There are many types of numbers, arranged in sets such as Natural numbers, Whole numbers, Integers, Rational numbers, Irrational numbers etc.
Natural numbers:
The set of natural numbers is denoted by N, begins with 1 and contains all the numbers which are used for counting.
N = {1,2,3,4,5 ,…}
Whole numbers:
The set of whole numbers denoted by W, has all the natural numbers and also a zero.
W={0,1,2,3,4,…}
Additive inverse of a natural number:
The additive inverse of a number x is –x.
Example: The additive inverse of 4 is -4
Note:
a) The sum of a number and its additive inverse is zero.
Example: 4+ (-4) =0.
b) The aditive inverse of 0 is 0. Because 0+0=0.
Integers:
The set of integers denoted by Z or I, is the set of all the whole numbers and their additive inverses.
Z or I = {…, -3, -2, -1, 0, 1, 2, 3,…}
Rational number:
The set of rational numbers denoted by Q contains the numbers of the form p/q, where p and q are integers and q≠0.
Examples:
Insertion of rational numbers:
There exists infinite number of rational numbers between any two real numbers.
Example: Find any two rational numbers between 2.1 and 3.5.
Solution:
The average of 2 numbers lies between those 2 numbers.
Average of 2.1 and 3.5= 
Average of 2.1 and 2.8 = 
So, 2 rational numbers between 2.1 and 3.5 are 2.8 and 2.45.
Note:
Similarly we can find infinite number of rational numbers.
For example, the average of 2.8 and 3.5 also lies between given two numbers,
The average of 2.45 and 3.5 also lies between given two numbers etc.
SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Oakley visit: Tutoring in Oakley.
