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| Behnke H., Bachmann F., Fladt K. — Fundamentals of Mathematics, Volume I: Foundations of Mathematics: The Real Number System and Algebra |
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| Предметный указатель |
Field(s), invariant 402
Field(s), multiplicative group of a 324 357
Field(s), of rational numbers 124
Field(s), of real numbers 141
Field(s), of relations 63
Field(s), of sets 53
Field(s), ordered 527
Field(s), power series 311
Field(s), prime 324
Field(s), quotient 125 325
Field(s), radical over a 452
Field(s), real-closed 464
Field(s), skew 235 324 526n
Field(s), skew, of quaternions 470
Field(s), union of 436
figure 172
Figure, group of a 173
Fin, symbol 134
Finis superior (or supremum) 134n
Finished proof 46
Finitary 40
finite 55 102
Finite, above and below chain 524
Finite, ascending length 495
Finite, descending length 495
Finite, extension 418
Finite, field 440
Finite, group 168
Finite, length 495
Finite, rank, division algebra of 478
Finite, set, Dedekind definition of 103n21
Finite, system of generators 185
Finitely generated 185
First axiom for unions 60
First Cantor diagonal procedure 55
First domain 62
Fix-group 221
Flagged variables 43
Fonction polynome 301
Form(s): bilinear 264 268 271
Form(s): diagonal, of a matrix 260
Form(s): fundamental 270
Form(s): Hermitean 271
Form(s): Hesse normal 30
Form(s): linear 234 262 263 345n48
Form(s): multilinear 264 268
Form(s): prenex normal 518
Form(s): prepositional 11 22 94n2 535
Form(s): quadratic 268
Form(s): signature of a 272
Formalists 6
Formalization 9
Formally real (field) 464 527
Formula for rotations, Rodrigues' 477
Formula of de Moivre 458
Formula, inversion, of Mobius 389
Fraction(s) 122 325
Fraction(s), continued 333n29 373
Fraction(s), convergent of a 373
Fraction(s), dyadic 130n60
Fraction(s), Hurwitz 379
Fraction(s), partial 368
Fraction(s), partial, decomposition into 368
Fraction(s), proper 368
Fraction(s), regular 333n29 373
Free group 231
Free renaming of variables 44n18
Free variables 17
Free, square- 388
Free, torsion- 200
Frege, G. 10 51 72
Frobenius, theorem of 478
Function 64 509.
Function, algebraic 306
Function, choice 535
Function, computable 36
Function, constant 291
Function, continuous 462
Function, Dirac  - 5
Function, elementary symmetric 307n23
Function, Euler 382
Function, exponential 150
Function, identical 291
Function, inverse 64
Function, Moebius 288
Function, of a domain 50
Function, partition 406
Function, product 38
Function, range of a 50
Function, recursive 35 38
Function, signs 12 15
Function, sum 38
Function, summatory 371 388
Function, unity 388
Function, zero of a 293
Fundamental concepts 22 26
Fundamental domain 411
Fundamental form 270
Fundamental lemma of the theory of divisibility 359
Fundamental sequences 139
Fundamental sequences of Cantor 133
Fundamental system of solutions 257
Fundamental tensor 270
Fundamental theorem for cyclic groups 192
G, element, order of a group 193
Galois 447
Galois extension 420
Galois group 409 434
Galois theory 409
Gauss number 372
Gauss plane 457
Gaussian integers 316
Gebilde 508
General polynomial 453
Generalization of the prime number theorem 406
Generalized digital sum 386
Generalized predicate variable 72
GENERATED 185
Generated, finitely 185
Generating system 526
Generators 185
Generators, finite system of 185
Gentzen 43 76
Gentzen and Quine, rules of inference 43
Gibbs, Josiah Willard 476n
Glide reflections 205
Godelization 36
Goedel 31 38
Goedel completeness theorem 42
Goedel Incompleteness Theorem 72
Goedel index 36
Goedel numbers 76
Goldbach, conjecture of 10 76 405
graphs 186
Grassman 275
Greatest common divisor 332 358
Greatest common lower element 486
Greatest element 490 523
Greatest lower bound 68 132 486
Grelling, antinomy of 85
Ground set 62
Group element: exponent of a 193
Group element: order of a 193
Group(s) 167
Group(s), Abelian 111n33 168
Group(s), additive, of a ring 318 357
Group(s), alternating 227
Group(s), automorphism 191
Group(s), automorphism, of the 0
Group(s), commutative 111n33 168
| Group(s), commutator 197 217
Group(s), complexes of a 182
Group(s), composition of 436
Group(s), composition series of 438
Group(s), configuration 512
Group(s), cyclic 191
Group(s), cyclic, fundamental theorem for 192
Group(s), direct product of 394
Group(s), dual 483 488 517
Group(s), factor 196
Group(s), fix- 221
Group(s), free 231
Group(s), Galois 409 434
Group(s), Hamiltonian 194
Group(s), Klein four- 491
Group(s), length of a 216
Group(s), multiplication 28
Group(s), multiplication table for a 188
Group(s), multiplicative, of a field 324 357
Group(s), nilpotent 220
Group(s), of a figure 173
Group(s), of motions 172
Group(s), order of a 168
Group(s), P- 219 220
Group(s), planar rotation 214
Group(s), power of a 192
Group(s), quaternion 194
Group(s), simple 196
Group(s), structure problem for 191
Group(s), symmetric 171
Group(s), theory 28
Group(s), topological 232
Group(s), torsion 200
Group(s), type problems for 191
Group(s), union of 436
Group(s), with operators 518
Half-turns 205
Hamel, G. 146n88
Hamiltonian groups 194
Hankel, permanence principle of 105n26
Hausdorff — Birkhoff, maximal chain principle 530 533
Hemihedrism 209
Herbrand 38
Hereditary 93
Hereditary, meet- 518
Hermes, H. 484
Hermitian (Hermite): bilinear form 271
Hermitian (Hermite): dilative rotations 469
Hermitian (Hermite): form 271
Hermitian (Hermite): matrix 271
Hermitian (Hermite): metric 468
Hermitian (Hermite): rotations 468
Hertz, H. 6
Hesse diagram 485
Hesse normal form 30
Heterologic 85
Heteronomous system of axioms 27
High 529. See also Chain high
Hilbert, D. 6 21 406
Hoelder (and Jordan), theorem of 216 354 504
Holohedrism 209
Homogeneous 305
Homogeneous system 235
Homologous 511
Homomorphism 107 212 511
Homomorphism theorem 212
Homomorphism theorem, for rings 342
Horner, rule of 294 295
Hurwitz, continued fraction of 379
Hypercomplex system 345
Hypothesis: continuum 60
Hypothesis: continuum, special 60
Hypothesis: induction 95
Ideal(s) 338
Ideal(s), basis of an 339
Ideal(s), classes 404
Ideal(s), congruence modulo an 341
Ideal(s), direct sum of 392
Ideal(s), elimination 354
Ideal(s), left and right 357
Ideal(s), manifold of zeros of an 354
Ideal(s), maximal 403
Ideal(s), primary 342
Ideal(s), prime 342 403
Ideal(s), principal 339
Ideal(s), principal, ring 339
Ideal(s), theory, classical 343
Ideal(s), two-sided 357
Ideal(s), unit 338
Ideal(s), zero 338
Idealism 3
Idempotent 69n 392
Idempotent ring 69
Identical function 291
Identical permutation 170
Identification 5
Identitive 63
Identitive law 53
Identity 62 321
Identity element 167
Identity, modular 501
Image 64 212
Image domain 247
Image space 247
Image, pre- 64
Imaginary part 458
Implication 14
Impredicative 85
Impredicative, definitions 535
Improper real number 136
Improper subgroup 184
inclusion 62
Incompleteness of arithmetic 40
Incompleteness of extended predicate logic 42
Incompleteness theorem of Godel 72
Indecomposable 199
Independent indeterminates 304
Independent transcendents 304
Independent, linearly 240 526
Indeterminates 297
Indeterminates, independent 304
Index: Goedel 36
Index: kernel-, notation 246
Index: of a subgroup 186
Indirect proof 42—43
Individual(s) 21
Individual(s), domain of 21
Induction schema 75
Induction step 95
Induction,  - 43
Induction, axiom of 94
Induction, complete 57 94 117
Induction, complete starting from k 101
Induction, hypothesis 95
Induction, mathematical 94
Induction, modified principle of 101
Induction, transfinite 57
Inductive set 164
Inertia, Sylvester's law of 272
Inference 41
Inference, complete system of 41
Inference, of Gentzen and Quine 43
Inference, rules of 41
Inference, system of natural 42
Infimum (or greatest lower bound) 132
Infinite countably 151n90
Infinite decimal 130
Infinite distributive laws 490
Infinitely distant points 5
Infinitesimal 139
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