1549901369-Elements_of_Real_Analysis__Denlinger_

734 Index

nth root

existence of, 253
function, 275
nth term of a sequence, 50

odd function, 314, 401
one-sided continuity, 237
one-sided limits, 203
one-to-one (1-1) function, 620
1-1 correspondence, 620
onto function, 620
open
interval, 19
set, 139
open cover, 155
open set theorem, 139
ordered field, 11
Archimedean, 31
oscillation of a function, 292, 444

definition of, 429 , 540
irrationality of, 416
p-series, 456 , 462
P (set of positive elements of an or-
dered field), 11
partition of an interval, 360
mesh of, 372
regular, 379
tagged, 374
perfect set, 168 , 175
periodic
· functions, 202 , 266, 315
piecewise continuous function, 391
piecewise linear function, 574
piecewise monotone function, 391
pointwise convergence, 544
polygonal function, 574
polynomials, 34, 194
continuous everywhere, 228
limits of, 194
limits of, a t infinity, 220
Taylor, 329, 519
positive element, 11

power functions

natural number powers, 27 4

negative integral powers, 275

negative real number powers,

286

positive real number powers, 283

rational number powers, 275

power rule for differentiation, 305,

311-3 13

power series, 504

predicate, 595-596

product rule for differentiation, 306

progression

arithmetic, 19

geometric, 20

harmonic, 20

quadratic, 20

proof strategies, 606 - 611

by cases, 609

by contradiction, 609

by contrapositive, 608, 609

direct proof, 607

to prove a disjunction, 609

to prove an implication, 608

to prove several statements equiv-

alent, 610

proper interval, 293

proposition, 583

propositional function, 595 - 596

Q, 4, 29

QF, 28

quadratic mean, 20

quadratic progression, 20

quantifier

existential, 598 - 599

negation of, 600

universal, 597 - 598

quotient rule for differentiation, 306

Raabe's test, 471, 472

radius of convergence, 506 , 507

range of a function, 619

ratio test, 465 - 467