REAL NUMBERS DEFINITION Real Numbers mean that they are the collection of both rational and irrational numbers.

They can be represented in a real line. The diagram below shows the types of real numbers: EXAMPLES Irrational Numbers: √2 , π , 2.3236 . . . Rational Numbers: 2/3 , -5/4 , 3.8 , 2 , -3 , 2 1/5 Integers: . . . -3 , -2 , -1 , 0 , 1 , 2 , 3 . . . Whole Numbers: 0 , 1 , 2 , 3 . . . Properties of Real numbers Addition Multiplication

For all real a, b a + b = b + a Associative: For all real a, b, c a + (b + c) = (a + b) + c Commutative: Closure: a+b is a real number Identity: a+0=a, 0+a=a Inverse: a+ (-a)=0 Closure: ab is a real number Commutative:

ab=ba Associative: (ab)c = a(bc) Identity: a x1 = a, 1xa = a Inverse: a x 1/a = 1, a ≠ 0 Distributive: a(b+c) = ab + ac

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# Real Numbers

Presentation on Real Numbers