Sets and Venn Diagrams
Z or Integers
{ ...-3, -2, -1, 0, 1, 2, 3...}
W or Whole numbers
{ 0,1,2,3,4,5...}
N or Natural numbers
{ 1,2,3,4,5...}
INFINITE SET
a set with an infinite number of elements for example, the set of all even numbers { 2,4,6,8...}
SET BUILDER NOTATION
a way to describe sets of numbers
UNION
all elements which are in P OR Q
INTERSECTION
all elements which are in both set P AND set Q
I or Irrational numbers
all numbers that are not rational numbers, also called Q' (or not Q) like pi or square root of 2
ELEMENT
an object in a set, also called a member
MEMBER
an object in a set, also called an element
CLOSED CIRCLE ON A NUMBER LINE
numbers are included in a set <= and >= sign (less than or equal to, greater than or equal to)
OPEN CIRCLE ON A NUMBER LINE
numbers not included in a set < and > sign (less than, greater than)
Q or Rational numbers
numbers that can be written as a fraction where the numerator and the denominators are both integers and the denominator is NOT 0
n(S)
read as the number of elements in a set if D= {2,3,4,5,6,7,8,9,} then the n(D)=8
VENN DIAGRAM
represented by a rectangle represents the Universal Set the sets within are represented by circles
Z-
set of all negative integers
R or Real numbers
the set of all rational and irrational numbers
UNIVERSAL SET
the set of objects under consideration
MUTUALLY EXCLUSIVE SETS
two sets with absolutely nothing in common, also called disjoint
DISJOINT SETS
two sets with absolutely nothing in common, also called mutually exclusive
SUBSET
Every element of P is also an element of Q. For example if I tell you that Q = {1,2,3,4,5,6}, P ={2,4,6} and R ={2,4,6,8} then P is a subset of Q but R is not a subset of Q because 7 is not in Q
Z+
set of all positive integers
COMPLEMENT
the elements that are NOT in the stated set Example: A' is read ''complement of A'' and means all the elements that are NOT in A
EMPTY SET
A set with no elements { }
SET
a collection of objects or things
FINITE SET
a set with a given number of elements for example, the set of the outcomes when rolling a dice { 1,2,3,4,5,6}
