (ab)c= a(bc)

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