Sets 8th Grade Math Algebra I Honors
Rational Numbers
Q Any number that can be expressed as a fraction
Real Numbers
R all irrational and rational #s
RIQZWN
REAL IRRATIONAL Q RATIONAL Z INTEGERS WHOLE NATURAL
complements
can be represented as: A^c A' ~A Ā complement + original = what the complement is of, for example B= {1,2,3} A={1} Ā={2,3} A+Ā=B
inclusive
contains ALL endpoints, CLOSED circles
exclusive
contains NO endpoints, OPEN circles
Venn Diagram in Math
if circles are inside each other: the inner circle must also meet the rules of the outer circle Always put name/number on top outside of circles doesn't have the characteristics needed remember to count the overlapping stuff Challenge: A={1,2,3,4,5} B={2,4,5} C={1,2,14} (A ∩ B) U C = {1,2,4,14}
roster form
lists the elements of a set within braces
And
overlap/showing what is in common in between inequalities. {x: 2<x<5}
Multiples of 6 between 6 and 36 inclusive set H
H={6x: x E N 1 ≤ x ≤ 6}
Irrational Numers
I Non-terminating decimals with no repitition. ex: square root of 2.
Natural Numbers
N The set of numbers without 0: 1, 2, 3, 4, ... Also called counting numbers.
half-closed
ONE, but not another endpoint contained one circle open, one circle closed
disjunction
OR
conjunction
AND
Intersection
"and" ∩ excludes things that aren't in common Ex: A ∩ B=6 A={5,6,8} B={6,9,10} Ex: A ∩ B={x: x < 3} A= x<5 B= x<3 Ex: A ∩ B=[5,6] A= [5, infinity) B= (3, 6]
Union
"or" U all things in both sets together Ex: A U B={5,6,8,9,10} A={5,6,8} B={6,9,10} Ex: A U B={x: x < 5} A= x<5 B= x<3 Ex: A ∩ B=(3, infinity) A= [5, infinity) B= (3, 6]
interval notation
A notation for describing an interval on a number line. The interval's endpoint(s) are given, and a parenthesis or bracket is used to indicate whether each endpoint is included in the interval. brackets mean that they are included parenthesis mean that they are not included -infinity is always in parenthesis- (-3, 2] is equal to {x: -3<x≤2} *in interval notation, or is a U*
set-builder notation
A notation used to describe the elements of a set {x | x>2} or {x: x>2} or is a V { x: x>2 V x< -1}
Equivalent
Same # of elements
Equal
The same
Whole Numbers
W Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...
Integers
Z The set of whole numbers and their opposites ...-2, -1, 0, 1, 2...
null (empty) set
a set that contains no elements the null set is a subset of all sets { } or empty set or null ser or symbol in picture
subset
a set that is part of a larger set any set is a subset of itself the empty set is a subset of all sets A= {1,2,3} B={2} A is a subset of B
elements
∈ means "is an element of" elements are members of a set A= {x: x ∈ set of natural numbers and x<0} the answer to that would be the empty set because there are no natural numbers less than 0
