2. Real Numbers
A value that represents a quantity along a number
line.
It is a set of undefined elements a, b, c, etc. or
symbollically
R = { a, b, c, … }
It has two basic operation: addition and
multiplication.
5. Properties of Equality
Closure Property
For any real number a, b € R,
a+b € R and ab € R.
Example:
1+2=3
R = {1,2,3}; 1,2,3 € R.
6. Properties of Equality
Commutative Property
For any real number a, b € R,
a+b = b+a and ab = ba.
Example:
4 + 2 = 2 + 4
4 x 2 = 2 x 4
7. Properties of Equality
Associative Property
For any real number a, b, c € R,
(a + b) + c = a + (b + c)
(ab)c = a(bc).
Example:
(4 + 2) + 3 = 4 + (2 + 3)
(4 x 2) 3 = 4 (2 x 3)
8. Properties of Equality
Distributive Property
For any real number a, b, c € R,
a (b + c) = ab + ac.
Example:
4 (5 + 3) = 4 (5) + 4 (3)
9. Properties of Equality
Identity Property
Additive Identity
For any real number a € R,
a+0=a.
Example:
4+0=4
Zero is the identity element for
addition or additive identity.
Multiplicative Identity
For any real number a € R,
a . 1 =a.
Example:
4 . 1 =4
One is the identity element for
multiplication or multiplicative identity.
10. Properties of Equality
Inverse Property
Additive Inverse
For any real number a, there is a
real number called additive
inverse of a denoted by “-a” such
that a + (-a) = 1.
Example:
-(ab) + (ab) = 0
Multiplicative Inverse
For any real number a, there is a
real number called multiplicative
inverse of a denoted by “1/a” such
that a . 1/a = 1.
Example:
4 . ¼ = 1
11. The Real Number System
Real Numbers
Rational Numbers
Integers
Positive
Natural
Numbers
Fractions
Zero Negative
Irrational Numbers