1. Section 1.4 The Real Number System
Natural Numbers, Whole Numbers, Integers, Rational Numbers, and Irrational Numbers

2. Natural Numbers Also called “Counting Numbers”
These are numbers you use to “count your cattle”, “count the number of marbles in a cup”, etc.
Look at the VALUE of the number you’re looking at, not its APPEARANCE!
Examples:
1, 2, 3, 4, 5, …
Also…

3. Whole Numbers Includes all Natural Numbers AND 0
These are numbers you use to “count your cattle” and have something to use if all the cattle are gone.
Look at the VALUE of the number you’re looking at, not its APPEARANCE!
Examples:
0, 1, 2, 3, 4, 5, …
Also…

4. Integers Includes all Natural Numbers, 0, AND Negative “whole” Numbers
These are numbers you need if you might have a “whole” value less than 0
Still NO Fractions or Decimals
Look at the VALUE of the number you’re looking at, not its APPEARANCE!
Examples:
…, -3, -2, -1, 0, 1, 2, 3,…
Also…

5. Rational Numbers
Includes all numbers the CAN BE written as the quotient of integers…. (can be written as fractions of “whole numbers” – negative or positive)
Or – CAN BE written as decimals that either terminate (stop on their own) or repeat (show a pattern that repeats forever)
Look at how the number CAN be written, not its given APPEARANCE!
Examples:
Also…

6. Irrational Numbers
Includes all numbers the CANNOT BE written as the quotient of integers…. (can’t be written as fractions of “whole numbers” – negative or positive)
Or – CANNOT BE written as decimals that either terminate (stop on their own) or repeat (show a pattern that repeats forever)
Usually can tell these from their APPEARANCE!
Examples:
This is because…

7. REAL Numbers
Includes all Natural Numbers, all Whole Numbers, all Integers, all Rational Numbers, and All Irrational Numbers.
ANY number that you will work with in this course will be a REAL NUMBER!!!

8. OTHER THINGS YOU NEED TO REALIZE…
All NATURAL NUMBERS are also Whole Numbers, Integers, Rational Numbers, and Real Numbers
All WHOLE NUMBERS are also Integers, Rational Numbers, and Real Numbers
All INTEGERS are also Rational Numbers and Real Numbers
All RATIONAL NUMBERS are also Real Numbers
All IRRATIONAL NUMBERS are also Real Numbers

9. Lets Practice…….
For the following list of numbers, indicate which set each number is in…..

10. Place each number into the appropriate set(s)…
Natural Numbers - - -
Whole Numbers
Integers
Rational Numbers - - -
Irrational Numbers - -
Real Numbers

11. Lets make sure you understand the roots…….
Irrational