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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 |
Number(s): cardinal 54 94
Number(s): Cayley 481
Number(s): Cayley conjugate 481
Number(s): class 56 404
Number(s): deficient 371
Number(s): Fermat 372
Number(s): Gauss 372
Number(s): Goedel 76
Number(s): irrational 152n
Number(s): limit 56 161
Number(s): Mersenne 371
Number(s): natural 72
Number(s): natural, totality of 72
Number(s): perfect 7 371
Number(s): sequence of 104
Number(s): sum of 95
Number(s): theory, analytic 406
Number(s): torsion 203
Number(s): transcendental 401
Number, field of 124
Number, positive 125
Number, rational 122
Numerals, and numbers 39n14
Numerator 122
O-place predicates 16
Octaves, Cayley 481
One-to-one 510
One-to-one, (invertible) mapping 64
Onto 64 509
Onto, mapping 395n
Operation: binary 167
Operation: outer 510
Operator(s) of set formation 12
Operator(s): description 12 18
Operator(s): domains 511
Operator(s): group with 518
Operator(s): in logic 16
Order(s) 32 485 522
Order(s) of a group 168
Order(s) of a group element 193
Order(s) of element G 193
Order(s), -preserving isomorphism 144
Order(s), basis of kth 405
Order(s), diagram 485
Order(s), linear 485
Order(s), set- 523
Order(s), type 56
Orderable 527
ordered 524
Ordered field 527
Ordered linearly 522
Ordered module 120
Ordered module, complete 138
Ordered pairs 52
Ordered ring 120. See also Sets ordered
Ordering(s) 63
Ordering(s), Archmidean 127
Ordering(s), lexicographic 130
Ordering(s), partial 63
Ordering(s), quasi- 356
Ordering(s), semi- 63. See also Well-ordering(s)
Ordinal number(s) 56 153 158
Ordinal number(s), isolated 161
Ordinal number(s), multiplication of 160
Ordinal number(s), of the first kind 161
Ordinal number(s), of the second kind 161
Ordinal number(s), sum of 159
Ornament(s) 204
Ornament(s), elementary 204
Orthogonal 273 285
Orthogonal transformations 273
Orthogonality conditions 265
Outer operation 510
Outer product 235 275
P-group(s) 219
P-group(s), Sylow 220
Pairs, ordered 52
Paradox 80
Paradox of the Liar 77
Part: imaginary 458
Part: preperiodic 378
Part: real 458
Part: scalar 475
Part: vector 475
Partial fractions 368
Partial orderings 63
Partial well-orderings 64
Partition function 406
Pascal, triangle 296
Peano system 9 30
Peano system of axioms 93
Peano, Giuseppe 72 94
Pell, equation 397
Perfect 198
Perfect number 7 371
Period, primitive 378
Permanence principle of Hankel 105n26
Permutable element 168
Permutation(s) 169
Permutation(s), identical 170
Philon 14
Pigeon-hole principle 102 465
Planar rotation group 214
Plane: affine complex 468
Plane: dilatations of the 456
Plane: Gauss 457
Plane: rotation of the 456
Plato 4
Poincare, H. 535
Point(s) 169 490 506
Point(s), infinitely distant 5
Point(s), lattice 204
Polygon, constructibility of a regular 454
Polynomial(s) 299 304
Polynomial(s), cyclotomic 428 430
Polynomial(s), derivative of a 423
Polynomial(s), elementary symmetric 307
Polynomial(s), general 453
Polynomial(s), nonseparable 424
Polynomial(s), normal 453
Polynomial(s), primitive 335 449
Polynomial(s), ring 299 304
Polynomial(s), separable 422
Polynomial(s), value of a 300
Polynomial(s), zero of a 302
Positive definite 273
Positive integers 113
Positive rational numbers 125
Positivity, domain of 120 464 527
Potential infinity 7
Power 125
Power of a group 192
Power rule 200
Power set 52 54 485
Power set axiom 60
Power-series 308
Power-series field 311
Power-series ring 311
Pre-image 64
Predicate logic: completeness of 42
Predicate logic: elementary 73
Predicate logic: extended 23n 72
Predicate logic: incompleteness of extended 42
Predicate(s) 12 15—16 21
Predicate(s), k-place 16
Predicate(s), O-place 16
Predicate(s), two-place 16
Predicate(s), variable 11 22
Predicate(s), variable, generalized 72
Prenex normal form 518
| Preperiod 387
Preperiodic part 378
Primary 496
Primary, ideal 342
Prime 329
Prime divisor 358
Prime element 403
Prime field 324
Prime ideal 342 403
Prime number 75
Prime number theorem, generalization of 406
Prime, regular 405
Primitive period 378
Primitive polynomial 335 449
Primitive root 399
Primitive root of unity 427
Principal ideal(s) 339
Principal ideal(s), ring 339
Principia Mathematica (Whitehead and Russell) 42
Principle of duality 68
Principle of extensionality 51 58
Principle of recursion 96
Principle of two-valuedness 10 21
Principle, Hausdorff — Birkhoff maximal chain 530 533
Principle, high chain 522 530
Principle, high chain, sharpened 530n
Principle, permanence (Hankel) 105
Principle, pigeonhole 102 465
Principle, Russell's vicious circle 535
Problem(s): type and structure, for groups 191
Problem(s): Waring 406
Problem(s): word 35 232
Product(s) 167
Product(s), alternating 235 275
Product(s), complex- 182 266
Product(s), direct 198 493
Product(s), direct, of groups 394
Product(s), function 38
Product(s), inner 234 266 269
Product(s), outer 235 275
Product(s), quaternion 475
Product(s), relative 62
Product(s), scalar 234 266 269
Product(s), tensor 235 273
Product(s), vector 266
Projection 255
Projective line, complex 471
proof 41 43
Proof, algorithmic 33
Proof, finished 46
Proof, indirect 42—43
Proper chains 495
Proper divisor 357
Proper divisor chain 330
Proper factor 328
Proper fraction 368
Proper motions 214
Proper segments 156
Proper subset 52 95n5
Proper upper bound 523
Proper variable 34
Properly simple 196
Property(ies) 21
Property(ies), many-place 21
Property(ies), module 338
Property(ies), representing 535
Property(ies), two-place 21
Proposition, relevant 29
Propositional constants 12
Propositional form(s) 11 22 94n2 535
Propositional variables 15
Propositions 10 11
Pure congruences 399
Pure-elementary structures 521
Pythagorean Theorem 4 27
Pythagorean triples 398
Quadratic form 268
Quadratic reciprocity 400
Quadratic residue, Euler criterion for a 400
Quadratic residues 399
Quantifier(s) 12 16
Quantifier(s), existential 17 18
Quantifier(s), universal 17 18
quantum mechanics 10
Quasi-ordering 356
Quaternion(s) 317n1 470
Quaternion(s), conjugate 470
Quaternion(s), group 194
Quaternion(s), product 475
Quaternion(s), skew field of 470
Quine, W.V., and Gentzen 43
Quotient(s) 125
Quotient(s), field 125 325
Quotient(s), ring 368
Radical(s) over a field 452
Radical(s), solvability by 452
Ramified analysis 40
Range (of a function) 50
Rank column, of a matrix 253
Rank of a matrix 255 260 284
Rank of a transformation 247
Rational numbers 122
Rational numbers, field of 124
Rational numbers, positive 125
Real number(s) 134 135
Real number(s), field of 141
Real number(s), improper 136
Real number(s), levels of 8
Real number(s), multiplication of 146
Real part 458
Real-closed 463
Realism 3
Reciprocal 123
Reciprocity, generalized law of 400
Reciprocity, quadratic 400
Recursion, principle of 96
Recursive function 35 38
Recursive: definition 96
Recursive: definition of addition 98n12
Recursively enumerable 33 35
Reduced remainder 174
Reduced: modulo n 174
Reducible 328
Reflection(s) 205
Reflection(s), glide 205
Reflection(s), longitudinal 205
Reflection(s), rotatory 206
Reflection(s), transverse 205
Reflexive 63
Reflexive law 53
Reflexivity 29
regressions 157
Regular 253
Regular continued fraction 333n29 373
Regular prime 405
Regular representation 223
Relation(s) 21 509
Relation(s), congruence 65 514
Relation(s), connex 63
Relation(s), converse 62
Relation(s), empty 62
Relation(s), equivalence 29 65 108
Relation(s), field of 63
Relation(s), identitive 63
Relation(s), isomorphic 64
Relation(s), Lagrange 398
Relation(s), reflexive 63
Relation(s), successor 32
Relation(s), symmetric 63
Relation(s), theory of 9 61
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