1549901369-Elements_of_Real_Analysis__Denlinger_

elementary, 536
extension of, 264
graph of, 624
greatest integer, 208 , 241, 243,
396
integer floor, see greatest inte-
ger f. 241
integrable, 364, 366, 368, 369,
372 , 382, 383, 391, 395
inverse, 631
invertible, 631
locally bounded, 235
monotone, 240, 368, 393
monotone incr./decr., 240, 318,
325
nonintegrable, 364, 398
nth root, 253, 275
one-to-one ( 1-1), 620
onto, 620
periodic, 202 , 266, 315
piecewise continuous, 391
piecewise linear, 574
piecewise monotone, 391
polygonal, 574
range of, 619
signum, 227 , 234, 418
step function, 391
strictly incr./decr., 240, 325
strictly monotone, 240
Thomae's, 229, 236, 393, 395,
396 , 398, 418, 421, 449
transcendental, 536
trigonometric, 232, 313, 432, 538
uniformly continuous, 257
function space :F(S, IR), 625
fundamental theorem
of calculus
first form, 403
second form, 406
of monotone sequences, 91

general term test, 455
generalized Cantor sets, 175
generalized triangle inequality, 481

Index 731

geometric mean, 20

of sequences, 73

recursive, 116

geometric progression, 20

geometric series, 80, 89, 454

geometric sums

finite, 27

golden ratio, 122

graph of a function, 624

greatest element of a set, 35

greatest integer function, 208, 241,

243, 396

greatest lower bound, 37

grouping a series by inserting paren-

theses, 456

harmonic mean, 20

harmonic progression, 20

harmonic series, 101, 456

alternating, 4 78

Heine-Borel theorem, 158

Hilbert space, 502

horizontal line test, 624

hyperbolic functions, 418 , 533

hypergeometric series, 476

identity function on a set, 631

if and only if, 587 - 588

iff, 588

image of a set

under a function, 188 , 621

implication, 586

improper integrals

type 1, 434

type 2, 438

indefinite integral, 408

indeterminate forms, 86, 213, 341,

353

inductive set, 20

inf (infimum), 37, 75, 358

e criterion for, 39, 40

infinite series, 453

infinity as a limit

of a function, 209