Real Numbers
Set :- A set is a collection of objects called elements or members of a set.
Finite set :- if we can count the number of elements in the given set then it is a finite set.
Example: {1,2,3,4,5}
Infinite set :- if we can’t able to count or list all the elements of the set , it means it is a infinite set.
Example :
N = {1,2,3,4…..} , this set is called the natural numbers.
If we include a 0 in the natural number set , new set will be a set of whole numbers.
W = {0,1,2,3,4….}
Empty set :- if a set containing no elements, is called the empty set or null set.
We write it as ф or {}
Do not write { ф } for empty set, { ф } is a set with a element ф.
Set builder notation:- it is use to show the property of set x or to defined the sets of numbers.
Example : {x|x is natural number between 9 and 20}
We read it as “the set of all elements x such that x is natural number between 9 and 20”.
Above set is {10,11,12,13,14,15,16,17,18,19}
Sets of numbers :
Natural numbers or counting numbers
{1,2,3,4,5,6,7,…….}
Whole numbers
{ 0,1,2,3,4,5,6,7,…….}
Integers
{……….-4,-3,-2,-1,0,1,2,3,4,…….}
Rational numbers
{
p and q are integers, q 
0 }
Irrational numbers
{ x|x is a real number that is not rational }
Real numbers
{x|x is represented by a point on a number line}
Additive Inverses: – For each positive number, there is a negative number on the opposite side of 0 that lies the same distance from 0 on the number line. These pairs of the numbers are called additive inverses, negatives, or opposites of each other. For any real number a, the number –a is the additive inverse of a.
Absolute value:- absolute values represents the distance of the number from the 0 point on the number line, it is always positive as distance is always positive.
Absolute value of a or –a is |a|.
