• Natural or Counting Numbers = {1,2,3,4,….}• Whole Numbers= {1,2,3,4,5,….}• Integers{..-3, -2, -1, 0, 1, 2, 3,… • Rational Numbers= any number that can be

written as a fraction p/q where q≠ 0. Any decimals that are rational numbers are either terminating (0.25) or repeating (0.33333….)

• Irrational Numbers- Any number that is Not a rational number. Ex; is not a rational number- written as a decimal, it will never repeat or terminate

• Real Number- Any number that can be expressed as a decimal. All rational and Irrational numbers

• Imaginary Number- NOT a real Number. Numbers, that when squared, give a negative result. This is impossible (it must be your imagination to come up with such a thing!) • Denoted with “i”

COPY and fill in the Circle Chart with the correct Terms

Sets of Numbers

N- Natural NumbersW- Whole NumbersZ= IntegersR= Rational NumbersE= Real Numbers

i = Imaginary Numbers

All Numbers, Real and Imaginary

i

Z

RE

N

W

Sets, Subsets, Compliments

Complement of a Set

• For any set (A) within Universal set (U), it is the set of elements of U that are not Elements of A•U stands for “Universal set” ; All numbers or elements possible•Pretty much, a compliment is the opposite, everything that is not in set A • U= {cats, birds, geckos, dog}• A= {birds}• Find A’

Subsets

• A set within a set• If we have set A={1,2,3,4,5,6,7,8,}• And we have set B= {2,5,7,8}• B is a subset of A because all of set B is in set A

• If two sets are the same, they are technically subsets•M={78, 26, 98} N={78, 26, 98}

• These are called equal sets• Every element of M is an element of N

• Proper subsets are NOT equal sets•A proper subset of a set has some but not ALL of the elements of that set•Which are proper subsets of Q?

Q= {1, 4, 7,13,14, 22}N= {1, 4 , 7, 14, 22}R= {1, 4, 7, 13, 14, 22}S= {7}T= { 22, 23}

Proper Subsets

Different from just “subsets”Notation;A

• The number of subsets you have depends on the number of combinations you can make with the elements• N – number of elements• Formula; •Number of subsets = 2n

Number of SubsetsThe number of elements in a set determines the number of subsets

Number of Elements 0 1 2 3

4

Number of sets 1= 20 2=21 4=22 8= 23

16= 24

• Q= {1,2,3,}•Subsets• {}, {1}, {2}, {3}, {1,2},

{1,3}, {2,3}, {1,2,3}• 8 subsets• 23= 8

ExampleNumber of subsets

• U= {5, 10, 15, 20, 25, 30}• T= {10, 20, 30}•Find T’=• T’= {5, 15, 25}

•Find n(T’)• 23 = 8

ExampleNumber of subsets

•Formula for Number of Proper Subsets

•2n-1• You have to take away the subset that has all the same elements

Number of Proper SubsetsProper subsets- have some but not ALL of the same elements of a set

• Q= {1,2,3,}•Subsets• {}, {1}, {2}, {3}, {1,2},

{1,3}, {2,3}, {1,2,3}• 8 subsets• Take away {1,2,3}• 7 subsets• 23-1= 7

ExampleNumber of proper subsets