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Dodge C.W. — Sets, logic & numbers
Dodge C.W. — Sets, logic & numbers

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Название: Sets, logic & numbers

Автор: Dodge C.W.

Аннотация:

This text is designed to give the student a background in the foundations of algebra and analysis. The algebra of symbolic logic and the concept of set are introduced early in the text so that the main definitional development of the complex number system flows easily from a set of postulates for the natural numbers. Important concepts are introduced when needed to provide better motivation through immediate usage. Thus, the approach is integrated for a greater continuity of ideas than would be possible if a course in sets were followed by a course in the number systems.
A preliminary edition of the text was class-tested in a two-course sequence of two semester-hours each at the University of Maine. It was taught, primarily, to freshman and sophomore students who intended to major in or to teach mathematics. This sequence provided a total of sixty class sessions, or about one fifty-minute class period for each section of the text. There was more than enough material for such use, but most topics were covered in the allotted time.


Язык: en

Рубрика: Математика/Школьный уровень/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1970

Количество страниц: 346

Добавлена в каталог: 11.12.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
abacus      151
Absolute value      165 232
Absorption laws      88 240
Absurdity      10
Addition      105 110 140 143 155 156 173 180 194 201 204 207 209 221 225 242 250 274
Addition, law of      13
Aleph      261
Algebra, fundamental theorem of      254
Algebraic number      263
Algorithm, division      173 254
Alice in Wonderland      42 82 102 150 176
Analysis, arithmetization of      260
Ancestor      32
Ancient geometric proof      36
AND      6
antisymmetric      118
Applied mathematics      26
Archimedean property      189 232
Archimedes      83 103
Area      40
Argument, logical      14
Argument, testing      15
Aristotle      84
Arithmetic, modular      107 198—209
Arithmetic, parking meter      105—106
Arithmetization of analysis      260
Associative      13 54 76 85 109 110 144 147 158 174 181 194 201 204 225 238 242 244 250 275
Auxiliary theorem      34
Axiom      24 26 45 47
Axiom of Choice      279
Barber paradox      278
Bell, E. T.      211
Belongs to      45
Bernoulli family      104 178 259
Biconditional      7 13
BINARY      75 270
Binomial theorem      177
Bolyai, Wolfgang      211
Book of Reckoning      151 152
Boole, George      85 105
Boolean algebra      85—100 209
Boolean algebra, axioms for      85
Boolean ring      209
Bound, greatest lower      236 239 240
Bound, least upper      236 240
Bound, lower      236 239 240
Bound, upper      236 240
Bounded      131
Branch of mathematics      26
Burali — Forti, paradox      277
Calculus      177
Cancellation      60 88 89 111 112 196
Cantor, diagonal process      191 266
Cantor, paradox      277
CAP      85
Cardano, Girolamo      105
cardinal number      142
Cardinal number, transfinite      271
Cardinal use      147
Cartesian product      63
Cauchy, Augustin Louis      247 259
Cauchy, sequence      213 220 233 285
Choice, axiom of      279
circle      78 137
Class, equivalence      68 155 156 180 181 199—204
Class, residue      202
Closure      75 85 110 143 147 158 161 163 181 201 225 227 242 244 250
Coefficient      217 251
Cohen, Paul J.      279 280
Coin game      40
Common multiple      91
Commutative      13 54 76 85 110 144 147 158 173 181 194 201 204 205 225 238 242 244 250 275
Complement      56 86
Complete lattice      240
Complete ordered field      238 '
Completeness      233—235 237 239 245 285
Complex conjugate      251
complex numbers      153 249—257 250
Composite      120
compound statement      6
Conclusion      15
Conditional      7
Congruent      199
Conjunction      6
Connective      6
Consistent      86
Constant      71
Contingency      10
Continuum      267
Continuum, hypothesis      280
Contradiction      13 30
Contrapositive      12 30
Converge      214
CONVERSE      12 17
Coordinate      62
Correspondence, one-to-one      72 142 146
Cup      85
Cut, Dedekind      45 213 241
De Moivre, Abraham      105
de Morgan, Augustus      57 105
De Morgan, laws      13 57 91
decimal      212 265
Decreasing      223
Dedekind, cut      45 213 241
Dedekind, Richard      241
Deduction      27
Deductive reasoning      2
Defined on      64
Definition by mathematical induction      128
Degree      217 263
Dense      190 232
Denumerable      261
Dependent      134
Desargues’ two-triangle theorem      41
Descartes, Ren6      63 105
Determinate      118
Diagonal process      191 266
Diagram, Euler      21
Diagram, Venn      51
Difference      118 145 153 161 184 221 227 272
Discourse, pattern of      26
Discourse, simple      29—33
Disjoint      48
Disjunction      6 13
Distributive      13 55 78 86 110 147 158 174 181 194 201 204 238 244 250 275
divides      120
Division      119 161 185 229 251 272
Division by zero      185 227
Division of congruences      200 201
Division, algorithm      173 254
Division, permissible      78 153 185
Division, synthetic      255—256 286—291 288
Divisor, greatest common      91
Divisor, zero      202 203
DMN      65
Domain      65
Duality      60 86
Dyadic      62
D’Alembert, Jean-le-Rond      259
Electric circuits      93—100
Element      45
Elements      25 83
Empty set      3 47
En quad      30
Equals      46 67
EQUIVALENCE      7 33 67 68 142 154 155 156 179 180 181 199—204 207 224 225
Equivalence of postulate sets      33
Equivalence, class      68 155 156 180 181 199—204 225
Equivalence, relation      67 179 199 224
Equivalence, set      142
Eratosthenes      104
Euclid      37 83 84 246
Euclid, Elements      25 83
Euclidean geometry      24
Euclidean space      226 249
Eudoxus      44 260
Euler diagram      21
Existence theorem      30
Existential quantifier      19
EXPONENT      128 268 293
Extension      161
Extraneous root      167
Factor      120
Factor Theorem      254
Factorial      127 132 146 273
Fallacious proof      127
Farmer problem      100
fibonacci      151—152
Fibonacci, numbers      133 134 152
Field      194 253
Field, complete ordered      238
Field, operations      198
Field, ordered      194 231 253 273
Field, quotient      207
Filament      94
finite      261 262 291
Finite induction      122 (see also “Mathematical induction”)
FRACTION      183
Frege, Gottlob      277
Function      62 71
Fundamental theorem of algebra      254
Galileo      177
Galois, Evariste      104
Gauss, Karl Friedrich      211—212 247
Geometric mean      41 190
Geometric proof      36
Given statement      12
Godel, Kurt      279 280
Greater than      115 187 231 267
Greatest common divisor      91
Greatest lower bound      236 239 240
Halmos, Paul R.      30
Harmonic mean      41 190
Height      264
High school for mathematics      246
Hippasus      44 103
Hypatia      103
Hypothesis      15
Hypothesis, continuum      280
Idempotent      13 87 121 240
Identification      148
Identity      56 76 85 110 144 147 159 174 182 194 205 238 250
Identity, map      75
Identity, ring with      205
IFF      7
Image      65
Imaginary      251
Imbedded      161
Implication      7
IN      45
Increasing      223
Independent      135 137 140
induce      69
Induction      26
Induction, finite or mathematical      108 110 122—141 147 169—173 174 194
Inequality      115 163 164 186—190 231 267
Inequality, solving      165 167—169 188 189
Inequality, strict      116
Inequality, weak      116
Infimum      236
Infinite      261 291
infinity      3
Integer(s)      154 156
Integer(s), postulates for      173
Integral domain      205
Intersection      51
INTO      71
Invalid      15
Inverse      12 72 76 86 160 174 184 185 194 205 227 228 238 243 250
Irrational      44 192 229 244
Irrationality of $\sqrt{2}$      44 192
Irreflexive      118
Isomorphism      160
Isomorphism, ring      160 175 183 229 244 251
Kleene, Stephen C      139
Lattice      240
Lattice, complete      240
Laws of logic      10 13
Least natural number      130
Leibniz, Gottfried Wilhelm      177 259
Leonardo of Pisa      151
Less than      115 163 187 231 267
Lim      214
LIMIT      214
Limit, sequence      234
Linear order      118
Logarithm      263
Logic      1—41
Logic, laws of      10 13
Logical argument      14
Logical discourse      29—33
Logical discourse, pattern of      26
Lower bound      236 239 240
Lowest terms      188
Many-to-one      72
MAP      71
Map, identity      75
March of the ordinals      275
Mathematical induction      108 110 122—141 147 169—173 174 194
Mathematical induction, definition by      128
Mathematical induction, principles of      122 132 169 171 172
Matrix      205—207
MAX      216
Mean      41 190
Meaningful set      19
MIN      216
Model      26 86 137—139 175
Modular arithmetic      107 198—209
Monotone      223
Muller, Johann      103
Multiple      91 120
Multiplication      105 110 140 147 155 156 173 180 194 201 204 205 207 209 221 225 244 250 274
Natural number(s)      105—149 110 139 143 153
Natural number(s), postulates for      110 135 139
Negation      6
Negative      159 230 243
Newton, Isaac      177—178
Null sequence      221
Null set      3 47
Number theory      44
Number(s), algebraic      263
Number(s), complex      153 249—257
Number(s), Fibonacci      133 134 152
Number(s), integers      153—175
Number(s), natural      105—149 153
Number(s), rational      153 180 229
Number(s), real      153 225 238
Number(s), transfinite      271
Number(s), whole      143
One      110 139 174 183 194 227
One-to-one      72
One-to-one correspondence      72 142 146
Onto      71
Open sentence      19
Operation      75
OR      6
Order      115 230—233
Order, linear      118
Order, partial      118 240
Order, reverse      274
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