1. Classification of Numbers
Any number that is found on the Real Number Line is
Called a Real Number represented by
A real number runs from negative infinity to positive
Infinity

2. Natural Number Natural Numbers are {0,1,2,3,4,5,6, .....} No decimals
No Negatives
Zero is part of the natural numbers
The Symbol for Natural Numbers is

3. Integers Integers are numbers like {-3,-2,-1,0,1,2,3}
They are both negative and positive
Only Whole numbers
No Decimals
Zero is included
The symbol for integers is

4. Rational Number Numbers that are Fractions or Repeating decimals
Like ½, 1/3 ,-2/3 , 4/6 ,-8/9, , etc
Rational comes from Ratio , which means we are dealing with a numerator and denominator
The numerator and denominator are both INTEGERS or (The denominator is never 0)
The symbol for Rational Numbers is

5. Irrational Numbers
A number with an INFINITE , NON REPEATING DECIMAL representation is irrational
E.g =
Are irrational numbers represented by

6. The real numbers (Exam Question)
Classify the following number
Based on where they belong
3.146, 1/5, -1, 5, -3,0.33..
,0.4, …

7. The real numbers (Exam Question)
3.1416
1/5 -1 5 -3
0.4
0.33..

8. Some questions Q: Are all Natural Numbers also Integers?
Ans: Yes the set of Natural Numbers is contained in the set of integers
Q: Are all Integers also Natural Numbers?
Ans: No ! For example -2 , etc are not Natural Numbers, but they are integers
Q: Are all Integers also Rational Numbers?
Ans: Yes the set of Integers is Contained in the set of Rational Numbers

9. Some questions Q: Are all irrational numbers also Real Numbers?
Ans: Yes, every number that exists on the real number line is a real number!
Natural Numbers, Integers, Rational and Irrational Numbers are all Real Numbers.