I&C SCI 6D Lecture Notes - Lecture 2: Empty Set, Subset
25 Feb 2017
School
Department
Course
Professor
Sets and Functions
1. Sets:
i. A set is an unordered collection of items
ii. Curly braces {} denote that order does not matter
b. Cardinality of sets:
i. An infinite set has an inf number of elements
ii. A finite set has a finite number of elements
iii. If S is a finite set then the cardinality, S is denoted as |s|, is the number of
elements in S
iv. S = {A,B,C,D}
1. |S| = 4
c. DOUBLE LINED NOTATION:
i. Z = the set of all integers
ii. R = the set of real numbers
iii. Q = the set of rational numbers
iv. N = natural numbers (positive integers)
v. o/ The empty set
vi. Clarification:
1. Postiive if x > 0
2. Negative if x < 0
3. Non-negative if x >= 0
4. Non-positive if x <= 0
5. A+ denotes the subset of A with all the positive elements in A
d. Specifying a set
i. Roster notationl
1. List the elements with curly braces
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
A set is an unordered collection of items: curly braces {} denote that order does not matter, cardinality of sets: An infinite set has an inf number of elements. A finite set has a finite number of elements. If s is a finite set then the cardinality, s is denoted as |s|, is the number of elements in s. S = {a,b,c,d: |s| = 4, double lined notation: Set builder notation: {x:x s and some additiona conditions on x, {x s: additional conditions, ex: {1,3,5,,99, {x z+: x is odd and 0
