Index Index
\(r\)-permutation, Definition
addition rule, Section Assemblage
adjacent
edges, Paragraph
vertices, Paragraph
ancestor
of a vertex, Item
argument, Section Assemblage
arrow diagram, Paragraph
arthmetic sequence, Definition
bijection, Definition. See also one-to-one correspondence
binary tree, Paragraph
full, Paragraph
binomial, Paragraph
binomial coefficient, Paragraph
bit string, Paragraph
branch vertex, Definition
Cartesian product, Definition
cases
proof by, Assemblage
child
of a vertex, Item
choose, Definition
Euler, Definition
Hamiltonian, Definition
simple, Item
trivial, Paragraph
circuit-free graph, Definition
closed form
closed walk, Item
codomain, Definition
relation, Paragraph
combination, Section Definition
complement
of a set, Definition
complete bipartite graph, Definition
complete graph, Definition
complete set of residues, Section
composite, Definition
conclusion, Assemblage
conditional
negation of, Item
congruent mod \(d\), Definition Paragraph
connected
graph, Definition
vertices, Definition
connective
biconditional, Item
conditional, Item
conjunction, Item
disjunction, Item
negation, Item
constructive proof
existential statement, Assemblage
contradiction, Definition
proof, Section Assemblage
contrapositive, Item
proof, Section Assemblage
universal conditional, Definition
converse, Item
universal conditional, Definition
converse error, Assemblage
quantifier, Assemblage
counterexample, Paragraph Assemblage
degree
of a vertex, Definition
DeMorgan’s Laws, Paragraph
descendant
of a vertex, Item
difference
of sets, Definition
digraph, Definition
direct proof, Section Assemblage
directed graph, Definition
disjoint sets, Definition
divides, Item
divisible, Definition
Division Algorithm. See Quotient-Remainder Theorem
divisor, Item
domain, Definition
for a quantified statement, Definition
relation, Paragraph
edge, Paragraph Definition
adjacent, Paragraph
parallel, Paragraph
empty graph, Paragraph
empty set, Paragraph
proof, Assemblage
endpoints of an edge, Definition
equivalence class, Paragraph
equivalence relation, Section Definition
Euler circuit, Definition
Euler path, Definition
even integer, Definition
existential
proof of, Assemblage
quantifier, Item
statement, Item
universal, Item
explicit formula
by iteration, Example
proof, Assemblage
explicit sequence, Example
factor, Item
factorial, Definition Paragraph
Fibonacci sequence, Example
explicit formula, Example
forest, Definition
function, Definition Section Definition
inverse, Theorem
one-to-one, Section
onto, Section
Fundamental Theorem of Arithmetic. See Unique Factorization Theorem
geometric sequence, Definition
geometric sum, Paragraph
circuit, Section
circuit-free, Definition
complete, Definition
complete bipartite, Definition
directed, Definition
path, Section
total degree, Definition
tree, Section
image, Definition
incident
edge, Paragraph
inclusion-exclusion rule, Theorem
induction, Section
proof structure, Assemblage
strong, Assemblage
integer, Item
remainder representation, Paragraph
internal vertex, Definition
intersection
of sets, Definition
invalid argument, Definition Paragraph
inverse
function, Section
image, Paragraph
of conditional, Item
relation, Definition
inverse error, Assemblage
quantifier, Assemblage
inverse function, Paragraph
irrational number, Definition
isolated vertex, Paragraph
iteration, Section
method of, Section
leaf, Definition
level
of vertex, Item
logical argument, Paragraph
logical equivalence, Definition Assemblage
logical statement, Paragraph
loop, Paragraph
modus ponens, Assemblage
universal, Assemblage
modus tollens, Assemblage
universal, Assemblage
multiple, Item
multiplication rule, Section
natural number, Item
negation
logical statement, Assemblage
of conditional, Item
null string, Paragraph
odd integer, Definition
one-to-one correspondence, Definition
one-to-one function, Section Definition
proof, Assemblage
onto function, Section Definition
proof, Assemblage
pairwise disjoint sets, Paragraph
parallel edges, Paragraph
parent
of a vertex, Item
partition, Definition
Pascal’s Formula, Theorem
permutation, Definition
generalized, Theorem
power set, Definition Paragraph
predicate, Paragraph
preimage, Definition Paragraph
premise, Assemblage
prime, Definition
prime factorization
standard form, Paragraph
probability, Section
product, Section
product notation, Paragraph
product of sets, Definition
proof
by cases, Section Assemblage
by contradiction, Section Assemblage
by contrapositive, Section Assemblage
by induction, Assemblage
direct, Section Assemblage
method of exaustion, Assemblage
proper subset, Definition Definition
quantifier, Section
existential, Item
negation, Section Assemblage Assemblage
universal, Item
quotient, Paragraph
proof, Section
range, Definition
rational number, Item Section Definition
real number, Item
recurrence relation, Paragraph
iteration, Section
proof, Assemblage
proof of explicit formula, Assemblage
recursively defined sequence, Paragraph
reflexive, Item
proof, Assemblage
relation, Definition Section Definition Section
codomain, Paragraph
domain, Paragraph
equivalence, Section
function, Assemblage
reflexive, Section
symmetric, Section
transitive, Section
remainder, Paragraph
residue, Section
rooted tree, Paragraph
sequence, Section Definition
arithmetic, Definition
explicit, Example
explicit formula proof, Assemblage
Fibonacci, Example
geometric, Definition
index, Paragraph
initial term, Paragraph
recursive, Section
recursive formula proof, Assemblage
term, Paragraph
set, Paragraph
complement, Definition
difference, Definition
disjoint, Definition
identities, Assemblage
intersection, Definition
pairwise disjoint, Paragraph
proof of equality, Assemblage
properties, Section
union, Definition
universal, Paragraph
set roster notation, Example
set theory, Section
sets of sets, Example
sibling
of a vertex, Item
simple circuit, Item
simple graph, Paragraph
statement
existential, Definition
universal, Definition
universal conditional, Definition
vacuously true, Paragraph
string, Paragraph
binary, Paragraph
strong induction, Section Assemblage
proof structure, Assemblage
subgraph, Definition
subset, Definition Definition
proof technique, Assemblage
proper, Definition
properties, Assemblage
successor function, Activity
sum, Section
closed form, Paragraph
summation
closed form, Paragraph
summation notation, Assemblage
symmetric, Item
proof, Assemblage
tautology, Definition
terminal vertex, Definition
total degree, Definition
trail, Item
transitive, Item
argument, Assemblage
proof, Assemblage
transitive closure, Paragraph
tree, Section Definition
height, Item
rooted, Paragraph
truth set
for a predicate, Definition
truth-table, Paragraph
union
of sets, Definition
Unique Factorization Theorem, Theorem
universal
conditional, Item
existential, Item
quantifier, Item
statement, Item
universal conditional, Definition
contrapositive, Definition
converse, Definition
vacuously true, Paragraph
valid argument, Definition Paragraph
variable, Paragraph
Venn diagram, Assemblage
quantified argument, Paragraph
vertex, Paragraph Definition
adjacent, Paragraph
ancestor, Item
branch, Definition
child, Item
degree, Definition
descendant, Item
level, Item
parent, Item
sibling, Item
