732 Index
of a sequence, 82, 100
integer floor function, see greatest
integer f. 208
integers, 4, 28
of an ordered field F, 28
integrable function(s)
algebra of, 397 - 401
approximation by step functions,
391
composition theorem, 398
Darboux' definition, 364
Lebesgue's criterion, 444, 446,
447
Riemann's criterion, 368, 382
Riemann/Darboux criterion, 372,
383
sequential criterion, 366
squeeze principle, 402
with infinitely many points of
discontinuity, 390
integral form of remainder, 412, 520
integral off over [a, b]
additivity of, 387, 404
continuity of, 405
Darboux' definition, 364
first mean value theorem, 413
inequalities involving, 397-400
irrelevance of the value of f at
finitely many points, 389,
390
linearity of, 397
second mean value theorem, 413
Integral test for nonnegative series,
459 - 460
integration
by parts, 411
indefinite, 408
method of substitution, 409
interchange of limits, 559
interior point of a set, 141
intermediate value
property and theorem, 251, 256
property of derivatives, 319
intersection of sets, 614, 615 , 617
interval, 18
closed, 18
of convergence, 506
open, 19
proper, 293
inverse
additive, 6
multiplicative, 6
of a function, 631
of a proposition, 593
inverse function theorem
for continuous functions, 268
for differentiable functions, 310
inverse image of a set
under a function, 188, 621
invertible function, 631
irrational numbers, 29
denseness in R, 33, 76
e, 338, 537
er for rational r, 415
7r, 416
J2, 29
uncountability of, 129
isolated point of a set, 143L'H6pital's rule, 344, 348
Lagrange form of remainder, 334,
520
law of trichotomy, 11
least element of a set, 35
least upper bound, 37
Lebesgue's criterion for Riemann
integrability, 444, 446, 447
Leibniz
L. 's differential notation, 409
L.'s rule for derivatives, 315
length of a vector, 500
lim inf of a sequence, 133
limit comparison test, 89 , 464
limit criterion for integrability, 375,
383
limit of a function, 178, 183
at infinity, 217, 220
from the left/right, 203, 204