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| Daepp U., Gorkin P. — Reading, writing and proving. Close look at mathematics |
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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 , infimum version 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  -function 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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