**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
**addition (field operation)**- 2.3
**addition in**- 2.2
**addition laws for sine and cosine**- 12.6
**addition of inequalities**- 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
**Arnold, Vladimir (1937-??)**- 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
**Bhaskara (born 1114-1185)**- 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
**commutativity of addition in field**- 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
**convergence, radius of**- 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****functions, addition and multiplication of****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****inequalities, addition of****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****Madhava of Sangamagramma (c. 1340-1425)****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****paradox****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****quadratic formula****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****radius of convergence****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****Russell's paradox****1.6****Russell, Bertrand 1872-1970****1.6****S****Sangamagramma, Madhava (c. 1340-1425)****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**