728 Indexc, 5
cancellation laws, 5
Cantor set, 165, 270, 444, 450
Cantor's function, 270 - 274, 321
Cantor's nested intervals theorem,
103
Cantor-like sets, 172 , 174
cardinal number of a set, 620
categorical propositions, 601-602
category
first c. set, 293
second c. set, 293
Cauchy criterion
for conve'rgence of sequences, 117
for convergence of series, 457
for limits of functions, 202
for limits of functions at infin-
ity, 223
for uniform convergence, 551
Cauchy mean value theorem, 342
Cauchy product of series, 488
Cauchy sequence, 11 7
Cauchy's form of remainder, 520
Cauchy-Schwarz inequality, 500
chain rule, 309
change of variables
in integration, 409
in limits, 199 - 200
characteristic function of a set, 244,
365, 406 , 450
closed
interval, 18
set, 146
closed set theorem, 146
closure of a set, 149
cluster point
of a sequence, 111
of a set, 147
codomain of a function, 619
collections of sets, 617 , 623
commutative property, 3
compact et, 154 , 156, 247
comparison test
for improper integrals, 436, 439,
440
for infinite limits of functions,
214
for nonnegative series, 463
for sequences, 84
complement of a set, 614
completeness property, 40
properties equivalent to, 123
complex numbers, 5, 16
composite functions, 231, 629
composition theorem for integrabil-
ity, 398
conditional convergence of series, 480
conjunction, 584
constant function, 189, 324
constant sequence, 62
continuity of a function
at a point, 226
everywhere, 228
on a compact interval, 252
on a compact set, 248, 261
on a set, 228 , 257
on an interval, 269
one-sided (from the left/ right),
237
continuity of the integral, 405
continuous function, 228
continuous, nowhere differentiable
function, 570
contraction mapping, 121
contractive sequence, 120
contrapositive, 593
convergence
absolute c. of a series, 480
conditional c. of a series, 480
of a sequence of numbers, 52
of a sequence of functions, 544,
548
of a series of real numbers, 453
of improper integrals, 434, 435,
438, 439
of power series, 504-506