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| Hein J.L. — Discrete Mathematics |
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| Предметный указатель |
Digraph 44
Dilemmas 350
Direct proof 7
Directed acyclic graph 47
Directed graph 44
Directed multigraph 44
Disagreement set 465
Disjoint sets 18
Disjunction 2 313
Disjunctive normal form 323
Disjunctive syllogism 334
Dist See Distribute function
Distribute function 76 157
divides 5 216
Divisible 5
Division algorithm 68
Divisor 5
DNF See Disjunctive normal form
Domain 63 362
Doyle, Arthur Conan 1
DS See Disjunctive syllogism
Duality principle 525
EA See Equality axiom
EDGE 43
EE See Equals for equals
EG See Existential generalization
El See Existential instantiation
Element 10 31
Ellipsis 11
Embedding 92
Empty clause 454
Empty list 35
Empty relation 42
Empty set 11
Empty string 37
Empty substitution 462
Empty tuple 32
Encoding 565
Epimorphism 573
Equal bags 25
Equal functions 64
Equal sets 11
Equal tuples 32
Equality 412—419
Equality axiom 413
Equality axioms for terms 415
Equality problem 197
Equality relation 42
Equality, basic 178
Equals for equals 413
Equipotent 94
Equivalence class 199
Equivalence problem 209
Equivalence relation 197—212
Equivalence relation, quotient 200
Equivalence relation, smallest 205
Equivalence, algebraic expressions 511
Equivalence, first-order predicate calculus 372
Equivalence, prepositional calculus 317
Eratosthenes 172
Euclid 8 449
Euclid's Algorithm 69
Euler circuit 48
Euler trail 48
Euler, L. 48
Event 271
Excluded middle, law of 352
Existential closure 368
Existential generalization 399
Existential instantiation 391
Existential quantifier 357
Expectation 275
Expected value 275
Expression 462
Expression, algebraic 510
Extensionality, principle of 414
Factorial function 155 560
Factoring 476
Family tree problem 473
Fibonacci numbers 153 173 175 248 252 286 299 563
Fibonacci, Leonardo 153
Field 519
FIFO property 545
Finite set 12
Finite sums 283
First-order logic 444
First-order predicate calculus 359—369
First-order predicate calculus, atomic formula, atom 360
First-order predicate calculus, equivalence 372—384
First-order predicate calculus, existential quantifier 357
First-order predicate calculus, formal proofs 386—405
First-order predicate calculus, literal 380
First-order predicate calculus, meaning, semantics 362—369
First-order predicate calculus, renaming rule 376 399
First-order predicate calculus, restricted, equivalences 377
First-order predicate calculus, term 360
First-order predicate calculus, universal quantifier 357
First-order predicate calculus, validity 366—369
First-order predicate calculus, well-formed formula 360
First-order theory 411
First-order theory, partial order 417
First-order theorywith equality 412
Fischer, M.J. 209 640
Fixed point 78
Flagged variable 392
Flatten function 550
Floor function 67
Floyd's algorithm 191
Floyd, R.W. 190 439 639
Formal power series 286
Formal reasoning system 334
Formal theory 335
Formalizing English sentences 381—383
Four-color theorem 44
FP (functional programming language 557
fp algebra 559
FP algebra, axioms 560
FP algebra, carriers 560
FP algebra, operations 560
Franklin, Benjamin 253
Free to replace 388 389
Free variable 362
Full adder 531
Full conjunctive normal form 325
Full disjunctive normal form 324
Function 62—98
Function constants 360
Function, argument of 63
Function, arity of 63
Function, average case 275
Function, codomain of 63
Function, composition 79
Function, definition by cases 65
Function, definition of 62
Function, distribute 157
Function, domain of 63
Function, equality 64
Function, generating 286—296
Function, higher-order 85—90 161
Function, if-then-else 65
Function, image of 64
Function, partial 76
Function, pre-image, inverse image of 64
Function, range of 63
Function, recursively defined 151—173
Function, total 76
Function, tupling 80
Function, type 63
Function, value of 63
Functional algebra 556
| Fundamental conjunction 323
Fundamental disjunction 325
Fuzzy logic 353
Galler, B.A. 209 640
Gallier, J. 476 641
Gate 528
Gauss, Karl Friedrich 238
GCD See Greatest common divisor
Generalized list 36
Generating equivalence relations 204—209
Generating function 286—296 521
Generator of a binary relation 183
Gentzen, G. 369 640
Geometric progression 240
Geometric series 287
Geometry 449
Gib See Greatest lower bound
Goal 480 483 484
Goedel, K. 409 448 640
Goethe, Johann Wolfgang von 453
Graham, R.L. 308 640
Grammar 133—148
Grammar, abstract syntax tree 148
Grammar, ambiguous 146
Grammar, combining rules 143
Grammar, derivation 136 138
Grammar, four parts 137
Grammar, language of 139
Grammar, leftmost derivation 139
Grammar, nonterminals 137
Grammar, parse or derivation tree 134
Grammar, production 137
Grammar, recursive 140
Grammar, recursive production 140
Grammar, rightmost derivation 139
Grammar, rule or production 134
Grammar, sentential form 138
Grammar, start symbol 135 137
Grammar, terminals 137
Graph 43
Graph, acyclic 47
Graph, breadth-first traversal 48
Graph, chromatic number 44
Graph, complete 44
Graph, connected 47
Graph, depth-first traversal 49
Graph, directed, digraph 44
Graph, edge 43
Graph, multigraph 44
Graph, n-colorable 44
Graph, path problems 188—193
Graph, planar 44
Graph, spanning tree 53
Graph, subgraph 46
Graph, traversal 48
Graph, vertex, node 43
Graph, weighted 45
Greatest common divisor 26 67 249
Greatest common divisor, properties 68
Greatest element 219
Greatest lower bound 219
Group 517
Groupoid 517
Growth rates 299—306
Growth rates, big oh 304
Growth rates, big omega 305
Growth rates, big theta 300
Growth rates, little oh 303
Growth rates, lower 303
Growth rates, same order 299
Haken, W. 44 639
half-adder 530
Halmos, P.R. 232
Hamilton, A.G. 640
Hash function 96
Hasse diagram 218
Hasse, Helmut 218
Head of list 35 116
Head of string 121
Height 50
Hein, J.L. xv 640
Henneeey, M. 556 640
High school algebra 509
Higher-order function 85—90 161
Higher-order function, altMap 87
Higher-order function, apply 87
Higher-order function, insert 89
Higher-order function, map 86 161
Higher-order logic 442—450
Higher-order reasoning 448
Higher-order semantics 447
Higher-order unification 476
Higher-order wff 444
Hilbert, D. 345 449 640
Hisab al-jabr w'al-muqabala 507
Hoare, C.A.R. 439 640
Homomorphism 573
Horn clause 483
HS See Hypothetical syllogism
Hypothesis 3 313 332
Idempotent 525
Identifier 145
Identity element 512
Identity function 80
If and only if 8
If-then rule 426
If-then-else function 65
If-then-else rule 427
IFF See If and only if
Image 64
Immediate predecessor 217
Immediate successor 217
Implication 313
Implies 3
Incidence matrix 188
Inconsistent 335
Indegree 44
Indirect proof 341—343
Indirect proof rule 341
Individual constants 360
Individual variables 360
Induced relation 183
Induction algebra 515
Inductive definition 112
Inductive definition, binary trees 123
Inductive definition, language of a grammar 140
Inductive definition, lists 116
Inductive definition, natural numbers 113
Inductive definition, product sets 124
Inductive definition, strings 120
Inductive proof 234—248
Inductive set 112
Inference rule 310 332
Inference rule, addition 334
Inference rule, binary resolution 476
Inference rule, conjunction 334
Inference rule, constructive dilemma 351
Inference rule, destructive dilemma 351
Inference rule, disjunctive syllogism 334
Inference rule, existential generalization 399
Inference rule, existential instantiation 391
Inference rule, factoring 476
Inference rule, hypothetical syllogism 334
Inference rule, modus ponens 310 333
Inference rule, modus tollens 310 333
Inference rule, paramodulation 476
Inference rule, resolution 454
Inference rule, simplification 334
Inference rule, universal generalization 394
Inference rule, universal instantiation 389
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