Page 396 - HOW TO PROVE IT: A Structured Approach, Second Edition

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382 Index
division algorithm, 290, 291 iff, 52
domain, 172, 230 image, 227, 230, 255–259
double negation law, 21, 22, 23, 25, 47 inclusion-exclusion principle, 369
inclusive or, 15
edge, 181 index, 74
element, 27 index set, 74
empty set, 32 indexed family, 74, 75
equinumerous sets, 306–312 induction
equivalence class, 214, 215 step, 260, 270
equivalence relation, 213–222, 309 strong, 288–295
equivalent formulas, 19, 21 inductive hypothesis, 263, 265, 268, 272
even integer, 134, 312 inference, rule of, 107
exclusive cases, 138 infinite sets, 306
exclusive or, 15, 24 injections, 236
exhaustive cases, 136 instance of a theorem, 85
existential instantiation, 115 integers, 31, 32
existential quantifier, 55, 58 intersection
of family of sets, 77, 78
factorial, 282 of indexed family of sets, 79
family of sets, 75 of two sets, 34
Fermat numbers, 276 interval, 31, 328
Fermat, Pierre de, 276 inverse, 173, 245–252
Fibonacci, 291 inverse image, 255–259
Fibonacci numbers, 291–293, 296, 297 irrational number, 161–162
finite sequence, 317, 321–322 irreflexive, 204
finite set, 306
fixed point, 255 largest element, 197
formula, 12 least upper bound, 197
free variable, 28, 55 lemma, 217
function limit, 161
compatible with an equivalence relation, logarithm, 252
225 loop, 184
composition of, 232–233 lower bound, 197
domain of, 230 Lucas, Edouard, 297
function of, 229 Lucas numbers, 297
identity, 227
inverse of, 245–252 main connective, 17
one-to-one, 236 mathematical induction. See induction
onto, 236 maximal element, 197
range of, 239 Mersenne, Marin, 5
restriction of, 234, 243 minimal element, 192, 267–269
modulo, 215, 221
geometric mean, 357 modus ponens, 103
Gibonacci sequence, 297 modus tollens, 103, 104, 105, 107
givens, 88
goal, 88 nand, 24
G¨odel, Kurt, 327 natural number, 31
graph, 183 necessary condition, 50
greatest common divisor, 299 negation, 10
greatest lower bound (g.l.b.), 197 nor, 24, 133
null set, 32
harmonic mean, 277
harmonic numbers, 286 odd integer, 24, 133, 134
Hilbert, David, 326 one-to-one, 236
hypothesis, 85 one-to-one correspondence, 242
onto, 236
idempotent laws, 21, 22 ordered pair, 163–171
identity relation, 183, 203–204, 213 ordered triple or quadruple, 169