Index
You may find Appendix J useful
absolute value, 358
absurd absurdums, 449
abuse of language, 396
algebraically closed, 116
algebraists, dislike metrics, 123, 568
alternating series test, 76
antiderivative, existence and uniqueness, 177
area, general problems, 161-164, 203-206,
218-220
authors, other
Beardon, 56, 372
Berlinski, 20
Billingsly, 218
Boas, 59, 145, 201
Bourbaki, 355, 396
Burn, 62
Conway, 422, 449
Dieudonne, xiii, 25, 59, 147, 196
Halmos, 355, 369
Hardy, xiii, 43, 81, 100, 147, 281
Klein, 109, 396
Kline, 354
Littlewood, 79
Petard, H., 16
Plato, 28
Poincare, 355
axiom
fundamental, 9, 12, 21, 353
of Archimedes, 10, 12, 352, 388
of choice, 164, 239
axioms
for a metric space, 230
for an ordered field, 357
general discussion, 230, 344-345, 355-356
Zermelo-Fraenkel, 355
tracking down particular ideas.
balls
open and closed, 50, 232
packing, 221-223
packing in F%, 225-226
Banach, 230, 287
Bernstein polynomial, 521
Big Oh and little oh, 483
bijective function, 449
binomial expansion
for general exponent, 280
positive integral exponent, 543
binomial theorem, 280, 543
bisection, bisection search, see lion hunting
Bishop's constructive analysis, 391-394
Bolzano-Weierstrass
and compactness, 395
and sequential compactness, 258
and total boundedness, 259
equivalent to fundamental axiom, 40
for closed bounded sets in
Mm,
49
for metric spaces, 258-260
for R, 37-39
in E m , 47
bounded variation, functions of, 172, 492-
495, 579
brachistochrone problem, 181
calculus of variations
problems, 189-192
successes, 181-189
used, 245
Cantor set, 533
Cauchy
condensation test, 74
father of modern analysis, xiii, 544
function not given by Taylor series, 137
585
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