Index
Abel's summation by parts, 494
Abel's t est for series, 498
Abel's theorem, 515
absolute convergence
of improper integrals, 436, 440
of series, 480
absolute value, 16
in limits of functions, 188
in limits of sequences, 62
of a function, 542, 626
absolutely summable sequence, 501
additive function, 236
additive inverse, 6
algebra of continuous functions, 230
algebra of derivatives, 306
algebra of functions, 542-543, 625 -
627
algebra of limits
of functions, 191 , 212-2 14
of functions a t infinity, 220
of sequences, 66, 85-87
algebra of sets, 615-617
algebraic
function, 536
number, 130, 536
almost everywhere, 451
alternating ha rmonic series, 478, 486
alternating series, 4 77
analytic function, 519
anti-symmetric property, 12
antiderivative, 403
Archimedean property, 31, 34
arcsine defined as integral, 428
arithmetic mean, 19
of sequences, 72
727recursive, 116, 120
recursive weighted, 121
arithmetic progression, 19
arithmetic-geometric mean , 116
associative property, 3
in set theory, 616
asymptote
horizontal, 221
vertical, 216definition of, 280Baire category theorem, 294
base-b decimals, 165
Bernoulli's inequality, 27
bi-implication, 587
binomial coefficients, 27
binomial series, 523
binomial theorem , 27
Balzano-Weierstrass theorem
for sequences, 112
for sets, 149
bounda ry point, 142
bounded
a bove, 36
away from zero, 65 , 190
b elow, 36
function, 164 , 189, 248, 260
sequence, 64
set, 36
boundedness theorems
for functions, 248 , 260
for sequences, 64
bracket function, see greatest inte-
ger f. 241