Page 2 - (1-1)eng

Elly fat mn 3omry ( 1 – 1 )
Real Numbers

All the numbers that can be represented by points on the number line are called real numbers.
We denote the set of real numbers by .

3 2 31
 1 3.5
4 3 5

– 2 – 1 0 1 2 3 4 5 6 7 8

1 5 5 1 7.6
2 4

The set of natural numbers,  = { 0, 1, 2, 3, 4, 5, 6, …}  '

 2
The set of integers,  = { ... , – 3, – 2, – 1, 0, 1, 2, 3, …} 1  0 3 5
 a  2 2 5 
b
a
The set of rational numbers,  = b : , b  0 – 1 – 4
,
The set of irrational numbers, ' = { x : x   , x   }

Real numbers

Rational numbers Irrational numbers

Integer numbers Non-integer numbers
numbers numbers
Natural numbers Negative integers
numbers

Zero Positive integers
numbers

Inequalities

– 2 is to the left of 1 ; – 1 is to the right of – 4;
Therefore – 2 < 1 Therefore – 1 > – 4

– 5 – 4 – 3 – 2 – 1 0 1 2 3 4 – 5 – 4 – 3 – 2 – 1 0 1 2 3 4

 Note. 7 > 6 and 6 < 7 give the same information even though they are read differently.
 The inequality a  b is read "a is less than or equal to b."


 either a b 
This means: if   is true, then a  b is true.

 or a b 
For example, 2  3 is true because 2 < 3 is true (even though 2 = 3 is not true).

 2  
3
Remember, only one of the two statements   need be true in order that 2  3 be true.
 2  3 

Calculus 1 Unit (1)