## IndexA | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | W | Z

A
absolute convergence
11.4
absolute summability
11.4
absolute value, of complex number
6.1
absolute value, product formula
2.7
absolute value, quotient formula for
2.7
absolute value
2.7
2.3
2.2
addition laws for sine and cosine
12.6
2.6
Alembert, Jean (1717-1783)
11.4
alternating series
11.3
alternating series test
11.3
ambiguous,
12.1
ambiguous, sequence notation
5.1
and, logical connective
1.2
Archimedean property
5.2 | 5.2 | 5.2 | 5.3
Archimedes
5.3
argument(of a complex number
12.6
Aristotle (384-322 B.C.)
2.3 | 3.2
Arnold cats
6.5
6.5
Ars Magna
4.2
Artin, Emil (1898-1962)
2.7
associative operation
2.1
associative
2.2
associativity of
B.
associativity of
4.1 | B.
axiom, completeness
5.2
axioms for a field
2.3
axioms, for ordered field
2.6
axioms
intro
axis, imaginary
6.2
axis, real
6.2
B
Bernoulli, Jacob (1654-1705)
2.3 | 11.4 | 11.4 | 12.9
between
9.2
3.1
binary operation
2.1
binary search sequence
5.1
Bolzano, Bernhard, (1781-1848)
9.2
Boole, George (1815-1864)
2.2
bound for a function
8.3
bound for a set
8.3
bound for sequence
7.5
bound, lower
7.8
bound, upper
7.8
bounded function
8.3
bounded sequence
7.5 | 7.5
bounded set
8.3
boundedness theorem
9.1
bug
2.2
Buhler, Joe (1950-??)
intro
C
calculator operations
2.2
cancellation law
2.1 | 2.4
Cardano, Girolamo (1501-1576)
2.7 | 4.2
Cartesian product
1.4
cat, Arnold
6.5
cat, discontinuous image of
8.3
cat, exponential of
12.6
cat, inverse of
6.5
cat, square of
6.5
Cauchy, Augustin(1789-1857)
3.5 | 4.2 | 9.2
chain rule
10.1
circle of convergence
12.2
circle,unit
6.2
circle
6.2
Clenias
3.2
closed interval
5.1
codomain of function
1.5
commensurable
3.2
commutative operation
2.1
commutative
2.2
2.4
comparison test (limit)
11.2
comparison test for series
11.2
comparison theorem for null sequences
7.3
complete
5.2
completeness axiom
5.2
completeness
5.3
complex conjugate
4.2
complex function
8.1
complex numbers
6.1
complexification
4.1
composition of continuous functions
8.2
composition of functions
8.2
composition
8.1
conjugate, complex
4.2
conjugate
4.2
constant sequence
7.1 | 7.2
continuity of , (in theorem 12.27)
12.4
continuity of roots
8.2
continuity, of
12.5
continuity
5.3
continuous at a point
8.2
continuous on a set
8.2
continuous
8.2
convergence of geometric sequence
7.6
convergence of geometric series
7.6
convergence of search sequence
5.1
convergence, absolute
11.4
convergence, circle of
12.2
convergence, disc of
12.2
12.2
convergence
7.2
convergent sequence, limit of
7.5
convergent sequence, product theorem
7.5
convergent sequence, reciprocal theorem
7.5
convergent sequence, sum theorem
7.5
convergent sequence, uniqueness theorem
7.5
convergent sequence
7.2
convergent sequences, quotient theorem
7.5
convergent sequences
7.5
copy (of in )
4.1
cosine, complex
11.4
cosine
12.3 | 12.7
critical point theorem
10.2
critical point
10.2
D
D'Alembert, Jean (1717-1783)
11.4
De Moivre's formula
6.2
De Moivre, Abraham (1667-1754)
6.5
decimal notation
7.6
decimals
intro
decomposition theorem
7.5
decreasing function
5.3
decreasing sequence
7.8
definition by recursion
3.3
derivative
10.1
Descartes, Rene, 1596-1650
3.5
Dickson, Leonard Eugene, (1874-1954
2.3
difference of sets
1.4
difference, symmetric
2.1
differential equation
12.4
differentiation of power series
12.3 | 12.8
digits
2.4
direction in
6.3
direction of complex number
6.3
disc of convergence
12.2
disc open
6.2
disc, closed
6.2
disc, unit
6.2
distance (in ordered field)
2.7
distributive law in
B.
distributive law in a field
2.5
distributive law
2.3
distributive
2.2
divergence of search sequence
5.1
divergence test
7.7
divergent sequence
7.2
division in a field
2.5
domain of function
1.5
double inverse theorem
2.1 | 2.4
draughts
3.2
dull sequence
7.3
E
12.4 | 12.9
empty set
1.1
endpoints of an interval
2.7
entertainments
intro
Epicureans
6.2
equality of functions
1.5
equality of objects
1.3
equality of ordered pairs
1.4
equality of rules
1.5
equality of sets
1.1
equality, reflexive property
1.3
equality, substition property
1.3
equality, symmetric property
1.3
equality, transitive property
1.3
equivalence for sets of propositions
2.5
equivalence of propositions
1.2
Euclid (365-300BC??)
3.1 | 3.2 | 3.2 | 5.3 | 6.2
Euler, Leonard (1707-1783)
4.2 | 6.5 | 11.2 | 12.9
Euler, summation notation
3.5
even integer
3.2
even number
3.1
exercises
intro
exponential function
12.4
exponents, laws for fractional
5.3
exponents, rational
5.3
extreme value theorem
9.1
F
factorial function
3.3
factorial
3.5
factorization of
3.4
factorization (depends on field)
3.4
feature
2.2
field, axioms for
2.3
field, orderable
2.6
field, real
5.2
function, complex
8.1
function, increasing and decreasing
5.3
function, recursive
3.3
function
1.5
5.3
G
Göttingen
11.4
Gauss, Carl (1777-1855)
12.7
geometric sequence, convergence of
7.6
geometric sequence
7.1 | 11.1
geometric series, convergence of
7.6
geometric series
3.4
geometric series
7.1 | 11.1
graph
5.3
Gregory, John (1638-1675)
11.4 | 12.9
H
Hamilton, William R. (1805-1865)
2.2 | 4.2
harmonic series
11.1 | 11.4
Huntington, Edward (1874-1952)
2.5 | 2.7
hyperbolic functions
12.6
I
identity element for binary operation
2.1
image of a function
6.5
imaginary axis
6.2
imaginary part of complex number
6.1
implication
1.2
incommensurables
3.2 | 3.2
increasing function
5.3
increasing sequence
7.8
induction theorem (generalized)
3.1
induction theorem
3.1
inductive
3.1
2.6
inequalities, multiplication of
2.6
inequality theorem
7.7
inequality, triangle
2.7
infinite series
11.1
integer, even
3.2
integer, odd
3.2
integers in a field
3.2
integers, informal definition
1.1
integers
3.2
interior point
10.2
interior
10.2
intermediate value theorem
9.2 | 9.2 | 9.2
intersection
1.4
interval, closed or open
5.1
interval
2.7
inverse for binary operation
2.1
inverse of cat
6.5
invertible element for binary operation
2.1
J
Jones, William, (1675-1749)
12.9
K
Koch, Helge von (1870-1924)
7.8
Kramp, Christian, 1760-1826
3.5
L
Lagrange, Joseph, (1736-1813)
11.4
Landau, Edmund (1877-1938)
11.4
The Laws
3.2
laws of exponents (fractional)
5.3
laws of signs
2.6
Laws of Thought
2.2
least element principle
3.1
Leibniz, Gottfried (1646-1716)
11.4 | 11.4 | 12.9
length of complex number
6.3
limit comparison test
11.2
limit of a function
8.3
limit of sequence
7.5
limit point
8.3
limit, uniqueness of
8.3
line segment
10.2
logarithm
12.5
lower bound for a set
9.1
lower bound for sequence
7.8
M
10.3 | 11.4 | 12.9
Mahavira (ninth century)
3.1
Maple
2.2 | 3.5 | 3.5 | 4.2 | 12.6 | 12.9 | 12.9
maps to
7.1
Mathematica
3.5 | 3.5 | 4.2 | 12.6 | 12.9 | 12.9
maximizing set
9.1
maximum function
3.5 | 3.5
maximum, critical point theorem
10.2
maximum
9.1
mean value theorem
10.2
Mercator, Nicolaus(1620-1687)
11.4
midpoint
5.1
minimum
9.1
monotonic sequence
7.8
multiplication (field operation)
2.3
multiplication in
2.2
multiplication of inequalities
2.6
multiplication table
2.2
Mycielski, Jan
7.8
N
natural numbers, informal definition
1.1
natural numbers
3.1 | 3.2
negative elements in ordered field
2.6
Newton, Isaac (1643-1727)
5.3 | 10.3 | 11.4
not, negation
1.2
null sequence, comparision theorem
7.3
null sequence, root theorem
7.3
null sequence, sum theorem
7.4
null sequence
7.3
null sequences, product theorem
7.4
null-times-bounded theorem
7.5
number, odd
3.1
number, even
3.1
numbers natural
3.2
numbers, complex
6.1
numbers, natural
3.1
numbers, rational
3.2
numbers, real
5.2
O
odd integer
3.2
odd number
3.1
open interval
5.1
opposite sign
2.6
or, logical connective
1.2
orderable field
2.6
ordered field, axioms for
2.6
ordered field, completemess of
5.2
ordered pair
1.4
ordered triple
1.4
Oresme, Nicole (1323-1382)
11.4
P
pair, ordered
1.4
1.6
parentheses
2.3
Pascal, Blaise (1623-1662)
3.1
path
10.2
Peano,Giuseppe (1858-1932)
3.1
periodicity of
12.6
periodicity of and ,
12.59A h) and i) | 12.6
Philitas of Cos
1.6
pi
12.6 | 12.9
Plato (427?-347B.C.), The Laws
3.2
polar decomposition
6.3
polygon representation for a complex sequence
7.1
polygon, snowflake
7.6
positive elements in ordered field
2.6
power function
3.3 | 3.5
power rule for differentiation
10.1
power series
12.1
power, integer
3.3
precedence
2.3
precision function
7.3 | 7.8
Priora Analytica
3.2
Proclus
6.2
product formula for absolute value
2.7
product of functions
5.3
product rule for differentiation
10.1
product theorem for null sequences
7.4
product theorem for continuous functions
8.2
product theorem for convergent sequences
7.5
product theorem for limits of functions
8.3
proposition form
1.4
proposition
1.2
propositions, equivalence of
1.2
Pythagorean theorem
6.2
Q
2.5
quotient formula for absolute value
2.7
quotient rule for differentiation
10.1
quotient theorem for continuous functions
8.2
quotient theorem for convergent sequences
7.5
quotient, of functions
5.3
R
12.2
ratio for a geometric sequence
7.1
ratio for geometric series
7.1
ratio test
11.2 | 11.4
rational exponents
5.3
rational numbers in a field
3.2
rational numbers, informally defined
1.1
rational numbers
3.2
rational, (in sense of Euclid)
3.2
real axis
6.2
real field
5.2
real part of comlex number
6.1
reciprocal rule for differentiation
10.1
reciprocal theorem for convergent sequences
7.5
recursion
3.3
Reed College
intro
restriction theorem
10.2
reverse triangle inequality
7.5
Rolle's theorem
10.2
Rolle, Michel (1672-1719)
10.3
root of complex number
6.3
root of real number (theorem 5.49)
5.3
root theorem for null sequences
7.3
roots of complex numbers
12.6
roots, continuity of
8.2
rule, recursive
3.3
1.6
Russell, Bertrand 1872-1970
1.6
S
10.3
Schreier, Otto (1901-1929)
2.7
search sequence, convergence of
5.1
search sequence
5.1
segment
10.2
sequence, bounded
7.5 | 7.5
sequence, constant
7.1 | 7.2
sequence, convergent
7.2 | 7.2 | 7.5
sequence, decreasing
7.8
sequence, divergent
7.2
sequence, dull
7.3
sequence, increasing
7.8
sequence, lower bound
7.8
sequence, null
7.3
sequence, search
5.1
sequence, summable
11.1
sequence, upper bound
7.8
sequence
5.1 | 7.1
series alternating
11.3
series operator
11.1
series, power series
12.1
series, sum of
11.1
series
11.1
Servois, Francois-Joseph (1767-1847)
2.2
set
1.1
set difference
1.4
set empty
1.1
sine, complex
11.4
sine
12.3 | 12.7
Skolem functions
7.8
snowflake
7.6 | 7.8
square
2.5
square root of complex number
6.4
square root
2.6
subset
1.1 | 1.1
substition property of equality
1.3
subtraction in a field
2.5
sum of a series
11.1
sum of functions
5.3
sum theorem for continuous functions
8.2
sum theorem for convergent sequences
7.5
sum theorem for differentiable functions
10.1
sum theorem for limits of fumctions
8.3
sum theorem for null sequences
7.4
sum theorem for series
11.1
summable sequence
11.1
summable, absolutely
11.4
summation function
3.5
summation
3.4
symmetric difference
2.1
T
transitivity of
2.6
transitivity of equality
1.3
transitivity of implication
1.2
translate of a sequence
7.7
translation theorem
7.7
triangle inequality , in
6.1
triangle inequality, reverse
7.5
triangle inequality
2.7 | 6.2
trichotomy
2.6
trigonometric functions
11.4 | 12.3 | 12.6 | 12.7
triple, ordered
1.4
U
union
1.4
uniqueness of
5.2
uniqueness of identities
2.1
uniqueness of inverses
2.1
uniqueness of limits
8.3
uniqueness theorem for convergent sequences
7.5
unit circle
6.2
unit disc
6.2
upper bound for a set
9.1
upper bound for sequence
7.8
W
Waring, Edward, (1734-1798)
11.4
Weber, Heinrich Martin (1842-1913)
2.5
Weierstrass, Karl (1815-1897)
2.7 | 9.2
Z
zero-one law
2.3