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Introduction to Proofs: An Active Exploration of Mathematical Language

Jennifer Firkins Nordstrom

Index Index

antisymmetric, Definition Paragraph
argument
general form, Assemblage
invalid, Definition Section
valid, Definition Section
bijection, Definition. See also one-to-one correspondence
binomial, Paragraph
binomial coefficient, Paragraph
Binomial Theorem, Section Theorem
cardinality, Section
cardinality of a set, Definition
Cartesian product, Paragraph
cases
proof by, Assemblage
closed form of a sum, Paragraph
codomain, Definition
combination, Definition
complement of a set, Paragraph
composite, Definition
conclusion, Paragraph
conditional
logical equvalences for, Section Assemblage
negation of, Item
conditional statement, Paragraph Item Section
congruent mod \(d\), Definition
conjecture, Paragraph
connective
and, Section Section
biconditional, Item
conditional, Item
conjunction, Item
disjunction, Item Item
exclusive or, Item
if and only if, Section
if...then, Section
nand, Section Item
negation, Item
not, Section
or, Section
contradiction, Definition
proof by, Section Subsection Assemblage
contrapositive, Item Item
proof by, Section Subsection Assemblage
universal conditional, Definition
converse, Item Item
universal conditional, Definition
converse error, Paragraph
corollary, Paragraph
countable infinite set, Definition
countable set, Definition
counterexample, Paragraph Assemblage
DeMorgan's Laws, Paragraph
disjoint sets, Definition
divides, Subsection Item
divisibility, Section
divisible, Subsection Definition
Division Algorithm, Theorem Paragraph Theorem
proof of existence, Section
proof of uniqueness, Section
divisor, Item
domain, Definition
element, Section
empty set, Paragraph Paragraph
equivalence class, Section Paragraph
equivalence relation, Section Definition
even integer, Definition Definition
existence proof, Section
existential quantifier, Item
existential statement, Item Paragraph Example
factor, Item
factorial, Paragraph
Fibonacci sequence, Paragraph Definition
function, Section Definition
one-to-one, Definition
onto, Definition
geometric sum, Paragraph
Goldbach's Conjecture, Claim
image, Definition
integer, Definition Item
intersection of sets, Paragraph
invalid argument, Definition Paragraph
inverse
error, Paragraph
function, Paragraph
of a conditional, Item Item
irrational number, Definition
logical argument, Paragraph
logical connectives, Section
logical equivalence, Definition Assemblage
logical statement, Paragraph
mathematical induction, Section Section
Principle of, Assemblage
proof by, Assemblage
strong, Assemblage
modus ponens, Paragraph Activity
multiple, Item
natural number, Item
odd integer, Definition
one-to-one
correspondence, Definition Definition
function, Section Definition
proof, Assemblage
onto
function, Section Definition
proof, Assemblage
partial order, Section Definition
partially ordered set, Section Definition
partition, Definition
Pascal's Formula, Theorem
poset, Definition
predicate, Paragraph
premise, Paragraph
prime, Definition
product notation, Paragraph
product of sets, Paragraph
proof
by cases, Section Paragraph Assemblage
by contradiction, Assemblage
by contrapositive, Assemblage
by induction, Assemblage
by strong induction, Assemblage
direct proof, Assemblage
existential statement, Assemblage
method of exaustion, Paragraph
uniqueness statement, Assemblage
proper subset, Definition
quantifier, Section Assemblage
negation, Assemblage
quantifiers
negation, Assemblage
quotient, Paragraph
range, Definition
rational number, Item Section Definition
real number, Item
reflexive, Item Item
relation, Section Definition
on a set, Definition
properties, Definition
relations
properties
proof, Assemblage
remainder, Paragraph
sequence, Paragraph Paragraph
general term, Paragraph
index, Paragraph
initial term, Paragraph
term, Paragraph
set, Section Paragraph
properties, Assemblage
set difference, Paragraph
set equality
proof, Assemblage
set identities, Assemblage
set roster notation, Example
set theory, Section
strong induction, Section Assemblage
proof by, Assemblage
subset, Section Paragraph Definition
proof, Assemblage
subset relations, Paragraph
summation notation, Section Assemblage
symmetric, Item Item
tautology, Definition
total order, Section Definition
totally ordered set, Section Definition Theorem
transitive, Item Item
transitive argument, Paragraph Example
truth table, Paragraph
uncountable set, Definition
union of sets, Paragraph
uniqueness proof, Section
universal conditional
disprove, Assemblage
prove, Assemblage
statement, Paragraph
universal quantifier, Item
universal set, Paragraph
universal statement, Item Paragraph
vacuously true statement, Paragraph
valid argument, Definition Paragraph
variable, Paragraph
well-defined function, Paragraph
Well-Ordering Principle, Theorem
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