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Daepp U., Gorkin P. - Reading, writing and proving. Close look at mathematics
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Название: Reading, writing and proving. Close look at mathematicsАвторы: Daepp U., Gorkin P. Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2003Количество страниц: 406Добавлена в каталог: 18.11.2012Операции: Положить на полку |
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Предметный указатель
Absolute value 56 Absolute value, function 151 237 Adleman, L.M. 338 371 Algebraic number 368 Antecedent 20 Archimedean property 134 Associative property 379 Associative property, compound statement 32 Associative property, sets 83 asymmetric 143 Axiom 134 Axiom of infinity 351 Ball, open 297 Ball, unit 297 Barber problem 72 Bernoulli's inequality 216 Bernoulli, Joh. 158 Bijective 163 Binomial coefficient 220 Binomial theorem 220 Birthday calendar 329 Bounded sequence 225 Bounded sequence, above 225 Bounded sequence, below 225 Bounded set 130 Bounded set, above 130 Bounded set, below 130 Caesar cipher 10 Cantor diagonalization argument 277 Cantor set 362 Cantor, G. 271 278 369 Cardinality 265 Cartesian product 98 106 Cauchy sequence 250 Cauchy sequence, metric space 295 Cauchy - Bunyakovsky - Schwarz inequality 367 Characteristic function 159 Cipher 3 Clock arithmetic 313 Closed set 302 Closed set, closed interval 40 Closed set, not closed 309 Closed set, unbounded interval 40 Closure 312 Cocks, C. 338 Code 334 371 Codomain 148 Commutative property 379 Commutative property, compound statements 32 Commutative property, sets 83 Complement 69 Completeness axiom of 134 Completeness axiom of 134 140 complex numbers 40 Composite function 175 Composite number 349 composition 175 Conclusion 20 Congruence modulo n 314 Conjecture 57 Conjunction 20 Connectives 18 Contained 65 Contradiction 22 Contrapositive 32 Convergent sequence 237 Convergent sequence, metric space 287 Convergent sequence, proving convergence 240 Convergent sequence, theorems 244 249 CONVERSE 34 Convex set 218 Convex set, 367 Countable set 271 Countably infinite set 271 Counterexample 58 Counterfeit coin problem 13 de Fermat, last theorem 58 de Fermat, little theorem 332 de Fermat, P. 58 331 Decreasing sequence 227 Dedekind, R. 158 DeMorgan's laws 31 83 93 Diffie, W. 338 371 Dirichlet drawer principle 262 Dirichlet function 157 Dirichlet pigeonhole principle 261 Dirichlet principle 200 262 Dirichlet problem 199 Dirichlet, P.G.L. 157 262 Discrete metric 285 Disjoint 69 Disjoint, pairwise 96 Disjunction 19 Distance 237 283 Distributive property 380 Distributive property, compound statements 31 Distributive property, sets 80 83 95 Divergent sequence 238 242 Divergent sequence, diverges to 250 divides 54 313 Division algorithm 315 Domain 148 Double Negation 31 Element 39 63 Ellis, J. 338 Empty set 63 68 Equivalence of statements 21 Equivalence relation 110-111 122 Equivalence relation, classes 111 Equivalent sets 252 Equivalent statement 22 Equivalent statement forms 22 Euclid 58 Euclid, Elements 58 317 327 350 Euclidean algorithm 317 327-328 Euclidean metric 285 Euclidean n-space 40 Euler 332 Euler theorem 333 371 Euler, L. 58 157 158 331 358 Factorial 220 229 Family of set 90 fibonacci 229 Fibonacci numbers 230 248 Fibonacci sequence 230 Field 380 Field, ordered 380 Finite set 253 Fourier, J. 158 Frenicle de Bessy, B. 331 Function 147 157 Function, defined in cases 149 Function, equality 152 Function, notation 148 Function, preserves distance 311 Function, recursively defined 229 Function, well-defined 147 Fundamental Theorem of Arithmetic 218 Gauss, C.F. 209 GCHQ 338 Gelfond - Schneider theorem 376 Gelfond, A.O. 376 Geometric series 356 365 Golden ratio 248 Greatest common divisor 315 Greatest lower bound 133 Greatest lower bound, sequence 226 Green, G. 200 Halmos, P.R. 106 115 Hardy, G.H. 55 58 356 Harmonic series 216 Heine, H.E. 158 Hellman, M. 338 371 Hermite, C. 376 Hilbert, D. 200 251 278 374 Hotel Infinity 251 Identity 379 380 Identity function 180 Image 191 Image theorems 195 Implication 20 Increasing sequence 227 Index set 90 Indexed family 90 161 Induction 208 221 352 Induction, second principle 218 Infimum 133 199 Infimum sequence 226 Infimum uniqueness 133 143 Infinite set 253 Injective 163 Integers 40 Integers, modulo n 314 Integers, positive 40 Interior point 311 Intersection 69 91 Intersection, family of sets 91 Intersection, finitely many sets 89 Intersection, infinitely many sets 90 Inverse 177 379 380 Inverse image 192 Inverse image theorems 195 Inverse, composition 181 Inverse, uniqueness 180 Irrational number 48 353-358 Josephus problem 223 Kronecker, L. 278 Lacroix, S.-F. 158 Lambert, J.H. 358 Least common multiple 324 Least upper bound 131 Least upper bound, sequence 227 Lemma 121 LIMIT 238 Limit point 311 Limit, inferior 249 Limit, superior 249 Limit, uniqueness 243 Lindemann, F. 376 linear combination 316 Lower bound, sequence 225 Lower bound, set 130 133 Lower triangle inequality 61 Lucas sequence 235 MAP 147 Max metric 286 Maximum 130 Member 39 63 Merkle, R. 338 Metric 284 Metric space 284 Metric, bounded associated 293 Metric, definiteness 284 Metric, discrete 285 Metric, Euclidean 285 Metric, max 286 Metric, nonnegativity 284 Metric, symmetry 284 Metric, taxicab 286 Metric, triangle inequality 284 Metric, usual 284 Minimum 130 199 Minkowski, H. 278 Monotone sequence 250 Natural numbers 40 Negation 19 22-23 42-45 Negation of implication 22 Negation of quantifier 42 Niven, I. 355 358 NSA 338 One-to-one 163 One-to-one, not one-to-one 169 Onto 163 Onto, not onto 169 Open set 299 Open set, ball 297 Open set, ball, unit ball 297 Open set, not open 301 Open set, open interval 40 Open set, unbounded interval 40 Ordered pair 98 106 Pairwise disjoint 96 Paradox 72 Partial order 142 Partition 119 122 Pascal, B. 360 Pascal, triangle 360 Peano axioms 352 Perfect number 349-350 Pigeonhole Principle 261 263 Pisano, L. 229 Plaintext 373 Plane 40 76 Poincare, H. 278 Polya, the list 2 11 382 Polynomial 115 Polynomial degree 115 Polynomial root 61 Positive definite 284 Power set 97 Primality testing 374 Prime number 35 59 349 Product notation 211 Proof in cases 53 56-57 79 Proof, contradiction 53-56 Proof, direct 53-54 Proof, if and only if 82 Proof, reductio ad absurdum 54 Proof, top down, bottom up 66 80 Proof, uniqueness 131-132 Proof, working backwards 152 240 288 Proper divisor 349 Proper subset 65 Prym, F. 200 Public key encryption 335 Pythagorean Theorem 346 Quantifier, existential 41 Quantifier, universal 41 RANGE 152 Rational numbers 40 353-355 Rational numbers, closed under addition 353 Rational numbers, closed under multiplication 353 Real numbers 40 Real numbers, positive 380 Reciprocal modulo n 322 Recursion 229 Reflexive 109 142 Relation 101 109 Relation from X to Y 101 Relation on X 101 Relation, equivalence 110 Relatively prime 315 Restriction 188 255 Riemann, G.F.B. 200 Rivest, R. 338 371 RSA-key 371 Russell, B. 72 278 Schneider, T. 376 SEQUENCE 224 Sequence, bounded 225
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