1. The real number system, symbols, Sets, and subsets
1.1(b) notes
The real number system, symbols,
Sets, and subsets

2. Real Number System Name of set Description Examples
Natural numbers (counting numbers)
The numbers you used when you learned to count
1, 2, 3, 4…
Whole Numbers
The natural numbers plus zero
0, 1, 2, 3…
Integers
The set of all whole numbers and their opposites
…-3, -2, -1, 0, 1, 2, 3…
Rational Numbers
Numbers that can be expressed as an integer divided by a non-zero integer
, , 10, -6
Irrational Numbers
Numbers whose decimal representations neither terminate nor repeat
π, e, , -π,

3. Classify
Place the following numbers in the correct place on the chart below. -6

4. Sets The set consisting of the first 10 even natural numbers
Roster Notation:
{2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
Set-Builder Notation:
{x | x is an even number between 1 and 21}
YOU TRY!
In both roster and set-builder notation represent the set of all multiples of 5 between 1 and 21.

5. symbols
Symbol Meaning & Example

6. subsets
When every element of one set is an element of another set, the first set is a subset of the second set.
- “is a subset of”
Which of the sets we just defined are subsets of each other? Tell me using symbols.

7. Two examples
Example 1:
Use roster notation and set builder notation to write the set of the first 5 even natural numbers.
 Example 2:
Write the set using set builder notation {-4, -3, -2, -1, 0}

8. 1.1(b) HW:
p. 10 #53, 59, 63, 65-75(odd), 85, 86