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