736 Indexset(s) of real numbers
boundary of, 142
Cantor set, 164, 270, 444 , 450
Cantor-like, 172, 174
closed, 146
closure of, 149
cluster point of, 147
compact, 154, 156, 159, 247
countable, 126
dense, 151
dense in itself, 34
denumerable, 126
diameter of, 163
exterior of, 142
fat Cantor-like, 172, 174
finite, 126 , 144
first category, 293
F,,, 293
generalized Cantor, 175
interior of, 141
isolated point of, 143
meager, 294
nowhere dense, 169, 175, 293
of measure zero, 170 , 444
open, 139
perfect, 168, 175
second category, 293
uncounta ble, 126
signum function, 227 , 234, 418
sine function, 233 , 313, 429 , 538,
540
slowly divergent sequence, 100
square summable sequence, 501
squeeze principle
for functions, 196
for functions at infinity, 220
for integrability, 402
for sequences, 73 , 74
step function, 391
strict inequalities, 11
strictly increasing/ decreasing
function, 240, 325
sequence, 89
strictly monotone
function, 240
sequence, 90
subsequence, 107
subseries, 484
subset, 615
subtraction, 8
sum of a series, 453
summable sequence, 501
sup (supremum), 37, 75, 358
€ criterion for, 38, 40
norm of function, 548tagged partition of an interval, 374
tail of a sequence, 69
tautology, 590
Taylor polynomials, 329, 519
Taylor remainder, 334 , 412, 519
Cauchy's form, 520
integral form, 412, 520
Lagrange form, 334 , 520
Taylor series, 512
Taylor's theorem, 334, 411, 412, 519-
520
telescoping series, 456
ternary decimals, 165
tests for convergence of series
Abel's test, 498
alternating series test, 477
Cauchy criterion, 457
comparison test, 463
Dirichlet's test, 495
general term test, 455
integral test, 459 - 460
limit comparison test, 464
p-series test, 462
Raabe's test, 471, 472
ratio test, 465 - 467
root t est , 468
Thomae's function, 229, 236, 393,
395,396,398,418,421,449
topological term, 154
transcendental
function, 536
number, 130, 418 , 536
transitive property
of implication, 607