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| Dodge C.W. — Foundations of algebra and analysis |
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| Предметный указатель |
abacus 151
Absolute value 165 232
Absorption laws 88 240
Absurdity 10
Addition 105 110 140 143 155 156 173 180 194 201 204 205 207 209 221 225 242 250 274
Addition, law of 13
Aleph 261
Algebra, fundamental theorem of 254
Algebraic number 263
Algorithm, division 173 254
Alice in Wonderland 42 82 102 150 176 210 258
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 131 222
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, Augustin Louis, sequence 213 220 233 285
Choice, axiom of 279
circle 78 137
Class, equivalence 68 155 156 180 181 199—204 225
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, Augustus, laws 13 57 91
decimal 212 265
Decreasing 223
Dedekind, Richard 241
Dedekind, Richard, cut 45 213 241
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, Reno 63 105
Determinate 118
Diagonal process 191 266
Diagram, Euler 21
Diagram, Venn 51 85
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 of congruences 200 201
Division, algorithm 173 254
Division, by zero 185 227
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 49
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
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 115 163 187 231 267
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 261 262 291 292
infinity 3
Integer(s) 154 156 173
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  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 91
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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