Introduction to Sets Flashcards
Roster Notation
A : {0,1,2,3}
Set
unordered collection of objects
elements
objects in a set
subset
when every element in a subset A is in B
proper subset
A is a proper subset of B if A != B
cardinality
number of elements in a set (distinct)
empty set
set with no elements
important sets
Z, Z^+, N, Q, R
Z
set of integers
N
set of non-negative numbers
Q
set of rational numbers
R
set of real numbers
set builder notation of A = {1,3,5,7,9}
{x | x is an odd positive integer less than 10}
universal set
set containing all elements mentioned in a particular context
power set
given a set S, the power set is a set of all subsets
cardinality of a power set
2^|s| = 2^n
string
sequence of characters
alphabet
set of characters used in a set of strings, for the set of strings
length of string
the number of characters
binary string
string whose alphabet is {0,1}
bit
character in a binary string
n-bit string
string of length n
the set of binary strings of length n
{0,1}^n
empty string
unique string whose length is 0 and is usually denoted by alpha
{0,1}^0
{alpha}
concatenation
of strings s and t (st) is a longer string obtained by putting s and t together
disjoint
if intersection of two sets is empty (empty set)
pairwise disjoint
a sequence of sets A1,A2, A3…. An, if every pair of distinct sets in the sequence is disjoint
partition of non-empty set
a collection of non-empty subsets of A such that each element of A is in exactly one of the subsets
