Notation
This table defines the notation used in this course.
Symbol 
Description 
x ∈ A 
x is an element of A 
x ∉ A 
x is not an element of A 
A 
The number of elements in a finite set A 
A ⊆ B 
A is a subset of B 
∅ 
The empty set 
A ∩ B 
The intersection of A and B 
A ∪ B 
The union of A and B 
B − A 
The complement of A relative to B 
A^{c} 
The complement of A relative to the universe 
A ⊕ B 
The symmetric difference of A and B 
A × B 
The cartesian product of A with B 
The power set of A, the set of all subsets of A 

n! 
n factorial, the product of the first n positive integers 
n choose k, the number of k element subsets of a n set 

p ∧ q 
The conjunction, p and q 
p ∨ q 
The disjunction, p or q 
¬p 
The negation of p, “not p" 
p → q 
The conditional proposition If p then q 
p ↔ q 
The biconditional proposition p if and only if q 
1 
The symbol for a tautology 
0 
The symbol for a contradiction 
r ⇐⇒ s 
r is logically equivalent to s 
r ⇒ s 
r implies s 
p  q 
The Sheffer Stroke of p and q 
T_{p} 
The truth set of p 
The statement that p(n) is true for at least one value of n 

The statement that p(n) is always true 

0_{m }_{× }_{n} 
The m by n zero matrix 
I_{n} 
The n × n identity matrix 
A^{−}^{1} 
A inverse, the multiplicative inverse of A 
det A or A 
The determinant of A, 2 by 2 case 
a  b 
a divides b, or a divides evenly into b 
xsy 
x is related to y through the relation s 
rs 
The composition of relation r with relation s 
a ≡_{n} b 
a is congruent to b modulo n 
a ≡ b (mod n) 
a is congruent to b modulo n 
c(a) 
the equivalence class of a under r 
r+ 
The transitive closure of r 
f : A → B 
A function, f, from A into B 
B^{A} 
The set of all functions from A into B 
f(a) 
The image of a under f 
f(X) 
Range of function f : X → Y 
A = n 
A has cardinality n 
(g ◦ f)(x) = g(f (x)) 
The composition of g with f 
f ◦ f = f^{2} 
The "square" of a function 
i or i_{A} 
The identity function (on a set A) 
f^{−1} 
The inverse of function f, read "f inverse" 
log_{b}a 
Logarithm, base b of a 
S ↑ 
S pop 
S ↓ 
S push 
S ∗ T 
Convolution of sequences S and T 
S ↑ p 
Multiple pop operation on S 
S ↓ p 
Multiple push operation on S 
K_{n} 
A complete undirected graph with n vertices 
deg(v), indeg(v), outdeg(v) 
degree, indegree, and outdegree of vertex v 
e(v) 
The eccentricity of a vertex 
d(G) 
The diameter of graph G 
r(G) 
The radius of graph G 
C (G) 
The center of graph G 
Q_{n} 
The ncube 
V (f) 
The value of flow f 
P_{n} 
A path graph of length n 
The chromatic number of G 

C_{n} 
A cycle with n edges 
∗ 
The generic symbol for a binary operation 
string1 + string2 
The concatenation of string1 and string2 
[G; ∗] 
A group with elements G and binary operation 
gcd(a, b) 
The greatest common divisor of a and b 
a +_{n} b 
The mod n sum of a and b 
a ×_{n} b 
The mod n product of a and b 
The Additive Group of Integer Modulo n 

The Multiplicative Group of Integer Modulo n 

W ≤ V 
W is a subsystem of V 
⟨a⟩ 
The cyclic subgroup generated by a 
ord(a) 
Order of a 
V_{1} × V_{2} × · · · × V_{n} 
The direct product of algebraic structures V_{1}, V_{2}, ..., V_{n} 
G_{1} ≅ G_{2} 
G_{1} is isomorphic to G_{2} 
dim(V) 
The dimension of vector space V 
0 
The least element in a poset 
1 
The greatest element in a poset 
D_{n} 
The set of divisors of integer n 
a ∨ b 
The join, or least upper bound of a and b 
a ∧ b 
The meet, or greatest lower bound of a and b 
[L; ∨, ∧] 
A lattice with domain having meet and join operations 
The complement of lattice element a 

[B; ∨, ∧, ¯ ] 
A boolean algebra with operations join, meet, and complementation 
A^{∗} 
The set of all strings over an alphabet A 
A_{n} 
The set of all strings of length n over an alphabet A 
The empty string 

s_{1} + s_{2} 
The concatenation of strings s_{1} and s_{2} 
L(G) 
Language created by phrase structure grammar 
(S, X, Z, w, t) 
A finitestate machine with states S, input alphabet X, output alphabet Z, output function w, and nextstate function t 
m(M) 
The machine of monoid M 
a ∗ H, H ∗ a 
The left and right cosets generated by a 
G/H 
The factor group G mod H 
S_{A} 
The group of permutations of the set A 
S_{n} 
The group of permutations on a set with n elements 
A_{n} 
The Alternating Group 
D_{n} 
The nth dihedral group 
H ◁ G 
H is a normal subgroup of G 
kerθ 
The kernel of homomorphism θ 
[R; +, ·] 
A ring with domain R and operations + and · 
U (R) 
The set of units of a ring R 
D 
A generic integral domain 
deg f(x) 
The degree of polynomial f(x) 
R[x] 
The set of all polynomials in x over R 
R[[x]] 
The set of all powers series in R 
Pre and post values of a variable x 

M(A)_{i,j} 
The i, j minor of A 
C(A)_{i,j} 
The i, j cofactor of A 
det(A) or A 
The determinant of A 
Source: Al Doerr and Ken Levasseur, http://faculty.uml.edu/klevasseur/adslatex/ads.pdf
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