MA 201 Exam 1 Flashcards
What are elements?
Objects
What’s a set?
A group of objects
What’s the listing method?
A method where you list out every method
Listing method example
A= {1,2,3,4}
What type of brackets do you use in a set?
Squiggly brackets
{ }
2 ways of describing sets
Listing method and set-builder notation
What’s the set-builder notation?
A notation where you have a placeholder variable and a defining quality of the elements of the set
Set-builder notation example
A= {1,2,3,4}
A= {x | x is a whole number from 1 to 5}What’s a null set?
AKA empty set
A set with no elements
How is the null set denoted?
{ } or (do not) sign
What does it mean for sets to be equal?
If and only if they have the same elements
Does order matter in an equal set?
no
What’s cardinality?
The number of unique elements of the set
Characteristics of sets
Finite
Infinite
Finite cardinality?
Is where you can say exactly how many elements a set contains
What’s a natural number?
The set of all cardinalities of nonempty finite sets
What’s a whole number?
The set of all cardinalities of finite sets
1-to-1 correspondence
When 2 sets have the same cardinality
What’s a subset?
If and only if a set has every element in another set
What’s the denotation of a subset?
An underlined sideways union
Subset characteristics
.2 equal sets are subsets of each other
.The null set is a subset of every set
What’s a proper subset?
A set that’s a subset which does not contain at least on element of it’s parent set
How is a proper set denoted?
A sideways union
What’s a way to talk about inequalities?
By cardinalities of sets
What’s a numeral?
Any collection of symbols used to represent a number
What’s the base-ten system?
A positional numeral system based on powers of ten
What’s a positional numeral system?
A system in which the value of a digit depends on its position or value
Expanded form of a number
Writing out a number based on its place values
What’s the decision digit?
The digit after the given place value
Number line characteristics
.Tic marks represent whole numbers at regular intervals
.Numbers increase from left to right
.Arrows are drawn to represent that the number line never ends
What systems do other cultures use?
Base-b systems
b is a number
What are base-b systems?
Numeral systems that have different symbols foe each power of b
What’s the positional value in base-b systems?
ones, bs, b^2s, b^3s,…
Binary numeral system
Base: 2
Only uses 0 and 1
Hexadecimal numeral system
Base:16
Uses 0-9 & A-F
The Mayan numeral system
Base: 20
Uses symbols: dots, lines, & football
Is vertical
400s
20s
1sReflexive property
A whole # equal itself
Symmetric property
The order of the equality of the while #’s doesn’t matter
Transitive property
2 whole #’s that are equal to the same whole #
Non-positional numeral system
The symbols in a numeral can be placed anywhere and still retain the same value
Ancient Egyptian numeral system
Base:10
Non-positional
Roman numeral system
.Equal or decreasing value are added
.Increasing value are group and the lower value is subtracted form the higher value
Roman numeral
,I=1 .V=5 .X=10 L=50 .C=100 .D=500 .M=1000
What does union mean?
The two sets is the set of everything either in one set or the other
What’s the cardinality of a union?
The sum of cardinalities of the original sets
What are addends?
’s that are being added
What’s the sum
A # that results from an addition problem
Commutative property of addition
The sum of 2 #’s doesn’t depend on the order of the addends
Associative property of addition
The sum of #’s doesn’t depend on the grouping of addends
Additive identity property
The sum of any # with the additive identity is the original #
What’s the additive identity?
0
Number line model of addition
Go the # of the first addend starting at 0 and then continuing to a # by moving the number of units to the right of the first addend until you move the # of units of the second addend
Standard algorithm of addition
Regrouping
Expanded algorithm of addition
Writing the answer of each place value sum
What’s the inverse operation of addition?
Subtraction
What’s a subtrahend?
The # that the minuend is subtracted from
What’s a minuend?
The number that’s being added to the subtrahend
What’s the difference?
AKA missing addend
.The minuend-subtrahend
Take-away method
Draw a pic & x out the elements you don’t need anymore
Number line model of subtraction
Go right the # of units the minuend is starting at 0 then go left at the stopping point of the minuend.
Base-ten blocks of subtractions
Start with the minuend and then remove the subtrahend.
Austrian algorithm of subtraction
Subtract in each place value. If not enough in that position, place a 1 between the relevant columns
What’s multiplication?
n*a= a+a+a+…+a
What’s a product?
The answer of the multiplication problem
What are factors?
The #’s of a multiplication problem
Multiplicative identity property
a*1=a
Zero multiplication property
a*0=0
What are the factors of an area model?
Length & width
What is the product of an area model?
area
Expanded algorithm of multiplication
Multiply each place value of one number by each in the other.
Use place value positions
What’s the inverse operation of multiplication?
Division
