730 Indexe
as a function limit, 286
definition of, 95, 96
irrationality of, 338 , 415
number whose ln is 1, 423
transcendence of, 418
E: criterion for infimum, 39, 40
E: criterion for supremum, 38, 40
€-neighborhood, 138
E: - 8 game, 179
elementary function, 536
empty set, 614
equal functions, 620
equality, 611
equivalent propositions, 591
equivalent sets, 126
Euclidean n -space, 498
Euler's constant, 4 75
even function, 314, 401
eventually constant sequence, 63
eventually in a set, 108
eventually monotone sequence, 104
ex
as a function limit, 287
as a sequential limit, 288
definition of, 425- 426, 537-538
derivative of, 312, 426 , 537-5 38
irrationality of, 415
transcendence of, 418
exponential functions, 278, 280, 283,. 425 , 537
derivative of, 312, 313 , 426- 428
exponents
algebraic properties of, 281, 286 ,
426
integers as, 30
natural numbers as, 26, 274
negative integers as, 275
rational numbers as, 275
real numbers as, 280 , 281, 286
extension of a function, 264
exterior point of a set, 142
extreme value property /theorem, 249
factorials, 27
fat Cantor-like sets, 172 , 174
Fibonacci numbers, 121
field, 3
Archimedean ordered, 31
complet e ordered, 40
nonarchimedean, 34, 35
ordered, 11
finite intersection property, 161
finite set, 126, 144
finite subcover, 155
"finitizing the infinite, 53
first category set, 293
first derivative test, 328
fixed point theorem, 252
forcing principle, 33, 359
fraction notation, 8
frequently in a set, 108
Fa set, 293
function
additive, 236
algebraic, 536
analytic, 519
basic concepts of, 619
bracket, see greatest integer f.
241
Cantor's f., 270 - 274, 321
characteristic f. of a set, 244 ,
365, 406, 450
codomain of, 619
composite, 231, 629
constant, 189, 324
continuous, 226 , 228, 257
continuous from the left/right,
237
continuous, nowhere differentiable,
570
differentiable, 297, 300
differentiable from the left/right,
302
Dirichlet , 187, 228, 240, 364 ,
393, 450
discontinuous at a point, 226
domain of, 619