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| Авторизация |
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| Поиск по указателям |
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| Conway J.H. — On Numbers and Games |
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| Предметный указатель |
Integers, omnific 45
Inversion in  56
Inversion of numbers 20
Inversion of Welter function 163
Irreducible numbers 34
Ish 117
Jams, Traffic 135
Johnstone, Peter 135 202
Kayles 127 145
Kenyon, J. C 129
Khayyam, Omar 1 69
Knuth, Donald, vi 228
Kuratowski 65
Large and small games and numbers 212
Left and Right as busy men 71
Left and Right, boundaries of thermograph 105
Left and Right, options 16 71
Left and Right, sections and values 97
Legal moves 71 72
Length 4 misere games 141
Like and linked games 147
Lizzie Borden 165
Llanfairpwllgwyngyllgogerychwyrnd-robwllllantysiliogogogoch 135
Long games 97
Long rule 173
Lovers, and their bridge 169
Mach’s principle 218
Malcev — Neumann construction 33 40
Map,  - 31
Masses, atomic (etc.) 219
Mast 97 105 221
Mate 147 154
Maximal sum and product 28
Mean value 101
Mean weight, atomic 223
mex 124 140
Milnor, John 101
Misere games, counting 140
Misere games, subtraction of 150
Misere games, theory of 136—152
Misere Grundy numbers 140 144—145
Misere Nim-heaps, behaviour of 139
Misere outcome function 138 147
Misere play rule 136
Misere reduced form 149
Misere reduced games of length up to 4 141
Money, my Dad’s 79
Moneybag 130
Moore’s  181
Move, legal 71—72
Move, reversible 110 137
Multiples and submultiples of  207
Multiples of general games 214
Multiplication in 52 55
Multiplication of games 207
Multiplication of numbers 5 18
Natural sum and product 28
Negative games 73
Negative numbers, Nim-addition of 154
Negative of games 75
Negative of numbers 17
Neumann, J. von 4 43 65
Next transcendental, problem of 62
Nim game of 122
Nim infinite 124
Nim of an animating function 156
Nim Supernim 215
Nim-addition 51 125
Nim-addition of negative numbers 154
Nim-heaps, ambivalent 146
Nim-heaps, misere behaviour of 139
Nim-multiplication 52
Nim-sums 125
No (the Class of all numbers), construction of 4
No (the Class of all numbers), definitions of operations, etc 5
No (the Class of all numbers), Field property 4 22 43
No (the Class of all numbers), real-closed 42
Non-standard analysis 44
Normal form and sign-expansion 36
Normal form for gap 37
Normal form for general number 32
Normal form, Cantor’s, for ordinals 28
Normal play rule 71 174
Northcott, D. G., and his game 131
Norton, Simon 45 91 101 151 217
Norton, Simon, his lemma 210
nth roots in 56 60
nth roots in No 40
Number(s) and games 97 et
Number(s) of misere games 140
Number(s), addition of 5 17
Number(s), approximations for 29
Number(s), cardinal 3
Number(s), commensurate 31
Number(s), epsilon ( ) 34 135
Number(s), equality and identity of 5 15
Number(s), fairly large and small 212
Number(s), Grundy 125
Number(s), infinite 3 12 212
Number(s), infinitesimal 12 212
Number(s), irreducible 33
Number(s), misere Grundy 144—145
Number(s), multiplication of 5 18
Number(s), normal form for 32
Number(s), order among 4 16
Number(s), ordinal 27 125
Number(s), ordinary sized 212
Number(s), reducible 33—34
Number(s), sign-expansions of 30 36
Number(s), structure of general 29—38
Number(s), very large and small 212
Octal games 128—129
October 17, Theorem of 201
Odd and even games 151
ON 28 37
One of the King’s Horses 183 185
ONE rule 173
One-line proofs 17 101
Options, dominated 110
Options, Left, Right 16
Options, reversible 110 137
Order and addition, properties of 18
Order, among games 15 73 78
Order, among numbers 4 16
Order, games of finite 207
Ordinal addition 88
Ordinal numbers (ordinals), below first transcendental 59
Ordinal numbers (ordinals), embedding in No 27
Ordinal numbers (ordinals), normal form for 28
Ordinal numbers (ordinals), operations on 28
Ordinary sized numbers 212
Outcome classes 73 147
Oz 45
O’Beirne, Tom 165
Pellian equation 47
Pictures, in Hackenbush 86 165
Pictures, in Hackenbush, weight of 166
Play of several games at once 71 173
Play, misere rule 136 174
Play, normal rule 71 174
Players Left and Right 71
Poles of animating function 156
Polynomials, roots in No 41
Polynomials, roots in No, in 58
Pope, Alexander 15
Positions of games 71
Positions, Nim-sums of 126
| Positions, starting 72
Positions, stopping 99
Powers of 31
Powers of 195
Powers of numbers ? 43
Prim 129
Prime games (in the misere theory) 151
Prime numbers 46
Prime partition 151
Principle, Grundy’s 137
Principle, Mach’s 218
Problem, Delian 132
Proofs, 1-line 17 101
Proper Classes 27 138
Quarrel of Universe 64—67 69
Rational numbers 23
Real numbers, embedding in No 24
Real numbers, logical theory of 25—27
Rectangles, diminishing 132
Rectangles, shrinking 195
Reduced form of misere game 149
Reduced form of misere game, games of length up to 4 141
Refinement property 46
Remote stars 218
Remoteness function of game (Steinhaus) 176
Restive and restless games 145
Restrained Hackenbush 86
Reversible options 110 137
Robinson, Abraham 44
Roots of odd degree polynomials 41
Roots, nth 40
Roots, square, in 56
Roots, square, in No 22
Rules for play, long, short, SOME, ALL, ONE 173
Rules for play, misere 136 174
Rules for play, normal 71 174
Selective compound 174
Selective compound, shortened 174 175
Selective compound, who wins? 175
Semi-star ( or  *) 199
Semi-up ( or  ) 199
Sesqui-up 199
Several games at once, tactical summary 179
Short games 97
Short games of odd order? 207
Short rule 173
Shortened selective compound 174
Shrinking rectangles 195
Sign-expansions for gaps 37
Sign-expansions for numbers 30 36
Silver Dollar game 123 130
Simplest form of short game 111
Simplicity theorem 10 23 81
Simplifying games 109
Simultaneous displays 73
Small games or numbers 100
Small games or numbers, all 101
Small games or numbers, very, fairly 212
Small world, theory of 217
Smith, Cedric A. B. 128 133 139 175 180
Snort 91 96
Some of the King’s Horses 183 184
Sop and wop functions 189
Spassky, Boris 75
Spinster 154 172
Sprague — Grundy theory 122 125
Sprague, Roland 125
Square roots in 56
Square roots in No 22
Square roots of 13
Star (*) 72
Stars, Nim-heaps (*n) 122
Stars, remote 218
Starting position 72
Stopping positions 99
Strong man, ambidextrous 168
Subtraction of misere games 150
Subtraction of numbers 5 17
Sums of games 74
Sums of numbers 5 17
Sums, disjunctive 74 177
Sums, infinite 39
Sums, maximal or natural 28
Sums, Nim- 51 125 154
Sums, ordinal 31 88
Supercooling function 218
Supernim 215
Superstars 215—217
Superstars, their translation invariance 215
Surd numbers 39 84
Suspense numbers 177
Tactics for playing several games at once 179
Tame games 145 178
Temperature of game 107
Temperature, Left and Right 107
Temperature, theory 101
Theorem of 17 October (1972) 201
Theory of Grundy and Sprague 122
Theory of misere games 136—152
Theory of real numbers 25—27
Theory of small world 217
Theory, Smith’s, for infinite games 133
Theory, temperature 101
Theory, Welter’s 153 et
Thermograph of game 104
Thermograph, atomic mass 220
Thermograph, boundaries of 105
Traffic Jams 135
Transcendental, ordinals below first 59
Transcendental, problem of next 62
Translation invariance (property) of games other than numbers 112
Translation invariance (property) of superstars 215
Tree of numbers 11 31
Tritter, Alan 129
Tromino game 196
Twisted form of Bynum’s game 209
Ug 78 209
Umbrella, girl with, and bird 167
Universally embedding 42
Universe of sets 38
Universe, Quarrel of 69
University 38
Unrestrained Hackenbush 165
Up() 77 188
Up(), definition of 77
Up(), multiples and submultiples of 198
Up(), powers of 195
Up-x ( ) 194
Upstart equality 77
Value and form of game 76
Value, Left, Right, and mean 97
Very large and small numbers 212
Vout, Colin 91
Waririg’s problem 46
Weights of Hackenbush picture 166
Weights, atomic 219
Weights, mean 223
Welter, C. P. 153
Welter, C. P., Grundy numbers for 153 158
Welter, C. P., his game 153
Welter’s function (Welt) 158
Welter’s function (Welt) as norm of animating function 157 158
Welter’s function (Welt), inversion of 163
Wop and sop functions 189
Zermelo — Fraenkel set theory 64
Zero game 76
Zig-zag domino positions 117
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