INDEX 387Equivalence class, 228, 238, 240
representative of, 228, 344
Equivalence classes of Cauchy sequences,
356
product of, 356
sum of, 356
Equivalence of Cauchy sequences, 356
Equivalence relation, 227, 235, 236
determined by a partition, 241
Exclusive alternation, 56, 59
Exhaustive cases, 172, 173
Existence
proofs of, 212, 216-222
Existential quantifier, 88
Exponential function, 258
complex, 325
Exponential to the base a, 177
Extension of a mapping, 265
Extreme value theorem, 318
Even function, 59, 157, 166
Even integer, 59, 200, 211Factorial, 46
recursive definition of, 336, 342
Family of sets, 124: See also Collection of
sets
Fibonacci number, 336, 342
Field, 114, 294, 295
complete ordered, 294,296, 313
of complex numbers, 296, 321
of integers modulo p (p prime), 297
of quotients, 351
of rational numbers, 296
of real numbers, 294, 296
ordered, 294, 303, 304
sub-, 296, 359
Final form of a proof, 162, 164, 197
Finite set, 5, 6, 211, 279, 288
Fixed point of a mapping, 332
Formalist school, 219
Function(s), 227, 252, 253
absolute maximum and minimum of, 157
algebraic, 254, 264
bounded, 202
choice, 291
composition of, 252, 258, 260
constant, 255
continuous at a point, 129
continuous on an open interval, 144
dependent variable of, 254
derivative of, 24, 131, 141, 178, 180, 211
differentiable at a point, 71, 74
domain of, 253
dynamic view of, 254
equality of, 253, 264
even, 59, 157, 166
exponential, 258
from a set A to a set B, 256. See also
Mapping
greatest integer, 143
hyperbolic, 258
identity, 254, 255
image of, 253
image of a set under, 217,252,270-275,
29 1
increasing, 147, 160, 208, 21 1
independent variable of, 254
induced set, 275
inverse, 252, 258
inverse image of a set under, 252,270-275
invertible, 259
limit of, 52, 115, 128-145
linear, 254
logarithm, 258
nth power, 258
nth root, 258
odd, 157
one-to-one, 168, 208,211,252,256
operations on, 257
polynomial, 254, 264
propositional, 82. See also Predicate
range of, 253
rational, 254, 264
relative maximum of, 21 1
rule of correspondence defining, 253
static view of, 254
successor, 331
transcendental, 254,264
trigonometric, 258
uniformly continuous on an open interval,
144,223
Functional notation, 253
Fundamental counting principle, 44
Fundamental sequence, see Cauchy
sequenceGauss, Karl Friedrich, 319
Generalization, 23-24, 106
induction proofs involving, 183
Generalized DeMorgan's law, 127
Generalized distributivit y, 1 83
Generalized triangle inequality, 186
Geometry, 148
Greatest common divisor, 213, 221
Greatest element of a poset, 247
Greatest integer function, 143