# Introduction to Proofs: An Active Exploration of Mathematical Language

## IndexIndex

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