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Factoring

Another name for the distributive property when rewriting an expression as a product xy + xz = x( y + z)

Commutative Property of Addition of Equality

Given x & y are real numbers x + y = y + x

Commutative Property of Multiplication of Equality

Given x & y are real numbers xy = yx

Associative Property of Addition of Equality

Given x, y, and z are real numbers (x + y) + z = x + ( y + z)

Associative Property of Multiplication of Equality

Given x, y, and z are real numbers (xy)z = x(yz)

Additive Identity for Real Numbers

Given x is a real number x + 0 = x or x = 0 + x

Multiplicative Identity of One for Real Numbers

Given x is a real number x • 1 = x or x = x • 1

Multiplicative Inverse Property for Real Numbers

Given x is non-zero real number x • 1/x = 1

Additive Inverse Property for Real Numbers

Given x is a real number x + (-x) = 0

Multiplicative Property of Zero for Real Numbers

Given x is a real number x • 0 = 0

Addition Property of Inequality

Given x, y, and z are real numbers If x < y, then x + z < y + z

Subtraction Property of Inequality

Given x, y, and z are real numbers If x < y then x - z < y - z

Multiplication Property of Inequality

Given x, y, and z are real numbers

Division Property of Inequality

Given x, y, and z are real numbers

Transitive property of Inequality

Given x, y, and z are real numbers

Trichotomy of Comparison

Given x and y either x > y or x = y or x < y

Counting Numbers

the numbers in the set (1,2,3,4...)

Whole Numbers

Zero and the counting numbers 1, 2, 3, 4, 5, 6, and so on. If a number has a negative sign, a decimal point, or a part that's a fraction, it is NOT a whole number.

Integers

the set of positive whole numbers and their opposites(negative numbers) and 0

Rational numbers

Numbers that include integers, wholes, and natural numbers.

Irrational Number

A number that cannot be written as a fraction with a numerator and a denominator that are integers. The decimal representation of a rational number either ends or repeats.

real number

combonation of rational and irrational numbers

Set

A _ is a well-defined collection of objects.

elements

What are the objects in a set called?

Set-Builder Notation

Specify the conditions under which a number is an element of the set.

Digits

The numbers in a given set.

{0,1,2,3,4,5,6,7}

The set of all digits greater than or equal to 7.

What does E represent?

E represents the set of all digits greater than or equal to 7...

What does x represent?

X is a variable used to represent the elements of the set. For example...

What will this be in set-builder notation?

{x|x is a digit less than or equal to 7}

How do you represent a set in roster method?

List its elements inside a pair of braces, { } .

What does D represent?

D will represent the set of all digits greater than or equal to 7.So...

{4,5,6,7,8,9}

Using the roster method represent the given set. "The set of all digits greater than or equal to 4."

The order in which elements are listed in a set does not matter.

True, because a set is a well-defined collection of objects because the order is not important in a collection of objects.

What does A=B represent?

If two sets A and B have the same elements, then A equals B.

What does A(sideways U w/ a bold line underneath it)B mean?

If every element of a set A is also an element of a set B, then A is a subset of B.

When is the notation A(sideways U)B used? Note no bold line underneath the sideways U shape...

If A(sideways U w/ a bold line underneath)B and A(equal sign w/ a slash through it)B, then A is a proper subset of B.

What does the notation {O w/ a slash through it} mean?

This means that a set contains the set called the empty set.

What is used to denote the empty/null set?

Denoted by the symbol {} or (O w/ a slash through it)...

Facts about the empty set...

The empty set is a subset of every set.

is an element of

What does the symbol "£" mean?

Is zero a whole number?

True, zero is a whole number.

Empty Set/Null Set

A set that has no integers between it's digits. Ex) There are no integers between 31 and 32.

Rational Number

Any number that can be expressed as a ratio of two integers. Example; 6 can be expressed as 6/1, and 0.5 as 1/2.

Irrational Numbers

any number that cannot be expressed as a fraction.

real numbers

Any Number

Natural numbers

A group of numbers that include 1,2, 3,.....

The radical of 7 is a rational number.

False, the radical of 7 is an irrational number.

2.59 repeating is a rational number?

True, 2.59 repeating is a rational number.

Truncating Decimals

Drop all the digits after the one given in the direction. Do not round!

17.5072

Truncate 17.50724 to four decimal places.

<

Less than symbol?

>

Greater than symbol?