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Level 42

Classification of Numbers II


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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?