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Subject index

A    B    C    D    E    F    G    H    I    J    K    L    M    N    O    P    Q    R    S    T    U    V    W    X    Y    Z

A


abacus  
Abelian group
absolute continuity  
absolute term  
absolutely convergent infinite product
absolutely convergent integral  
absolutely convergent product  
accumulation point  
additive inverse  
adjacency relation
adjacent vertices
Against Heresies  
alefbet  
algebra
algebraic structure
aliquot part
aliquant part
alphabet
alternating group
alternating harmonic series
alternating series
alternating series test
alternating series error estimate
annihilator  
antisymmetry
Apocalypse of John  
arc
Arenarius  
argument
arithmetic mean  
arithmetic-geometric mean  
arithmetic-harmonic mean  
Arithmetica integra  
arity of an operation
arity of a relation
arrow
ascending continued fraction
associated element
associative ring
asymptotic basis
asymptotic density
asymptotic notation  
autonomous recurrence relation
axiom of choice     
axiom of comprehension     
axiom of existence
axiom of extensionality     
axiom of foundation  
axiom of infinity  
axiom of regularity  
axiom of replacement  
axiom of separation  
axioms of transformations  

B


Babylonian clay tablet YBC 7289
Babylonian method
Babylonian positional system  
Bachmann-Landau asymptotic notation  
backward difference operator  
Bacon’s code  
bag
base
Baudhayana sutra
Bernoulli number
Bessel functions
Beta function  
Bézout domain
Bézout’s theorem
bigit  
biconditional
bijection
bilinear function
binary operation        
        associative  
        commutative  
        external  
        non-commutative  
Binet’s formula  
binary digit     
binary operation
binary relation
binary system  
binit  
binomial coefficient
binomial theorem
bit  
Bolyai-Gerwien theorem  
Book of Daniel  
Book of Revelation  
Boolean algebra
Boolean ring
bounded sequence
bounded above sequence
bounded below sequence
bunch
Burroughs B5000  

C


cancelable element  
canonical homomorphism
Cantor’s diagonal argument
cardinality
Cartesian product
Cauchy’s complementary multiplication
Cauchy definition of continuity  
Cauchy functional equations  
Cauchy’s polygonal number theorem
Cauchy sequence
Cauchy-Bolzano convergence criterion for infinite products
Cauchy-Bolzano convergence criterion for infinite series
Cauchy-Bolzano convergence criterion for sequences
Cauchy-Riemann conditions  
Cayley numbers
Cayley square (table)  
Cayley table
Cebysev’s (Chebyshev) function
Cebysev’s (Chebyshev) polynomials  
center  
center of a ring
center of gravity
centrum  
chain
characteristic function
closed with respect to an operation
codomain
coefficient of a polynomial  
common logarithm
commutative group
commutative ring
commutativity rule
comparison test  
compatible with an operation
complement formula
complementary multiplication
complete distributive lattice
complete metric space
complete sequence
completed infinity
complex number
complex polygon  
componentwise definition
composite function
composite number
composition of relations
composition series
concave polygon  
           set
conditionally convergent series
concatenation
concyclic polygon  
conditionally convergent integral  
conjunction
constant term  
continuity of functions  
continued fraction ascending
continued fraction representation
continuous derivative
contraction
convergence tests of the first type
convergence tests of the second type
convergent infinite product
convergent improper integral
convergent sequence
convergent series
convergent subsequence
convex hull
convex polygon  
convex set
cube root
counting function
cycle
cycle
cyclic group
cyclic polygon  

D


De Augmentis Scientiarum  
De occulta philosophia  
decreasing sequence
Dedekind finite
Degen-Graves-Cayley identity
De Morgan Law
decreasing function
degree of a polynomial  
degree of a vertex
Die Coss
Di minor guisa  
De numeris multiplicibus  
diagonal  
diagonal
dictionary order
dicyclic group
difference equation  
difference quotient  
digraph
dihedral group
direct predecessor
direct successor
directed edge
directed graph
Dirichlet criterion for the convergence of Fourier series  
discrepancy
discrete-time delta operator  
disjunction
distribution
divergence test for infinite series
divergent improper integral
divergent infinite product
divergent sequence
divergent series
divided difference  
divisibility
divisor
division ring
divisor
domain
domino
doubling formula
duality principle  
duplication formula  

E


e
EC-130  
edge  
edge-labeled graph
eight-square identity
Ein Rechen Büchlin Vom End Christ  
element of a sequence
Elements
Elements d’arithmétique universelle
embedding of a ring
end
endpoint
end vertex
entire function  
entire ring
entire transcendental functions  
Epistola ad Magistrum Theodorum  
equiangular polygon  
equilateral polygon  
equivalence
Euclid’s Elements  
Euler Beta function  
Euler’s four-square identity
Euler function of the first kind  
Euler function of the second kind  
Euler Gamma function  
Euler-Maclaurin summation
Euler-Mascheroni constant         
Euler’s polyhedron theorem
Euler’s summation formula
even permutation
Exercices d’analyse numérique
Explication de l’Arithmétique Binaire  
exploratory data analysis  
exponential function
exponential integral
extension of a function
exterior angle  
extremal discrepancy
extreme value theorem  

F


factor
factorial
False
family of sets
Fast Fourier Transform  
Fourier series  
Fibonacci number  
Fibonacci product
field
figural (figurate) number  
finger multiplication
finite graph
finite group
finite set
finitely generated monoid
fireset
Flos  
forward difference operator  
four-square identity
free commutative monoid
free monoid
function
function iteration
function 'sum of all positive divisors'
functional equations  
functionally complete
fundamental parallelepiped  
fundamental parallelogram  
fundamental theorem of arithmetic
fundamental sequence
fuzzy logic
fuzzy set theory

G


Gamma function              
Gauß formula  
Gauß’s triangular number theorem
Gauß-Legendre multiplication formula  
gematria     
general harmonic series
generalized harmonic number
generating set
generator
geometric mean  
Gerwien theorem  
Goldbach conjecture
golden ratio     
graph
grayscale  
greatest common divisor
greatest element
Greek numerals  
group  
group of invertible elements
group of units of a ring
grupoid
groupoid        
        alternative  
        associative  
        commutative  
        division  
        free  
        inverse  
        left alternative  
        power associative  
        right alternative  
        with cancellation  
        with division  
        with unity  
grupoid operation  
group with left cancellation  
group with right cancellation  
gypsy multiplication

H


Hamiltonian cycle
Hamiltonian group
Hardy-Krause variation  
harmonic mean  
harmonic number  
harmonic of a tone
harmonic series
harmonic-geometric mean  
hartley  
Hausdorff space
Hasse diagram
head of an arc
heap
Hebrew alphabet  
heliocentric system  
Heine definition of continuity  
hereditary representation
Hewlett-Packard calculator 9100A  
Heyting algebra
Hilbert problems  
homogeneous recurrence relation
homomorphism
Horner’s rule  
HP-35  
hyperbolic functions  
hypergeometric function   
        generalized hypergeometric function
Hume’s principle
Hurwitz theorem
hypergraph

I


idempotent  
identity (element)     
        left  
        right  
image
implication
improper integral  
incidence relation
inclusion-exclusion principle
increasing sequence
indeterminate  
indicator function
infinitesimal
infinite descent
infinite graph
infinite limits of integration  
infinite product
infinite products with non-negative terms
infinite series
infinite set
infinity
infix notation  
initial conditions
injection
invertible function
inverse relation
integral domain
integral test  
integral unimodular matrix  
integral test for the convergence of infinite series
internal angle  
intermediate value theorem  
Introduction to Arithmetic
inverse (element)  
        additive  
        left  
        right  
inverse function
inverse image
inversion
intersection
involuted element  
irrational number
irreducible element
irreflexivity
isomorphism
isotropic operations  
isotopy  
Iverson’s bracket
improper integral
improper limit
intersection of sets  
invertible element     

J


Jordan decomposition of functions of bounded variation  
Jordan polygon  
juxtaposition

K


KDF9 machine  
kernel of a homomorphism
kibit  
Klein four-group
Knuth product
Kolmogorov’s three series theorem
Körper

L


L2-discrepancy
Landau’s asymptotic notation  
Lagrange’s four-square theorem
Lagrange’s theorem
last vertex
lattice  
lattice
lattice basis  
lattice constant  
lattice point  
lattice polygon  
lattice vectors  
Latin square  
law of composition
law of De Morgan
law of excluded middle
law of non-contradiction
law of syllogism
leading coefficient  
least common multiple
least element
Lebesgue decomposition of a function of bounded variation  
left annihilator  
left cancelable element  
left ideal
left identity (unity)  
left inverse  
left nucleus  
left principal ideal
left translation  
left translator  
left zero element
Legendre’s polygonal number theorem
length of a path
length of a sequence
length of a string
lexicographical order
Liber Abbaci  
Liber quadratorum  
Liber XVII Cento nuptalis  
LIFO     
LILO  
limit of a sequence
limit test  
line segment
linear order
linear recurrence relation
linear programming  
Liouville’s theorem  
Lipschitz condition  
loculus of Archimedius  
logarithmic function
logical connective
logical operator
logical value
longest common subsequence problem
loop     
Lowry-Wallace-Bolyai-Gerwien theorem  
Lucas numbers

M


Maclaurin series
Maclaurin-Cauchy integral test
magic square  
magma     
main (principal) branch
Mangoldt’s function
many-to-one function
martingale convergence theorem
maximal element
Metaphysics
Mathesis biceps: Vetus et nova  
Maya number system  
mean proportional  
Mersenne’s prime
method of infinite descent
Methodus incrementorum directa et inversa
metric space
middle nucleus  
minimal element
minimal functionally complete
mixed-base positional  
modified Bessel functions
modulus of continuity  
Moebius’ function
Moebius’ inversion formula
monad
monochrome  
monoid  
monoid
monoid bijection
monoid isomorphism
monoid homomorphism
monomial  
monotone convergence principle
monotone sequence
Moore-Smith convergence
mset
multigraph
multiple
multiple-membership set
multiplicative relation     
multiplication by 5
multiplication by 9, 99, 999, etc.
multiplication by 11
multiplication table
multiplicity
multi-valued logic systems
multary operation
multiset
multiset coefficient
multiplication table  
multiset
multivalued relation
murious  
myriad  

N


naïve set theory  
natural logarithm
natural quotient map
natural unit (nat)  
negation
neutral element     
New Foundations
New Testament  
Nth root
non-autonomous recurrence relation
non-convex polygon  
Nörlund difference quotient  
non-convex set
non-decreasing sequence
non-homogeneous recurrence relation
non-increasing sequence
non-trivial divisor
normal subgroup
normal loop  
nucleus  
nullary operation
null sequence
number of divisors of an integer
number sequence
numerology  
Numerorum Mysteria  

O


occurrence set
octonions
octaves
odd function
odd permutation
one-to-one function
operation
opposite element  
order  
order
order of a graph
order of a group
order of a relation
order of a ring
ordering
overmonoid
Ordnung
oscillating improper integral
oscillating sequence
oscillating series

P


π
p-test  
p-series
Paradoxien des Unendlichen
parallelogrammic lattice
parallelogrammic grid
partial function
partial operation
partial ordering
partially ordered set
partial sum
path
peasant multiplication  
perfect number
period  
permutation
Pfister theorem
Pick’s theorem     
piecewise continuity  
PIR
Pochhammer symbol     
point lattice  
point of discontinuity of the first kind  
point of discontinuity of the second kind  
pointed set  
Polish notation  
polychoron  
polygon  
polygon vertices
polygonal number  
polyhedron  
polytope  
positional numeral system  
power associative loop  
power series  
power set (powerset)
powerset axiom  
polyadic operation
polynomial  
poset
postfix notation  
Practica geometriae  
prefix
prefix notation  
preimage
preorder
prime element
prime-counting function
prime number
prime number function
primitive triangle  
principal ideal
principal ideal ring
principal (main) branch
principal N th root
principal polygon vertex  
product absolutely convergent  
product function
product of relations
product rule  
projective space  
proper divisor
proper limit
proper subsets  
proposition
Proposition 31 of Book VII
Proposition 20 of Book IX
Proposition 36 of Book IX
propositional operator
Psammites  
pseudograph
pseudo-ring
pure polynomials  
pyramidal number  
Pythagorean means  

Q


quasigroup     
quasi ordering
quaternary operation
quaternion
quaternion group
queue  
quinary operation
Quine’s set theory NF
quintic
quotient rule  

R


radicals
radix conversion  
raising factorial  
random harmonic series
range
rank of a monoid
rank of an operation
rational function
rearrangement of a series
recurrence relation
recurrent sequence
recurrence with constant coefficients
reflection formula
reflection relation
reflexivity
regula ignavi
regular element  
regular polygon  
Rein analytischer Beweis
relation (binary)
remainder
reverse Polish notation  
restriction of a function
Riemann hypothesis
Riemann’s integral  
Riemann integrable function
Riemann sum
Riemann surface
Riemann zeta-function
right annihilator  
right cancelable element  
right ideal
right identity (unity)  
right inverse  
right nucleus  
right principal ideal
right zero element
ring
ring-homomorphism
ring-isomorphism
ring of polynomials with integers coefficients
ring with identity
root
rng
Russell’s paradox  

S


sample
Savilian Chair at Oxford
semigroup     
semigroup with identity element
semi-convergent series
sequence
sequential continuity  
set
set theory  
        naïve set theory  
        Zermelo set theory  
        Zermelo-Fraenkel set theory  
set of all functions
sextary operation
Shrauta Sutras
Shulba Sutras
Srauta ritual
side  
sign of a permutation
signum function  
simple cycle
simple graph
simple path
simple polygon     
simple ring
simple transposition
size of a graph
single-valued relation
skew field
snake method  
software  
solvability of quintic in radicals
solvable group
square root
square root sign  
stack  
stacking of dominoes
standard basis  
standard form
star convex set
star discrepancy
start vertex
steganography  
Stern prime
Stirling’s formula  
stomachion  
strict ordering
strictly monotone sequence
string
string searching problem
subfield
subsequence
subseries of harmonic series
subset  
subset axiom  
substring
successor function  
suffix
submonoid
subring
sum function
summation rule  
sum-of-divisors functions
sum of squares
surjection
symbol
symmetric difference
symmetric group
symmetry

T


T2 space
tail of an arc
Taylor polynomial
Taylor series
terminal vertex
ternary operation
term of a sequence
term of a series
The Sand Reckoner  
topological space
total order
total relation
total variation of a function  
Traité du Triangle Arithmétique  
transcendental number
transitivity
transposition
Treatise of Fluxions
tree representation  
triangular number     
triangulization  
trigonometric functions  
trivial divisor
True
true color  
truth-functional connective
truth value
two sided-ideal
truth table

U


unary operation
unary system  
unbounded sequence
uncompleted infinity
undirected graph
uniform-base positional system  
uniform continuity  
uniform distribution
uniformly distributed sequence
union axiom  
union of sets  
unique factorization theorem
unit ring
unitary relation
unity element  
Univac 1100/42
univariate polynomial  
universal algebra
universal element
unlabeled graph
unordered pair axiom  
unoriented graph

V


variation in the sense of Vitali  
variation in the sense of Hardy-Krause  
variation of a function  
Vedic period
Vera Circuli et Hyperbolae Quadratura
vertex
vertex-labeled graph
Vierergruppe
Vinogradov’s asymptotic notation  
Vitali variation  
von Mangoldt’s function
von Staudt theorem
Vorlesungen über Zahlentheorie
Vulgata  

W


Wadi Murrabba’at documents  
Wallace-Bolyai-Gerwien theorem  
Wallis’s formula  
Was sind und was sollen die Zahlen?
weak absolute continuity  
weight of a path
weighted graph
weighted mean
weighted set
Weierstraß decomposition  
Weierstraß primary factor  
well ordering
Wolstenholme’s theorem
word
word calculus  
Wortrechnung     

X

Y


YBC 7289

Z


Zahlkörper
Zahlring
Zeckendorf’s theorem
Zermelo set theory  
Zermelo-Fraenkel set theory  
zero (element)  
zero polynomial  
zipper theorem

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