r.2 and r.3 Flashcards
∈
when a number is included in the set
∉
when a number is not included in the set
S
name of a set
infinite set
unending list of distinct elements
finite set
has a limited number of elements
{x|x is a natural number between 2 and 7} - what kind of notation.
set builder notation
{x - in set builder notation
set of all elements
- in set builder notation
such that
U - letter
universal set
∅
empty/null set
⊆ or subset
x has every element of y
a complement
everything from the U that’s not in x
∅ (set wise)
nothing in common
natural numbers
{1, 2, 3, 4, …} or counting numbers
whole numbers
{0, 1, 2, 3, 4, …}
integers
{…, -3, -2, -1, 0, 1, 2, 3, …}
correspondence forms
coordinate systems
rational element
{p/a = p and a are integers and a ≠ 0}
irrational numbers
{x|x is a real number but not rational}
real numbers
{x|x corresponds to a point on the number line}
inequalities
≤ or ≥
a < b < c
b is between a and c
absolute value
distance on a number line from a number to 0
|a| ≥ 0
absolute value is always positive or 0
|-a| = |a|
real number and its opposite are always equal
|a| ⋅ |b|…
= |ab|
|a|/|b|…
= |a/b|
|a+b|…
≤ |a| + |b|
-
opposite of
a/0
undefined
0/a
0
0/0
indeterminate
a^n = a ⋅ a ⋅ a ⋅ a… ⋅ a
n is any positive integer
order of operation
- fraction bar
- parenthesis
- power roots
- multiplication / division
- subtraction / addition
a+b is a real number or ab is a real number
closure properties
a+b=b+a or ab=ba
commutative property
(a+b)+c = a(b+c) or (ab)c = a(bc)
associative property
a+0=a or 0+a=a
identity properties
a+(-a)=0 or (-a)+a=0
inverse properties
a ⋅ 1/a = 1 or 1/a ⋅ a = 1
inverse properties
a(b+c) = ab+ac or a(b-c) = ab-ac
distributive properties
0 ⋅ a = a ⋅ 0 = 0
multiplication properties of 0
d( P, Q )
distance between points and number line
d( P, Q )
= |b-a| or |a-b|
∩
intersections
∪
union / combination of two sets
