Real Numbers

Real Numbers
Types of Real Numbers ? 1. Natural numbers N={1,2,3,4,?}
Z={0,?1,?2,?3,?4,?} 2.Integer numbers
3.Rational numbers Q
r=m/n ? m?Z ,n?N
Examples
1/2 , 5/3,-16/5,4=16/4,0.2=2/10
4.Irrational Numbers: These are numbers that cannot be expressed as a ratio
of integers.
Examples
?2 ,?5 ,? ,2^?3 , e

Certain sets of real numbers, called intervals, occur frequently in calculus and correspond geometrically to line segments. If a < b , then the open interval from a to b consists of all numbers between a and b and is denoted by the symbol (a,b). The closed interval from a to b includes the endpoints and is denoted [a,b]. Using set-builder notation, we can write

Certain sets of real numbers, called intervals, occur frequently in calculus and correspond geometrically to line segments. If a < b , then the open interval from a to b consists of all numbers between a and b and is denoted by the symbol (a,b). The closed interval from a to b includes the endpoints and is denoted [a,b]. Using set-builder notation, we can write