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| Dodge C.W. — Foundations of algebra and analysis |
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| Предметный указатель |
Order, simple 33 118 240
Order, type 273
Ordered by 273
Ordered field 194 231 253 273
Ordered field, complete 238
Ordered pair 62 154 179 207
Ordered set 273
Ordinal, number 275
Ordinal, use 148
Oughtred, William 105
Overlap 48
Pair, ordered 62 154 179 207
Paradox 277—278
Parking meter arithmetic 105—106
Partial order 118 240
Partition 69 204
Pattern of a logical discourse 26
Peano, Giuseppe 139
Peano, Giuseppe, postulates 139
Perfect number 281
Permissible division 78 153 185
Plato 84
Polynomial(s) 205 217 254
Polynomial(s), root of 254 288
Polynomial(s), test 217
Poretsky’s law 58 61 91 93
Positive 159 174 194 230 243
Postulate(s) 24 26 45 47
Postulate(s), Boolean algebra 85
Postulate(s), choice 279
Postulate(s), complete ordered field 238
Postulate(s), equivalence of 33
Postulate(s), integers 173
Postulate(s), natural numbers 110 135 139
Postulate(s), real numbers 238
Postulate(s), ring 204
Power set 59
Power(s) 128 268 293
Power(s) of i 253
Practical Geometry 152
Precedes 89 240 276
Preserved 160
Prime 120 127 133
Primitive proposition 6
Primitive term 25 26
Principle of Mathematical Induction 122
Principle of the smallest natural number 130
PRODUCT see “Multiplication”
Proof by contradiction 30
Proof by contrapositive 30
Proof by exhaustion 31
Proof, fallacious 127
Proof, geometric 36
Proof, rules for 34
Proposition 5
Proposition, primitive 6
Pure mathematics 26
Pythagoras 43—45 103 151
Pythagorean Society 43—45
Pythagorean Theorem 35 38 39
Quantifier 19 86
Quotient 119 161 185 229 251 272
Quotient, field 207
R-, S-, T-properties 67
RANGE 65
ratio 179
Rational number(s) 153 180 229 244
Rational number(s), rule for reduction of 180
Rational root theorem 255
Real coefficient 251
Real number(s) 153 225
Real number(s), postulates for 238
Real number(s), rational 229
Reductio ad absurdum 30
Reflexive 66
Relation 62 64
Relation, equivalence 67 179 199 224
Relation, precedes 89 240 276
Remainder 199
Remainder, theorem 254
Repetend 219
Residue class 202
Reverse order 274
Riemann, Georg F. B. 260
Ring 204
Ring with identity 205
Ring, isomorphism 160 175 183 229 244 251
Rng 65
Root 254 288
Root, extraneous 167
Rule for reduction of rational numbers 180
| Rules of proof 34
Russell, Bertrand 27 277
Self-dual 60
Sentence, open 19
SEQUENCE 214 233
Sequence, Cauchy 213 220 233 285
Sequence, limit 234
Sequence, null 221
Series 259
Set(s) 45—80
Set(s), builder 46
Set(s), complement 56
Set(s), empty 3 47
Set(s), equality 46
Set(s), equivalence 142
Set(s), intersection 51
Set(s), null 3 47
Set(s), ordered 273
Set(s), power 59
Set(s), proving theorems 49
Set(s), solution 45
Set(s), subset 48
Set(s), truth 19 45
Set(s), union 51
Set(s), universal 48
Similar 273
Simple order 33 118 240
Solution set 45
Square root 209
Square root of two 192 213 220
Star 75 137
Statement 5
Strict inequality 116 (see also “Inequality”)
Subset 48
Subtraction 118 145 153 161 184 221 227 272
Successor 139
SUM see “Addition”
Superset 48
Switching circuits 93—100
symmetric 66
Synthetic division 255—256 286—291
Table, addition 113
Table, multiplication 113
Table, truth 6
Tautology 10
Tautology, list of 11 13
Term(s), lowest 188
Term(s), primitive 25 26
Thales 1 —3 43 151
Theon 103
Theorem(s) 10
Theorem(s), existence 30
Theorem(s), factor 254
Theorem(s), fundamental, of algebra 254
Theorem(s), proving 49
Theorem(s), rational root 255
Theorem(s), remainder 254
Theorem(s), two-triangle 41
Theorem(s), understanding 34
Theorem(s), uniqueness 89 112 196
Theorem(s), well ordering 130 173 279
Transcendental 263
Transfinite 271
Transitive 66
Trichotomy 107 110 141 147 163 174 187 238—239 275
Truth set 19 45
Truth table 6 9
Truth value 19
Two, square root of 192 213 220
Umbugio, Euclide P. B. 151 152 177 211 247 283—284
Unbounded 222
union 51
Uniqueness theorem 89 112 196
Universal quantifier 19
Universal set 48
Upper bound 236 240
Use of numbers 147—148
Valid 15
Variable 19
Venn diagram 51 85
Weak inequality 116 (see also “Inequality”)
Weierstrass, Karl Wilhelm Theodor 259—261
Well defined 45 77 155 165 180 187 201 225 230 245 252
Well order 130 131 173 275 279
Whole numbers 143
Zeno 103
Zermelo, Ernst 279
Zero 153 159 174 183 194 226 243
Zero of a polynomial 254
Zero, division by 185 227
Zero, divisor 202 203
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