Studied by 10 peoplevariables
symbols (usually letters) used to represent unknown quantities
expressions
a mathematical representation using numbers, variables, exponents, and operations
rational numbers
3 subsets: natural (N) {1, 2, 3, …}, whole (W) {0, 1, 2, 3, …}, integer (Z or J) {…-3, -2, -1, 0, 1, 2, 3, …}
Terminating and repeating decimals can be written as a quotient of integers
irrational numbers
the set of non-repeating and non-termination decimals
commutative prop. (+/x)
switching order 5+4=4+5
associative prop. (+/x)
grouping/regrouping 4+7+x=(4+7)+x
distributive prop. (+/x)
3(x)+3(7) 3x+21 3(x=7)
inverse prop. (+)
3+(-3)=0 (opposite)
inverse prop. (x)
4x1/4=1 (reciprocal)
identity prop. (+)
7+0=7 add identity 0
identity prop. (x)
10x1=10 mult. identity 1
property of zero (x)
10x0=0
definition of =
1-7 1+-7
definition of div.
5/2 5x1/2
reflexive prop. (=) mirror
A=A x+7=x+7
symmetric prop. (=) switching
if A=B, then B=A 10=x+2 x+2=10
transitive prop. (=)
if A=B, and B=C, then A=C 3+4=7, 2+5=7 then 3+4=2+5
subtraction prop. (=)
x+4=10
-4 -4
addition prop. (=)
A=B, then A+C=B+C
multiplication prop. (=)
A=B, then AC=BC, C≠0
division prop. (=)
3x=12
/3 /3
set
a group of objects e.g. set of integers
element
each object within a set e.g. 2 E Z
empty set of null set
the set that contains no elements symbols: { }
The empty set is a subset of every set
subset ⊆
A is a subset of B if every element in A is also an element of B
Symbol: ⊆
Every set is a subset of itself
The empty set is a subset of every set
2^n = S
formula that represents relationship when n=# of elements and s=# of subsets
roster rule
lists members in set e.g. {1, 3, 5, 7, …}
literal rule
describes set e.g. {odd whole numbers}
algebraic rule
expression e.g. {2x-1|x⊆N} x=1, 2, 3, 4
union ∪
the union of A and B is a set C that contains all elements that are in either A or B
Put the two sets (A&B) together
intersection ∩
the intersection of A and B is a set C that contains all elements that in both A and B
Overlap or what two sets (A&B) only have in common
disjoint set
if A ∩ B = empty set
solution
a value that makes a sentence(s) true
conditional
one solution
contradiction
no solutions
identity
many solutions
transitive prop.
is a < b and b < c, then a < c
trichotomy prop.
if a and b are any real numbers then one of the following must be true a < b a > b a=b
set notation & interval notation
applications
coin problems, rate x time = distance
absolute value |n|
the distance from 0
conjunction
AND ∩ intersection means to share, in common
disjunction
OR ∪ union means to join
compound inequalities
Multiple inequalities
Scratchwork above number line
No intersection = no solution
Write answer in interval notation
CHAPTER 1 REVIEW
Evaluate expressions with variables
Use interval notation to solve inequalities
Name by letter all of the subsets or R which each is a member
Note
Flashcard