NUMBER SYSTEMS
Real Numbers
We started with Natural Numbers and gradually discovered that they were not enough.
Each new situation led us to a larger collection of numbers.
We eventually arrived at two groups:
Rational Numbers
Numbers that can be written as:
where p and q are integers and q ≠ 0.
Irrational Numbers
Numbers that cannot be written in the form:
KEY IDEA
Rational and Irrational Numbers together form the Real Numbers.
HOW THE NUMBER SYSTEMS FIT TOGETHER
Real Numbers
Rational Numbers
1/2 3/4 −5/2
Integers
−3 −1 0 1 2
Whole Numbers
0 1 2 3
Irrational Numbers
√2 √3 π
Every Real Number belongs to either the Rational or Irrational group.
NEXT IDEA
We can classify Real Numbers in this way, but there is another way to represent them.