Section P-1Section P-1

What are the properties of What are the properties of real numbers?real numbers?

Real NumbersReal Numbers

Symbol (R)Symbol (R)

May be described informally in many May be described informally in many different waysdifferent ways

Natural NumbersNatural Numbers

Symbol (N)Symbol (N)

Also called counting numbersAlso called counting numbers

Examples: {1,2,3,4…..}Examples: {1,2,3,4…..}

Whole NumbersWhole Numbers

Symbol (W)Symbol (W)

Also called counting numbers Also called counting numbers plus zeroplus zero

Examples: {0,1,2,3,4…..}Examples: {0,1,2,3,4…..}

IntegersIntegers

Symbol (J)Symbol (J)

Positive and negative whole numbersPositive and negative whole numbers

Examples: {…-3,-2,-1,0,1,2,3…}Examples: {…-3,-2,-1,0,1,2,3…}

Rational NumbersRational Numbers

Symbol (Q)Symbol (Q)

Numbers that can be written as fractionsNumbers that can be written as fractions

Ex: whole numbers 6/3=2Ex: whole numbers 6/3=2

repeating decimals 1.232323 . . .repeating decimals 1.232323 . . .

terminating decimals 1.85692terminating decimals 1.85692

Irrational Numbers Irrational Numbers

Symbol (I)Symbol (I)

Non-terminating numbersNon-terminating numbers Ex: Ex: ππ, Square root of 2, Square root of 2

Non-repeating decimals that never endNon-repeating decimals that never end Ex: 1.849573495638974….Ex: 1.849573495638974….

QuizQuiz

1.1. Zero is a real number?Zero is a real number?

2.2. Real numbers are a subset of rational Real numbers are a subset of rational numbers?numbers?

3.3. Irrational numbers are not a subset of Irrational numbers are not a subset of rational numbersrational numbers

4.4. 6/3 is a rational number6/3 is a rational number

5.5. 0 is a natural number0 is a natural number

Quiz AnswersQuiz Answers

1.True1.True

2.False2.False

3.True3.True

4.True4.True

5.False5.False

Define these propertiesDefine these properties

Closure PropertyClosure Property

Commutative PropertyCommutative Property

Associative PropertyAssociative Property

Distributive PropertyDistributive Property

Identity PropertyIdentity Property

Multiplication Property of ZeroMultiplication Property of Zero

Additive Inverse PropertyAdditive Inverse Property

Multiplicative inverse propertyMultiplicative inverse property

Define these propertiesDefine these properties

Reflexive PropertyReflexive Property

Symmetric PropertySymmetric Property

Transitive PropertyTransitive Property

Substitution PropertySubstitution Property

Trichotomy PropertyTrichotomy Property

VocabularyVocabulary

Additive IdentityAdditive Identity

Multiplicative IdentityMultiplicative Identity

Additive InverseAdditive Inverse

Multiplicative Inverse (aka ???)Multiplicative Inverse (aka ???)

Absolute ValueAbsolute Value

If a and b are any two points on the number line, then the distance between a and b is │a - b│. AKA, d(a,b) = │a - b│

PEMDASPEMDAS

Please (parenthesis, brackets, grouping Please (parenthesis, brackets, grouping symbols)symbols)

Excuse (Exponents)Excuse (Exponents)

My (Multiply)My (Multiply)

Dear (Divide)Dear (Divide)

Aunt (Add)Aunt (Add)

Sally (Subtract)Sally (Subtract)***multiply and divide are done in order from left to right. . . Same with add and subtract***multiply and divide are done in order from left to right. . . Same with add and subtract